# Properties

 Label 930.2.j.a.683.2 Level $930$ Weight $2$ Character 930.683 Analytic conductor $7.426$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$930 = 2 \cdot 3 \cdot 5 \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 930.j (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: $$7.42608738798$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 1$$ x^4 + 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 683.2 Root $$-0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 930.683 Dual form 930.2.j.a.497.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.292893 + 1.70711i) q^{3} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-0.707107 + 0.707107i) q^{8} +(-2.82843 + 1.00000i) q^{9} +(-2.00000 - 1.00000i) q^{10} +4.24264i q^{11} +(-1.70711 + 0.292893i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(-1.82843 - 3.41421i) q^{15} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(-2.70711 - 1.29289i) q^{18} -4.00000i q^{19} +(-0.707107 - 2.12132i) q^{20} +(-3.00000 + 3.00000i) q^{22} +(-1.41421 - 1.00000i) q^{24} +(4.00000 - 3.00000i) q^{25} -4.24264i q^{26} +(-2.53553 - 4.53553i) q^{27} -2.82843 q^{29} +(1.12132 - 3.70711i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.24264 + 1.24264i) q^{33} +2.00000i q^{34} +(-1.00000 - 2.82843i) q^{36} +(-5.00000 + 5.00000i) q^{37} +(2.82843 - 2.82843i) q^{38} +(4.24264 - 6.00000i) q^{39} +(1.00000 - 2.00000i) q^{40} +(8.00000 + 8.00000i) q^{43} -4.24264 q^{44} +(5.29289 - 4.12132i) q^{45} +(-4.24264 - 4.24264i) q^{47} +(-0.292893 - 1.70711i) q^{48} +7.00000i q^{49} +(4.94975 + 0.707107i) q^{50} +(-2.00000 + 2.82843i) q^{51} +(3.00000 - 3.00000i) q^{52} +(-4.24264 + 4.24264i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-3.00000 - 9.00000i) q^{55} +(6.82843 - 1.17157i) q^{57} +(-2.00000 - 2.00000i) q^{58} -5.65685 q^{59} +(3.41421 - 1.82843i) q^{60} -8.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} -1.00000i q^{64} +(8.48528 + 4.24264i) q^{65} +(-6.00000 - 4.24264i) q^{66} +(-1.00000 + 1.00000i) q^{67} +(-1.41421 + 1.41421i) q^{68} -1.41421i q^{71} +(1.29289 - 2.70711i) q^{72} +(2.00000 + 2.00000i) q^{73} -7.07107 q^{74} +(6.29289 + 5.94975i) q^{75} +4.00000 q^{76} +(7.24264 - 1.24264i) q^{78} +10.0000i q^{79} +(2.12132 - 0.707107i) q^{80} +(7.00000 - 5.65685i) q^{81} +(12.7279 - 12.7279i) q^{83} +(-4.00000 - 2.00000i) q^{85} +11.3137i q^{86} +(-0.828427 - 4.82843i) q^{87} +(-3.00000 - 3.00000i) q^{88} -7.07107 q^{89} +(6.65685 + 0.828427i) q^{90} +(-0.292893 - 1.70711i) q^{93} -6.00000i q^{94} +(2.82843 + 8.48528i) q^{95} +(1.00000 - 1.41421i) q^{96} +(3.00000 - 3.00000i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(-4.24264 - 12.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{3} - 4 q^{6}+O(q^{10})$$ 4 * q + 4 * q^3 - 4 * q^6 $$4 q + 4 q^{3} - 4 q^{6} - 8 q^{10} - 4 q^{12} - 12 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{18} - 12 q^{22} + 16 q^{25} + 4 q^{27} - 4 q^{30} - 4 q^{31} - 12 q^{33} - 4 q^{36} - 20 q^{37} + 4 q^{40} + 32 q^{43} + 24 q^{45} - 4 q^{48} - 8 q^{51} + 12 q^{52} - 12 q^{55} + 16 q^{57} - 8 q^{58} + 8 q^{60} - 32 q^{61} - 24 q^{66} - 4 q^{67} + 8 q^{72} + 8 q^{73} + 28 q^{75} + 16 q^{76} + 12 q^{78} + 28 q^{81} - 16 q^{85} + 8 q^{87} - 12 q^{88} + 4 q^{90} - 4 q^{93} + 4 q^{96} + 12 q^{97}+O(q^{100})$$ 4 * q + 4 * q^3 - 4 * q^6 - 8 * q^10 - 4 * q^12 - 12 * q^13 + 4 * q^15 - 4 * q^16 - 8 * q^18 - 12 * q^22 + 16 * q^25 + 4 * q^27 - 4 * q^30 - 4 * q^31 - 12 * q^33 - 4 * q^36 - 20 * q^37 + 4 * q^40 + 32 * q^43 + 24 * q^45 - 4 * q^48 - 8 * q^51 + 12 * q^52 - 12 * q^55 + 16 * q^57 - 8 * q^58 + 8 * q^60 - 32 * q^61 - 24 * q^66 - 4 * q^67 + 8 * q^72 + 8 * q^73 + 28 * q^75 + 16 * q^76 + 12 * q^78 + 28 * q^81 - 16 * q^85 + 8 * q^87 - 12 * q^88 + 4 * q^90 - 4 * q^93 + 4 * q^96 + 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$$.

 $$n$$ $$187$$ $$311$$ $$871$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.500000 + 0.500000i
$$3$$ 0.292893 + 1.70711i 0.169102 + 0.985599i
$$4$$ 1.00000i 0.500000i
$$5$$ −2.12132 + 0.707107i −0.948683 + 0.316228i
$$6$$ −1.00000 + 1.41421i −0.408248 + 0.577350i
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ −2.82843 + 1.00000i −0.942809 + 0.333333i
$$10$$ −2.00000 1.00000i −0.632456 0.316228i
$$11$$ 4.24264i 1.27920i 0.768706 + 0.639602i $$0.220901\pi$$
−0.768706 + 0.639602i $$0.779099\pi$$
$$12$$ −1.70711 + 0.292893i −0.492799 + 0.0845510i
$$13$$ −3.00000 3.00000i −0.832050 0.832050i 0.155747 0.987797i $$-0.450222\pi$$
−0.987797 + 0.155747i $$0.950222\pi$$
$$14$$ 0 0
$$15$$ −1.82843 3.41421i −0.472098 0.881546i
$$16$$ −1.00000 −0.250000
$$17$$ 1.41421 + 1.41421i 0.342997 + 0.342997i 0.857493 0.514496i $$-0.172021\pi$$
−0.514496 + 0.857493i $$0.672021\pi$$
$$18$$ −2.70711 1.29289i −0.638071 0.304738i
$$19$$ 4.00000i 0.917663i −0.888523 0.458831i $$-0.848268\pi$$
0.888523 0.458831i $$-0.151732\pi$$
$$20$$ −0.707107 2.12132i −0.158114 0.474342i
$$21$$ 0 0
$$22$$ −3.00000 + 3.00000i −0.639602 + 0.639602i
$$23$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ −1.41421 1.00000i −0.288675 0.204124i
$$25$$ 4.00000 3.00000i 0.800000 0.600000i
$$26$$ 4.24264i 0.832050i
$$27$$ −2.53553 4.53553i −0.487964 0.872864i
$$28$$ 0 0
$$29$$ −2.82843 −0.525226 −0.262613 0.964901i $$-0.584584\pi$$
−0.262613 + 0.964901i $$0.584584\pi$$
$$30$$ 1.12132 3.70711i 0.204724 0.676822i
$$31$$ −1.00000 −0.179605
$$32$$ −0.707107 0.707107i −0.125000 0.125000i
$$33$$ −7.24264 + 1.24264i −1.26078 + 0.216316i
$$34$$ 2.00000i 0.342997i
$$35$$ 0 0
$$36$$ −1.00000 2.82843i −0.166667 0.471405i
$$37$$ −5.00000 + 5.00000i −0.821995 + 0.821995i −0.986394 0.164399i $$-0.947432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 2.82843 2.82843i 0.458831 0.458831i
$$39$$ 4.24264 6.00000i 0.679366 0.960769i
$$40$$ 1.00000 2.00000i 0.158114 0.316228i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 8.00000 + 8.00000i 1.21999 + 1.21999i 0.967635 + 0.252353i $$0.0812046\pi$$
0.252353 + 0.967635i $$0.418795\pi$$
$$44$$ −4.24264 −0.639602
$$45$$ 5.29289 4.12132i 0.789018 0.614370i
$$46$$ 0 0
$$47$$ −4.24264 4.24264i −0.618853 0.618853i 0.326384 0.945237i $$-0.394170\pi$$
−0.945237 + 0.326384i $$0.894170\pi$$
$$48$$ −0.292893 1.70711i −0.0422755 0.246400i
$$49$$ 7.00000i 1.00000i
$$50$$ 4.94975 + 0.707107i 0.700000 + 0.100000i
$$51$$ −2.00000 + 2.82843i −0.280056 + 0.396059i
$$52$$ 3.00000 3.00000i 0.416025 0.416025i
$$53$$ −4.24264 + 4.24264i −0.582772 + 0.582772i −0.935664 0.352892i $$-0.885198\pi$$
0.352892 + 0.935664i $$0.385198\pi$$
$$54$$ 1.41421 5.00000i 0.192450 0.680414i
$$55$$ −3.00000 9.00000i −0.404520 1.21356i
$$56$$ 0 0
$$57$$ 6.82843 1.17157i 0.904447 0.155179i
$$58$$ −2.00000 2.00000i −0.262613 0.262613i
$$59$$ −5.65685 −0.736460 −0.368230 0.929735i $$-0.620036\pi$$
−0.368230 + 0.929735i $$0.620036\pi$$
$$60$$ 3.41421 1.82843i 0.440773 0.236049i
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ −0.707107 0.707107i −0.0898027 0.0898027i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ 8.48528 + 4.24264i 1.05247 + 0.526235i
$$66$$ −6.00000 4.24264i −0.738549 0.522233i
$$67$$ −1.00000 + 1.00000i −0.122169 + 0.122169i −0.765548 0.643379i $$-0.777532\pi$$
0.643379 + 0.765548i $$0.277532\pi$$
$$68$$ −1.41421 + 1.41421i −0.171499 + 0.171499i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.41421i 0.167836i −0.996473 0.0839181i $$-0.973257\pi$$
0.996473 0.0839181i $$-0.0267434\pi$$
$$72$$ 1.29289 2.70711i 0.152369 0.319036i
$$73$$ 2.00000 + 2.00000i 0.234082 + 0.234082i 0.814394 0.580312i $$-0.197069\pi$$
−0.580312 + 0.814394i $$0.697069\pi$$
$$74$$ −7.07107 −0.821995
$$75$$ 6.29289 + 5.94975i 0.726641 + 0.687018i
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 7.24264 1.24264i 0.820068 0.140701i
$$79$$ 10.0000i 1.12509i 0.826767 + 0.562544i $$0.190177\pi$$
−0.826767 + 0.562544i $$0.809823\pi$$
$$80$$ 2.12132 0.707107i 0.237171 0.0790569i
$$81$$ 7.00000 5.65685i 0.777778 0.628539i
$$82$$ 0 0
$$83$$ 12.7279 12.7279i 1.39707 1.39707i 0.588771 0.808300i $$-0.299612\pi$$
0.808300 0.588771i $$-0.200388\pi$$
$$84$$ 0 0
$$85$$ −4.00000 2.00000i −0.433861 0.216930i
$$86$$ 11.3137i 1.21999i
$$87$$ −0.828427 4.82843i −0.0888167 0.517662i
$$88$$ −3.00000 3.00000i −0.319801 0.319801i
$$89$$ −7.07107 −0.749532 −0.374766 0.927119i $$-0.622277\pi$$
−0.374766 + 0.927119i $$0.622277\pi$$
$$90$$ 6.65685 + 0.828427i 0.701694 + 0.0873239i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −0.292893 1.70711i −0.0303716 0.177019i
$$94$$ 6.00000i 0.618853i
$$95$$ 2.82843 + 8.48528i 0.290191 + 0.870572i
$$96$$ 1.00000 1.41421i 0.102062 0.144338i
$$97$$ 3.00000 3.00000i 0.304604 0.304604i −0.538208 0.842812i $$-0.680899\pi$$
0.842812 + 0.538208i $$0.180899\pi$$
$$98$$ −4.94975 + 4.94975i −0.500000 + 0.500000i
$$99$$ −4.24264 12.0000i −0.426401 1.20605i
$$100$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$101$$ 18.3848i 1.82935i 0.404186 + 0.914677i $$0.367555\pi$$
−0.404186 + 0.914677i $$0.632445\pi$$
$$102$$ −3.41421 + 0.585786i −0.338058 + 0.0580015i
$$103$$ 10.0000 + 10.0000i 0.985329 + 0.985329i 0.999894 0.0145647i $$-0.00463624\pi$$
−0.0145647 + 0.999894i $$0.504636\pi$$
$$104$$ 4.24264 0.416025
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ 2.82843 + 2.82843i 0.273434 + 0.273434i 0.830481 0.557047i $$-0.188066\pi$$
−0.557047 + 0.830481i $$0.688066\pi$$
$$108$$ 4.53553 2.53553i 0.436432 0.243982i
$$109$$ 6.00000i 0.574696i −0.957826 0.287348i $$-0.907226\pi$$
0.957826 0.287348i $$-0.0927736\pi$$
$$110$$ 4.24264 8.48528i 0.404520 0.809040i
$$111$$ −10.0000 7.07107i −0.949158 0.671156i
$$112$$ 0 0
$$113$$ 4.24264 4.24264i 0.399114 0.399114i −0.478806 0.877920i $$-0.658930\pi$$
0.877920 + 0.478806i $$0.158930\pi$$
$$114$$ 5.65685 + 4.00000i 0.529813 + 0.374634i
$$115$$ 0 0
$$116$$ 2.82843i 0.262613i
$$117$$ 11.4853 + 5.48528i 1.06181 + 0.507114i
$$118$$ −4.00000 4.00000i −0.368230 0.368230i
$$119$$ 0 0
$$120$$ 3.70711 + 1.12132i 0.338411 + 0.102362i
$$121$$ −7.00000 −0.636364
$$122$$ −5.65685 5.65685i −0.512148 0.512148i
$$123$$ 0 0
$$124$$ 1.00000i 0.0898027i
$$125$$ −6.36396 + 9.19239i −0.569210 + 0.822192i
$$126$$ 0 0
$$127$$ −9.00000 + 9.00000i −0.798621 + 0.798621i −0.982878 0.184257i $$-0.941012\pi$$
0.184257 + 0.982878i $$0.441012\pi$$
$$128$$ 0.707107 0.707107i 0.0625000 0.0625000i
$$129$$ −11.3137 + 16.0000i −0.996116 + 1.40872i
$$130$$ 3.00000 + 9.00000i 0.263117 + 0.789352i
$$131$$ 19.7990i 1.72985i 0.501905 + 0.864923i $$0.332633\pi$$
−0.501905 + 0.864923i $$0.667367\pi$$
$$132$$ −1.24264 7.24264i −0.108158 0.630391i
$$133$$ 0 0
$$134$$ −1.41421 −0.122169
$$135$$ 8.58579 + 7.82843i 0.738947 + 0.673764i
$$136$$ −2.00000 −0.171499
$$137$$ 12.7279 + 12.7279i 1.08742 + 1.08742i 0.995793 + 0.0916263i $$0.0292065\pi$$
0.0916263 + 0.995793i $$0.470793\pi$$
$$138$$ 0 0
$$139$$ 8.00000i 0.678551i 0.940687 + 0.339276i $$0.110182\pi$$
−0.940687 + 0.339276i $$0.889818\pi$$
$$140$$ 0 0
$$141$$ 6.00000 8.48528i 0.505291 0.714590i
$$142$$ 1.00000 1.00000i 0.0839181 0.0839181i
$$143$$ 12.7279 12.7279i 1.06436 1.06436i
$$144$$ 2.82843 1.00000i 0.235702 0.0833333i
$$145$$ 6.00000 2.00000i 0.498273 0.166091i
$$146$$ 2.82843i 0.234082i
$$147$$ −11.9497 + 2.05025i −0.985599 + 0.169102i
$$148$$ −5.00000 5.00000i −0.410997 0.410997i
$$149$$ −1.41421 −0.115857 −0.0579284 0.998321i $$-0.518450\pi$$
−0.0579284 + 0.998321i $$0.518450\pi$$
$$150$$ 0.242641 + 8.65685i 0.0198115 + 0.706829i
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 2.82843 + 2.82843i 0.229416 + 0.229416i
$$153$$ −5.41421 2.58579i −0.437713 0.209048i
$$154$$ 0 0
$$155$$ 2.12132 0.707107i 0.170389 0.0567962i
$$156$$ 6.00000 + 4.24264i 0.480384 + 0.339683i
$$157$$ −4.00000 + 4.00000i −0.319235 + 0.319235i −0.848473 0.529238i $$-0.822478\pi$$
0.529238 + 0.848473i $$0.322478\pi$$
$$158$$ −7.07107 + 7.07107i −0.562544 + 0.562544i
$$159$$ −8.48528 6.00000i −0.672927 0.475831i
$$160$$ 2.00000 + 1.00000i 0.158114 + 0.0790569i
$$161$$ 0 0
$$162$$ 8.94975 + 0.949747i 0.703159 + 0.0746192i
$$163$$ −11.0000 11.0000i −0.861586 0.861586i 0.129936 0.991522i $$-0.458523\pi$$
−0.991522 + 0.129936i $$0.958523\pi$$
$$164$$ 0 0
$$165$$ 14.4853 7.75736i 1.12768 0.603910i
$$166$$ 18.0000 1.39707
$$167$$ −8.48528 8.48528i −0.656611 0.656611i 0.297966 0.954577i $$-0.403692\pi$$
−0.954577 + 0.297966i $$0.903692\pi$$
$$168$$ 0 0
$$169$$ 5.00000i 0.384615i
$$170$$ −1.41421 4.24264i −0.108465 0.325396i
$$171$$ 4.00000 + 11.3137i 0.305888 + 0.865181i
$$172$$ −8.00000 + 8.00000i −0.609994 + 0.609994i
$$173$$ 8.48528 8.48528i 0.645124 0.645124i −0.306687 0.951811i $$-0.599220\pi$$
0.951811 + 0.306687i $$0.0992203\pi$$
$$174$$ 2.82843 4.00000i 0.214423 0.303239i
$$175$$ 0 0
$$176$$ 4.24264i 0.319801i
$$177$$ −1.65685 9.65685i −0.124537 0.725854i
$$178$$ −5.00000 5.00000i −0.374766 0.374766i
$$179$$ −18.3848 −1.37414 −0.687071 0.726590i $$-0.741104\pi$$
−0.687071 + 0.726590i $$0.741104\pi$$
$$180$$ 4.12132 + 5.29289i 0.307185 + 0.394509i
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ −2.34315 13.6569i −0.173210 1.00954i
$$184$$ 0 0
$$185$$ 7.07107 14.1421i 0.519875 1.03975i
$$186$$ 1.00000 1.41421i 0.0733236 0.103695i
$$187$$ −6.00000 + 6.00000i −0.438763 + 0.438763i
$$188$$ 4.24264 4.24264i 0.309426 0.309426i
$$189$$ 0 0
$$190$$ −4.00000 + 8.00000i −0.290191 + 0.580381i
$$191$$ 1.41421i 0.102329i −0.998690 0.0511645i $$-0.983707\pi$$
0.998690 0.0511645i $$-0.0162933\pi$$
$$192$$ 1.70711 0.292893i 0.123200 0.0211377i
$$193$$ 15.0000 + 15.0000i 1.07972 + 1.07972i 0.996534 + 0.0831899i $$0.0265108\pi$$
0.0831899 + 0.996534i $$0.473489\pi$$
$$194$$ 4.24264 0.304604
$$195$$ −4.75736 + 15.7279i −0.340682 + 1.12630i
$$196$$ −7.00000 −0.500000
$$197$$ 1.41421 + 1.41421i 0.100759 + 0.100759i 0.755689 0.654931i $$-0.227302\pi$$
−0.654931 + 0.755689i $$0.727302\pi$$
$$198$$ 5.48528 11.4853i 0.389822 0.816223i
$$199$$ 16.0000i 1.13421i 0.823646 + 0.567105i $$0.191937\pi$$
−0.823646 + 0.567105i $$0.808063\pi$$
$$200$$ −0.707107 + 4.94975i −0.0500000 + 0.350000i
$$201$$ −2.00000 1.41421i −0.141069 0.0997509i
$$202$$ −13.0000 + 13.0000i −0.914677 + 0.914677i
$$203$$ 0 0
$$204$$ −2.82843 2.00000i −0.198030 0.140028i
$$205$$ 0 0
$$206$$ 14.1421i 0.985329i
$$207$$ 0 0
$$208$$ 3.00000 + 3.00000i 0.208013 + 0.208013i
$$209$$ 16.9706 1.17388
$$210$$ 0 0
$$211$$ −6.00000 −0.413057 −0.206529 0.978441i $$-0.566217\pi$$
−0.206529 + 0.978441i $$0.566217\pi$$
$$212$$ −4.24264 4.24264i −0.291386 0.291386i
$$213$$ 2.41421 0.414214i 0.165419 0.0283814i
$$214$$ 4.00000i 0.273434i
$$215$$ −22.6274 11.3137i −1.54318 0.771589i
$$216$$ 5.00000 + 1.41421i 0.340207 + 0.0962250i
$$217$$ 0 0
$$218$$ 4.24264 4.24264i 0.287348 0.287348i
$$219$$ −2.82843 + 4.00000i −0.191127 + 0.270295i
$$220$$ 9.00000 3.00000i 0.606780 0.202260i
$$221$$ 8.48528i 0.570782i
$$222$$ −2.07107 12.0711i −0.139001 0.810157i
$$223$$ −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
$$225$$ −8.31371 + 12.4853i −0.554247 + 0.832352i
$$226$$ 6.00000 0.399114
$$227$$ 5.65685 + 5.65685i 0.375459 + 0.375459i 0.869461 0.494002i $$-0.164466\pi$$
−0.494002 + 0.869461i $$0.664466\pi$$
$$228$$ 1.17157 + 6.82843i 0.0775893 + 0.452224i
$$229$$ 10.0000i 0.660819i 0.943838 + 0.330409i $$0.107187\pi$$
−0.943838 + 0.330409i $$0.892813\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 2.00000 2.00000i 0.131306 0.131306i
$$233$$ 12.7279 12.7279i 0.833834 0.833834i −0.154205 0.988039i $$-0.549282\pi$$
0.988039 + 0.154205i $$0.0492816\pi$$
$$234$$ 4.24264 + 12.0000i 0.277350 + 0.784465i
$$235$$ 12.0000 + 6.00000i 0.782794 + 0.391397i
$$236$$ 5.65685i 0.368230i
$$237$$ −17.0711 + 2.92893i −1.10889 + 0.190255i
$$238$$ 0 0
$$239$$ −11.3137 −0.731823 −0.365911 0.930650i $$-0.619243\pi$$
−0.365911 + 0.930650i $$0.619243\pi$$
$$240$$ 1.82843 + 3.41421i 0.118024 + 0.220387i
$$241$$ 22.0000 1.41714 0.708572 0.705638i $$-0.249340\pi$$
0.708572 + 0.705638i $$0.249340\pi$$
$$242$$ −4.94975 4.94975i −0.318182 0.318182i
$$243$$ 11.7071 + 10.2929i 0.751011 + 0.660289i
$$244$$ 8.00000i 0.512148i
$$245$$ −4.94975 14.8492i −0.316228 0.948683i
$$246$$ 0 0
$$247$$ −12.0000 + 12.0000i −0.763542 + 0.763542i
$$248$$ 0.707107 0.707107i 0.0449013 0.0449013i
$$249$$ 25.4558 + 18.0000i 1.61320 + 1.14070i
$$250$$ −11.0000 + 2.00000i −0.695701 + 0.126491i
$$251$$ 21.2132i 1.33897i −0.742828 0.669483i $$-0.766516\pi$$
0.742828 0.669483i $$-0.233484\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −12.7279 −0.798621
$$255$$ 2.24264 7.41421i 0.140440 0.464296i
$$256$$ 1.00000 0.0625000
$$257$$ −4.24264 4.24264i −0.264649 0.264649i 0.562291 0.826940i $$-0.309920\pi$$
−0.826940 + 0.562291i $$0.809920\pi$$
$$258$$ −19.3137 + 3.31371i −1.20242 + 0.206302i
$$259$$ 0 0
$$260$$ −4.24264 + 8.48528i −0.263117 + 0.526235i
$$261$$ 8.00000 2.82843i 0.495188 0.175075i
$$262$$ −14.0000 + 14.0000i −0.864923 + 0.864923i
$$263$$ 19.7990 19.7990i 1.22086 1.22086i 0.253531 0.967327i $$-0.418408\pi$$
0.967327 0.253531i $$-0.0815919\pi$$
$$264$$ 4.24264 6.00000i 0.261116 0.369274i
$$265$$ 6.00000 12.0000i 0.368577 0.737154i
$$266$$ 0 0
$$267$$ −2.07107 12.0711i −0.126747 0.738737i
$$268$$ −1.00000 1.00000i −0.0610847 0.0610847i
$$269$$ −2.82843 −0.172452 −0.0862261 0.996276i $$-0.527481\pi$$
−0.0862261 + 0.996276i $$0.527481\pi$$
$$270$$ 0.535534 + 11.6066i 0.0325916 + 0.706355i
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ −1.41421 1.41421i −0.0857493 0.0857493i
$$273$$ 0 0
$$274$$ 18.0000i 1.08742i
$$275$$ 12.7279 + 16.9706i 0.767523 + 1.02336i
$$276$$ 0 0
$$277$$ −21.0000 + 21.0000i −1.26177 + 1.26177i −0.311532 + 0.950236i $$0.600842\pi$$
−0.950236 + 0.311532i $$0.899158\pi$$
$$278$$ −5.65685 + 5.65685i −0.339276 + 0.339276i
$$279$$ 2.82843 1.00000i 0.169334 0.0598684i
$$280$$ 0 0
$$281$$ 22.6274i 1.34984i 0.737892 + 0.674919i $$0.235822\pi$$
−0.737892 + 0.674919i $$0.764178\pi$$
$$282$$ 10.2426 1.75736i 0.609940 0.104649i
$$283$$ −3.00000 3.00000i −0.178331 0.178331i 0.612297 0.790628i $$-0.290246\pi$$
−0.790628 + 0.612297i $$0.790246\pi$$
$$284$$ 1.41421 0.0839181
$$285$$ −13.6569 + 7.31371i −0.808962 + 0.433227i
$$286$$ 18.0000 1.06436
$$287$$ 0 0
$$288$$ 2.70711 + 1.29289i 0.159518 + 0.0761845i
$$289$$ 13.0000i 0.764706i
$$290$$ 5.65685 + 2.82843i 0.332182 + 0.166091i
$$291$$ 6.00000 + 4.24264i 0.351726 + 0.248708i
$$292$$ −2.00000 + 2.00000i −0.117041 + 0.117041i
$$293$$ 5.65685 5.65685i 0.330477 0.330477i −0.522291 0.852768i $$-0.674922\pi$$
0.852768 + 0.522291i $$0.174922\pi$$
$$294$$ −9.89949 7.00000i −0.577350 0.408248i
$$295$$ 12.0000 4.00000i 0.698667 0.232889i
$$296$$ 7.07107i 0.410997i
$$297$$ 19.2426 10.7574i 1.11657 0.624205i
$$298$$ −1.00000 1.00000i −0.0579284 0.0579284i
$$299$$ 0 0
$$300$$ −5.94975 + 6.29289i −0.343509 + 0.363320i
$$301$$ 0 0
$$302$$ −11.3137 11.3137i −0.651031 0.651031i
$$303$$ −31.3848 + 5.38478i −1.80301 + 0.309347i
$$304$$ 4.00000i 0.229416i
$$305$$ 16.9706 5.65685i 0.971732 0.323911i
$$306$$ −2.00000 5.65685i −0.114332 0.323381i
$$307$$ 5.00000 5.00000i 0.285365 0.285365i −0.549879 0.835244i $$-0.685326\pi$$
0.835244 + 0.549879i $$0.185326\pi$$
$$308$$ 0 0
$$309$$ −14.1421 + 20.0000i −0.804518 + 1.13776i
$$310$$ 2.00000 + 1.00000i 0.113592 + 0.0567962i
$$311$$ 12.7279i 0.721734i −0.932617 0.360867i $$-0.882481\pi$$
0.932617 0.360867i $$-0.117519\pi$$
$$312$$ 1.24264 + 7.24264i 0.0703507 + 0.410034i
$$313$$ 14.0000 + 14.0000i 0.791327 + 0.791327i 0.981710 0.190383i $$-0.0609730\pi$$
−0.190383 + 0.981710i $$0.560973\pi$$
$$314$$ −5.65685 −0.319235
$$315$$ 0 0
$$316$$ −10.0000 −0.562544
$$317$$ 15.5563 + 15.5563i 0.873732 + 0.873732i 0.992877 0.119145i $$-0.0380154\pi$$
−0.119145 + 0.992877i $$0.538015\pi$$
$$318$$ −1.75736 10.2426i −0.0985478 0.574379i
$$319$$ 12.0000i 0.671871i
$$320$$ 0.707107 + 2.12132i 0.0395285 + 0.118585i
$$321$$ −4.00000 + 5.65685i −0.223258 + 0.315735i
$$322$$ 0 0
$$323$$ 5.65685 5.65685i 0.314756 0.314756i
$$324$$ 5.65685 + 7.00000i 0.314270 + 0.388889i
$$325$$ −21.0000 3.00000i −1.16487 0.166410i
$$326$$ 15.5563i 0.861586i
$$327$$ 10.2426 1.75736i 0.566419 0.0971822i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 15.7279 + 4.75736i 0.865794 + 0.261884i
$$331$$ −28.0000 −1.53902 −0.769510 0.638635i $$-0.779499\pi$$
−0.769510 + 0.638635i $$0.779499\pi$$
$$332$$ 12.7279 + 12.7279i 0.698535 + 0.698535i
$$333$$ 9.14214 19.1421i 0.500986 1.04898i
$$334$$ 12.0000i 0.656611i
$$335$$ 1.41421 2.82843i 0.0772667 0.154533i
$$336$$ 0 0
$$337$$ 24.0000 24.0000i 1.30736 1.30736i 0.384052 0.923312i $$-0.374528\pi$$
0.923312 0.384052i $$-0.125472\pi$$
$$338$$ −3.53553 + 3.53553i −0.192308 + 0.192308i
$$339$$ 8.48528 + 6.00000i 0.460857 + 0.325875i
$$340$$ 2.00000 4.00000i 0.108465 0.216930i
$$341$$ 4.24264i 0.229752i
$$342$$ −5.17157 + 10.8284i −0.279647 + 0.585534i
$$343$$ 0 0
$$344$$ −11.3137 −0.609994
$$345$$ 0 0
$$346$$ 12.0000 0.645124
$$347$$ 1.41421 + 1.41421i 0.0759190 + 0.0759190i 0.744047 0.668128i $$-0.232904\pi$$
−0.668128 + 0.744047i $$0.732904\pi$$
$$348$$ 4.82843 0.828427i 0.258831 0.0444084i
$$349$$ 14.0000i 0.749403i −0.927146 0.374701i $$-0.877745\pi$$
0.927146 0.374701i $$-0.122255\pi$$
$$350$$ 0 0
$$351$$ −6.00000 + 21.2132i −0.320256 + 1.13228i
$$352$$ 3.00000 3.00000i 0.159901 0.159901i
$$353$$ 2.82843 2.82843i 0.150542 0.150542i −0.627818 0.778360i $$-0.716052\pi$$
0.778360 + 0.627818i $$0.216052\pi$$
$$354$$ 5.65685 8.00000i 0.300658 0.425195i
$$355$$ 1.00000 + 3.00000i 0.0530745 + 0.159223i
$$356$$ 7.07107i 0.374766i
$$357$$ 0 0
$$358$$ −13.0000 13.0000i −0.687071 0.687071i
$$359$$ −4.24264 −0.223918 −0.111959 0.993713i $$-0.535713\pi$$
−0.111959 + 0.993713i $$0.535713\pi$$
$$360$$ −0.828427 + 6.65685i −0.0436619 + 0.350847i
$$361$$ 3.00000 0.157895
$$362$$ 7.07107 + 7.07107i 0.371647 + 0.371647i
$$363$$ −2.05025 11.9497i −0.107610 0.627199i
$$364$$ 0 0
$$365$$ −5.65685 2.82843i −0.296093 0.148047i
$$366$$ 8.00000 11.3137i 0.418167 0.591377i
$$367$$ 3.00000 3.00000i 0.156599 0.156599i −0.624459 0.781058i $$-0.714680\pi$$
0.781058 + 0.624459i $$0.214680\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 15.0000 5.00000i 0.779813 0.259938i
$$371$$ 0 0
$$372$$ 1.70711 0.292893i 0.0885094 0.0151858i
$$373$$ −16.0000 16.0000i −0.828449 0.828449i 0.158854 0.987302i $$-0.449220\pi$$
−0.987302 + 0.158854i $$0.949220\pi$$
$$374$$ −8.48528 −0.438763
$$375$$ −17.5563 8.17157i −0.906606 0.421978i
$$376$$ 6.00000 0.309426
$$377$$ 8.48528 + 8.48528i 0.437014 + 0.437014i
$$378$$ 0 0
$$379$$ 6.00000i 0.308199i −0.988055 0.154100i $$-0.950752\pi$$
0.988055 0.154100i $$-0.0492477\pi$$
$$380$$ −8.48528 + 2.82843i −0.435286 + 0.145095i
$$381$$ −18.0000 12.7279i −0.922168 0.652071i
$$382$$ 1.00000 1.00000i 0.0511645 0.0511645i
$$383$$ 16.9706 16.9706i 0.867155 0.867155i −0.125001 0.992157i $$-0.539894\pi$$
0.992157 + 0.125001i $$0.0398935\pi$$
$$384$$ 1.41421 + 1.00000i 0.0721688 + 0.0510310i
$$385$$ 0 0
$$386$$ 21.2132i 1.07972i
$$387$$ −30.6274 14.6274i −1.55688 0.743553i
$$388$$ 3.00000 + 3.00000i 0.152302 + 0.152302i
$$389$$ 22.6274 1.14726 0.573628 0.819116i $$-0.305536\pi$$
0.573628 + 0.819116i $$0.305536\pi$$
$$390$$ −14.4853 + 7.75736i −0.733491 + 0.392809i
$$391$$ 0 0
$$392$$ −4.94975 4.94975i −0.250000 0.250000i
$$393$$ −33.7990 + 5.79899i −1.70493 + 0.292520i
$$394$$ 2.00000i 0.100759i
$$395$$ −7.07107 21.2132i −0.355784 1.06735i
$$396$$ 12.0000 4.24264i 0.603023 0.213201i
$$397$$ 12.0000 12.0000i 0.602263 0.602263i −0.338650 0.940913i $$-0.609970\pi$$
0.940913 + 0.338650i $$0.109970\pi$$
$$398$$ −11.3137 + 11.3137i −0.567105 + 0.567105i
$$399$$ 0 0
$$400$$ −4.00000 + 3.00000i −0.200000 + 0.150000i
$$401$$ 26.8701i 1.34183i 0.741536 + 0.670913i $$0.234098\pi$$
−0.741536 + 0.670913i $$0.765902\pi$$
$$402$$ −0.414214 2.41421i −0.0206591 0.120410i
$$403$$ 3.00000 + 3.00000i 0.149441 + 0.149441i
$$404$$ −18.3848 −0.914677
$$405$$ −10.8492 + 16.9497i −0.539103 + 0.842240i
$$406$$ 0 0
$$407$$ −21.2132 21.2132i −1.05150 1.05150i
$$408$$ −0.585786 3.41421i −0.0290008 0.169029i
$$409$$ 30.0000i 1.48340i −0.670729 0.741702i $$-0.734019\pi$$
0.670729 0.741702i $$-0.265981\pi$$
$$410$$ 0 0
$$411$$ −18.0000 + 25.4558i −0.887875 + 1.25564i
$$412$$ −10.0000 + 10.0000i −0.492665 + 0.492665i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −18.0000 + 36.0000i −0.883585 + 1.76717i
$$416$$ 4.24264i 0.208013i
$$417$$ −13.6569 + 2.34315i −0.668779 + 0.114744i
$$418$$ 12.0000 + 12.0000i 0.586939 + 0.586939i
$$419$$ −22.6274 −1.10542 −0.552711 0.833373i $$-0.686407\pi$$
−0.552711 + 0.833373i $$0.686407\pi$$
$$420$$ 0 0
$$421$$ −6.00000 −0.292422 −0.146211 0.989253i $$-0.546708\pi$$
−0.146211 + 0.989253i $$0.546708\pi$$
$$422$$ −4.24264 4.24264i −0.206529 0.206529i
$$423$$ 16.2426 + 7.75736i 0.789744 + 0.377176i
$$424$$ 6.00000i 0.291386i
$$425$$ 9.89949 + 1.41421i 0.480196 + 0.0685994i
$$426$$ 2.00000 + 1.41421i 0.0969003 + 0.0685189i
$$427$$ 0 0
$$428$$ −2.82843 + 2.82843i −0.136717 + 0.136717i
$$429$$ 25.4558 + 18.0000i 1.22902 + 0.869048i
$$430$$ −8.00000 24.0000i −0.385794 1.15738i
$$431$$ 12.7279i 0.613082i −0.951857 0.306541i $$-0.900828\pi$$
0.951857 0.306541i $$-0.0991717\pi$$
$$432$$ 2.53553 + 4.53553i 0.121991 + 0.218216i
$$433$$ −26.0000 26.0000i −1.24948 1.24948i −0.955950 0.293531i $$-0.905170\pi$$
−0.293531 0.955950i $$-0.594830\pi$$
$$434$$ 0 0
$$435$$ 5.17157 + 9.65685i 0.247958 + 0.463011i
$$436$$ 6.00000 0.287348
$$437$$ 0 0
$$438$$ −4.82843 + 0.828427i −0.230711 + 0.0395838i
$$439$$ 16.0000i 0.763638i −0.924237 0.381819i $$-0.875298\pi$$
0.924237 0.381819i $$-0.124702\pi$$
$$440$$ 8.48528 + 4.24264i 0.404520 + 0.202260i
$$441$$ −7.00000 19.7990i −0.333333 0.942809i
$$442$$ 6.00000 6.00000i 0.285391 0.285391i
$$443$$ −11.3137 + 11.3137i −0.537531 + 0.537531i −0.922803 0.385272i $$-0.874107\pi$$
0.385272 + 0.922803i $$0.374107\pi$$
$$444$$ 7.07107 10.0000i 0.335578 0.474579i
$$445$$ 15.0000 5.00000i 0.711068 0.237023i
$$446$$ 1.41421i 0.0669650i
$$447$$ −0.414214 2.41421i −0.0195916 0.114188i
$$448$$ 0 0
$$449$$ 24.0416 1.13459 0.567297 0.823513i $$-0.307989\pi$$
0.567297 + 0.823513i $$0.307989\pi$$
$$450$$ −14.7071 + 2.94975i −0.693300 + 0.139052i
$$451$$ 0 0
$$452$$ 4.24264 + 4.24264i 0.199557 + 0.199557i
$$453$$ −4.68629 27.3137i −0.220181 1.28331i
$$454$$ 8.00000i 0.375459i
$$455$$ 0 0
$$456$$ −4.00000 + 5.65685i −0.187317 + 0.264906i
$$457$$ −8.00000 + 8.00000i −0.374224 + 0.374224i −0.869013 0.494789i $$-0.835245\pi$$
0.494789 + 0.869013i $$0.335245\pi$$
$$458$$ −7.07107 + 7.07107i −0.330409 + 0.330409i
$$459$$ 2.82843 10.0000i 0.132020 0.466760i
$$460$$ 0 0
$$461$$ 36.7696i 1.71253i 0.516538 + 0.856264i $$0.327221\pi$$
−0.516538 + 0.856264i $$0.672779\pi$$
$$462$$ 0 0
$$463$$ 3.00000 + 3.00000i 0.139422 + 0.139422i 0.773373 0.633951i $$-0.218568\pi$$
−0.633951 + 0.773373i $$0.718568\pi$$
$$464$$ 2.82843 0.131306
$$465$$ 1.82843 + 3.41421i 0.0847913 + 0.158330i
$$466$$ 18.0000 0.833834
$$467$$ −25.4558 25.4558i −1.17796 1.17796i −0.980264 0.197692i $$-0.936655\pi$$
−0.197692 0.980264i $$-0.563345\pi$$
$$468$$ −5.48528 + 11.4853i −0.253557 + 0.530907i
$$469$$ 0 0
$$470$$ 4.24264 + 12.7279i 0.195698 + 0.587095i
$$471$$ −8.00000 5.65685i −0.368621 0.260654i
$$472$$ 4.00000 4.00000i 0.184115 0.184115i
$$473$$ −33.9411 + 33.9411i −1.56061 + 1.56061i
$$474$$ −14.1421 10.0000i −0.649570 0.459315i
$$475$$ −12.0000 16.0000i −0.550598 0.734130i
$$476$$ 0 0
$$477$$ 7.75736 16.2426i 0.355185 0.743699i
$$478$$ −8.00000 8.00000i −0.365911 0.365911i
$$479$$ 7.07107 0.323085 0.161543 0.986866i $$-0.448353\pi$$
0.161543 + 0.986866i $$0.448353\pi$$
$$480$$ −1.12132 + 3.70711i −0.0511810 + 0.169206i
$$481$$ 30.0000 1.36788
$$482$$ 15.5563 + 15.5563i 0.708572 + 0.708572i
$$483$$ 0 0
$$484$$ 7.00000i 0.318182i
$$485$$ −4.24264 + 8.48528i −0.192648 + 0.385297i
$$486$$ 1.00000 + 15.5563i 0.0453609 + 0.705650i
$$487$$ 15.0000 15.0000i 0.679715 0.679715i −0.280221 0.959936i $$-0.590408\pi$$
0.959936 + 0.280221i $$0.0904077\pi$$
$$488$$ 5.65685 5.65685i 0.256074 0.256074i
$$489$$ 15.5563 22.0000i 0.703482 0.994874i
$$490$$ 7.00000 14.0000i 0.316228 0.632456i
$$491$$ 15.5563i 0.702048i 0.936366 + 0.351024i $$0.114166\pi$$
−0.936366 + 0.351024i $$0.885834\pi$$
$$492$$ 0 0
$$493$$ −4.00000 4.00000i −0.180151 0.180151i
$$494$$ −16.9706 −0.763542
$$495$$ 17.4853 + 22.4558i 0.785905 + 1.00932i
$$496$$ 1.00000 0.0449013
$$497$$ 0 0
$$498$$ 5.27208 + 30.7279i 0.236247 + 1.37695i
$$499$$ 40.0000i 1.79065i 0.445418 + 0.895323i $$0.353055\pi$$
−0.445418 + 0.895323i $$0.646945\pi$$
$$500$$ −9.19239 6.36396i −0.411096 0.284605i
$$501$$ 12.0000 16.9706i 0.536120 0.758189i
$$502$$ 15.0000 15.0000i 0.669483 0.669483i
$$503$$ 15.5563 15.5563i 0.693623 0.693623i −0.269404 0.963027i $$-0.586827\pi$$
0.963027 + 0.269404i $$0.0868267\pi$$
$$504$$ 0 0
$$505$$ −13.0000 39.0000i −0.578492 1.73548i
$$506$$ 0 0
$$507$$ −8.53553 + 1.46447i −0.379076 + 0.0650392i
$$508$$ −9.00000 9.00000i −0.399310 0.399310i
$$509$$ 39.5980 1.75515 0.877575 0.479440i $$-0.159160\pi$$
0.877575 + 0.479440i $$0.159160\pi$$
$$510$$ 6.82843 3.65685i 0.302368 0.161928i
$$511$$ 0 0
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ −18.1421 + 10.1421i −0.800995 + 0.447786i
$$514$$ 6.00000i 0.264649i
$$515$$ −28.2843 14.1421i −1.24635 0.623177i
$$516$$ −16.0000 11.3137i −0.704361 0.498058i
$$517$$ 18.0000 18.0000i 0.791639 0.791639i
$$518$$ 0 0
$$519$$ 16.9706 + 12.0000i 0.744925 + 0.526742i
$$520$$ −9.00000 + 3.00000i −0.394676 + 0.131559i
$$521$$ 14.1421i 0.619578i −0.950805 0.309789i $$-0.899742\pi$$
0.950805 0.309789i $$-0.100258\pi$$
$$522$$ 7.65685 + 3.65685i 0.335131 + 0.160056i
$$523$$ −6.00000 6.00000i −0.262362 0.262362i 0.563651 0.826013i $$-0.309396\pi$$
−0.826013 + 0.563651i $$0.809396\pi$$
$$524$$ −19.7990 −0.864923
$$525$$ 0 0
$$526$$ 28.0000 1.22086
$$527$$ −1.41421 1.41421i −0.0616041 0.0616041i
$$528$$ 7.24264 1.24264i 0.315195 0.0540790i
$$529$$ 23.0000i 1.00000i
$$530$$ 12.7279 4.24264i 0.552866 0.184289i
$$531$$ 16.0000 5.65685i 0.694341 0.245487i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 7.07107 10.0000i 0.305995 0.432742i
$$535$$ −8.00000 4.00000i −0.345870 0.172935i
$$536$$ 1.41421i 0.0610847i
$$537$$ −5.38478 31.3848i −0.232370 1.35435i
$$538$$ −2.00000 2.00000i −0.0862261 0.0862261i
$$539$$ −29.6985 −1.27920
$$540$$ −7.82843 + 8.58579i −0.336882 + 0.369473i
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 15.5563 + 15.5563i 0.668202 + 0.668202i
$$543$$ 2.92893 + 17.0711i 0.125693 + 0.732590i
$$544$$ 2.00000i 0.0857493i
$$545$$ 4.24264 + 12.7279i 0.181735 + 0.545204i
$$546$$ 0 0
$$547$$ 3.00000 3.00000i 0.128271 0.128271i −0.640057 0.768328i $$-0.721089\pi$$
0.768328 + 0.640057i $$0.221089\pi$$
$$548$$ −12.7279 + 12.7279i −0.543710 + 0.543710i
$$549$$ 22.6274 8.00000i 0.965715 0.341432i
$$550$$ −3.00000 + 21.0000i −0.127920 + 0.895443i
$$551$$ 11.3137i 0.481980i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −29.6985 −1.26177
$$555$$ 26.2132 + 7.92893i 1.11269 + 0.336564i
$$556$$ −8.00000 −0.339276
$$557$$ −9.89949 9.89949i −0.419455 0.419455i 0.465561 0.885016i $$-0.345853\pi$$
−0.885016 + 0.465561i $$0.845853\pi$$
$$558$$ 2.70711 + 1.29289i 0.114601 + 0.0547325i
$$559$$ 48.0000i 2.03018i
$$560$$ 0 0
$$561$$ −12.0000 8.48528i −0.506640 0.358249i
$$562$$ −16.0000 + 16.0000i −0.674919 + 0.674919i
$$563$$ −16.9706 + 16.9706i −0.715224 + 0.715224i −0.967623 0.252399i $$-0.918780\pi$$
0.252399 + 0.967623i $$0.418780\pi$$
$$564$$ 8.48528 + 6.00000i 0.357295 + 0.252646i
$$565$$ −6.00000 + 12.0000i −0.252422 + 0.504844i
$$566$$ 4.24264i 0.178331i
$$567$$ 0 0
$$568$$ 1.00000 + 1.00000i 0.0419591 + 0.0419591i
$$569$$ −4.24264 −0.177861 −0.0889304 0.996038i $$-0.528345\pi$$
−0.0889304 + 0.996038i $$0.528345\pi$$
$$570$$ −14.8284 4.48528i −0.621094 0.187868i
$$571$$ 36.0000 1.50655 0.753277 0.657704i $$-0.228472\pi$$
0.753277 + 0.657704i $$0.228472\pi$$
$$572$$ 12.7279 + 12.7279i 0.532181 + 0.532181i
$$573$$ 2.41421 0.414214i 0.100855 0.0173040i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 + 2.82843i 0.0416667 + 0.117851i
$$577$$ 13.0000 13.0000i 0.541197 0.541197i −0.382683 0.923880i $$-0.625000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$578$$ 9.19239 9.19239i 0.382353 0.382353i
$$579$$ −21.2132 + 30.0000i −0.881591 + 1.24676i
$$580$$ 2.00000 + 6.00000i 0.0830455 + 0.249136i
$$581$$ 0 0
$$582$$ 1.24264 + 7.24264i 0.0515091 + 0.300217i
$$583$$ −18.0000 18.0000i −0.745484 0.745484i
$$584$$ −2.82843 −0.117041
$$585$$ −28.2426 3.51472i −1.16769 0.145316i
$$586$$ 8.00000 0.330477
$$587$$ 19.7990 + 19.7990i 0.817192 + 0.817192i 0.985700 0.168508i $$-0.0538950\pi$$
−0.168508 + 0.985700i $$0.553895\pi$$
$$588$$ −2.05025 11.9497i −0.0845510 0.492799i
$$589$$ 4.00000i 0.164817i
$$590$$ 11.3137 + 5.65685i 0.465778 + 0.232889i
$$591$$ −2.00000 + 2.82843i −0.0822690 + 0.116346i
$$592$$ 5.00000 5.00000i 0.205499 0.205499i
$$593$$ −24.0416 + 24.0416i −0.987271 + 0.987271i −0.999920 0.0126486i $$-0.995974\pi$$
0.0126486 + 0.999920i $$0.495974\pi$$
$$594$$ 21.2132 + 6.00000i 0.870388 + 0.246183i
$$595$$ 0 0
$$596$$ 1.41421i 0.0579284i
$$597$$ −27.3137 + 4.68629i −1.11788 + 0.191797i
$$598$$ 0 0
$$599$$ −24.0416 −0.982314 −0.491157 0.871071i $$-0.663426\pi$$
−0.491157 + 0.871071i $$0.663426\pi$$
$$600$$ −8.65685 + 0.242641i −0.353415 + 0.00990576i
$$601$$ −30.0000 −1.22373 −0.611863 0.790964i $$-0.709580\pi$$
−0.611863 + 0.790964i $$0.709580\pi$$
$$602$$ 0 0
$$603$$ 1.82843 3.82843i 0.0744593 0.155906i
$$604$$ 16.0000i 0.651031i
$$605$$ 14.8492 4.94975i 0.603708 0.201236i
$$606$$ −26.0000 18.3848i −1.05618 0.746830i
$$607$$ −16.0000 + 16.0000i −0.649420 + 0.649420i −0.952853 0.303433i $$-0.901867\pi$$
0.303433 + 0.952853i $$0.401867\pi$$
$$608$$ −2.82843 + 2.82843i −0.114708 + 0.114708i
$$609$$ 0 0
$$610$$ 16.0000 + 8.00000i 0.647821 + 0.323911i
$$611$$ 25.4558i 1.02983i
$$612$$ 2.58579 5.41421i 0.104524 0.218857i
$$613$$ −19.0000 19.0000i −0.767403 0.767403i 0.210246 0.977649i $$-0.432574\pi$$
−0.977649 + 0.210246i $$0.932574\pi$$
$$614$$ 7.07107 0.285365
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −12.7279 12.7279i −0.512407 0.512407i 0.402856 0.915263i $$-0.368017\pi$$
−0.915263 + 0.402856i $$0.868017\pi$$
$$618$$ −24.1421 + 4.14214i −0.971139 + 0.166621i
$$619$$ 32.0000i 1.28619i 0.765787 + 0.643094i $$0.222350\pi$$
−0.765787 + 0.643094i $$0.777650\pi$$
$$620$$ 0.707107 + 2.12132i 0.0283981 + 0.0851943i
$$621$$ 0 0
$$622$$ 9.00000 9.00000i 0.360867 0.360867i
$$623$$ 0 0
$$624$$ −4.24264 + 6.00000i −0.169842 + 0.240192i
$$625$$ 7.00000 24.0000i 0.280000 0.960000i
$$626$$ 19.7990i 0.791327i
$$627$$ 4.97056 + 28.9706i 0.198505 + 1.15697i
$$628$$ −4.00000 4.00000i −0.159617 0.159617i
$$629$$ −14.1421 −0.563884
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ −7.07107 7.07107i −0.281272 0.281272i
$$633$$ −1.75736 10.2426i −0.0698488 0.407108i
$$634$$ 22.0000i 0.873732i
$$635$$ 12.7279 25.4558i 0.505092 1.01018i
$$636$$ 6.00000 8.48528i 0.237915 0.336463i
$$637$$ 21.0000 21.0000i 0.832050 0.832050i
$$638$$ 8.48528 8.48528i 0.335936 0.335936i
$$639$$ 1.41421 + 4.00000i 0.0559454 + 0.158238i
$$640$$ −1.00000 + 2.00000i −0.0395285 + 0.0790569i
$$641$$ 41.0122i 1.61988i −0.586510 0.809942i $$-0.699498\pi$$
0.586510 0.809942i $$-0.300502\pi$$
$$642$$ −6.82843 + 1.17157i −0.269497 + 0.0462383i
$$643$$ 30.0000 + 30.0000i 1.18308 + 1.18308i 0.978941 + 0.204144i $$0.0654409\pi$$
0.204144 + 0.978941i $$0.434559\pi$$
$$644$$ 0 0
$$645$$ 12.6863 41.9411i 0.499522 1.65143i
$$646$$ 8.00000 0.314756
$$647$$ 5.65685 + 5.65685i 0.222394 + 0.222394i 0.809506 0.587112i $$-0.199735\pi$$
−0.587112 + 0.809506i $$0.699735\pi$$
$$648$$ −0.949747 + 8.94975i −0.0373096 + 0.351579i
$$649$$ 24.0000i 0.942082i
$$650$$ −12.7279 16.9706i −0.499230 0.665640i
$$651$$ 0 0
$$652$$ 11.0000 11.0000i 0.430793 0.430793i
$$653$$ 24.0416 24.0416i 0.940822 0.940822i −0.0575225 0.998344i $$-0.518320\pi$$
0.998344 + 0.0575225i $$0.0183201\pi$$
$$654$$ 8.48528 + 6.00000i 0.331801 + 0.234619i
$$655$$ −14.0000 42.0000i −0.547025 1.64108i
$$656$$ 0 0
$$657$$ −7.65685 3.65685i −0.298722 0.142667i
$$658$$ 0 0
$$659$$ −22.6274 −0.881439 −0.440720 0.897645i $$-0.645277\pi$$
−0.440720 + 0.897645i $$0.645277\pi$$
$$660$$ 7.75736 + 14.4853i 0.301955 + 0.563839i
$$661$$ −2.00000 −0.0777910 −0.0388955 0.999243i $$-0.512384\pi$$
−0.0388955 + 0.999243i $$0.512384\pi$$
$$662$$ −19.7990 19.7990i −0.769510 0.769510i
$$663$$ 14.4853 2.48528i 0.562562 0.0965203i
$$664$$ 18.0000i 0.698535i
$$665$$ 0 0
$$666$$ 20.0000 7.07107i 0.774984 0.273998i
$$667$$ 0 0
$$668$$ 8.48528 8.48528i 0.328305 0.328305i
$$669$$ 1.41421 2.00000i 0.0546767 0.0773245i
$$670$$ 3.00000 1.00000i 0.115900 0.0386334i
$$671$$ 33.9411i 1.31028i
$$672$$ 0 0
$$673$$ 12.0000 + 12.0000i 0.462566 + 0.462566i 0.899496 0.436930i $$-0.143934\pi$$
−0.436930 + 0.899496i $$0.643934\pi$$
$$674$$ 33.9411 1.30736
$$675$$ −23.7487 10.5355i −0.914089 0.405513i
$$676$$ −5.00000 −0.192308
$$677$$ −4.24264 4.24264i −0.163058 0.163058i 0.620862 0.783920i $$-0.286783\pi$$
−0.783920 + 0.620862i $$0.786783\pi$$
$$678$$ 1.75736 + 10.2426i 0.0674910 + 0.393366i
$$679$$ 0 0
$$680$$ 4.24264 1.41421i 0.162698 0.0542326i
$$681$$ −8.00000 + 11.3137i −0.306561 + 0.433542i
$$682$$ 3.00000 3.00000i 0.114876 0.114876i
$$683$$ 11.3137 11.3137i 0.432907 0.432907i −0.456709 0.889616i $$-0.650972\pi$$
0.889616 + 0.456709i $$0.150972\pi$$
$$684$$ −11.3137 + 4.00000i −0.432590 + 0.152944i
$$685$$ −36.0000 18.0000i −1.37549 0.687745i
$$686$$ 0 0
$$687$$ −17.0711 + 2.92893i −0.651302 + 0.111746i
$$688$$ −8.00000 8.00000i −0.304997 0.304997i
$$689$$ 25.4558 0.969790
$$690$$ 0 0
$$691$$ −46.0000 −1.74992 −0.874961 0.484193i $$-0.839113\pi$$
−0.874961 + 0.484193i $$0.839113\pi$$
$$692$$ 8.48528 + 8.48528i 0.322562 + 0.322562i
$$693$$ 0 0
$$694$$ 2.00000i 0.0759190i
$$695$$ −5.65685 16.9706i −0.214577 0.643730i
$$696$$ 4.00000 + 2.82843i 0.151620 + 0.107211i
$$697$$ 0 0
$$698$$ 9.89949 9.89949i 0.374701 0.374701i
$$699$$ 25.4558 + 18.0000i 0.962828 + 0.680823i
$$700$$ 0 0
$$701$$ 41.0122i 1.54901i 0.632568 + 0.774505i $$0.282001\pi$$
−0.632568 + 0.774505i $$0.717999\pi$$
$$702$$ −19.2426 + 10.7574i −0.726267 + 0.406010i
$$703$$ 20.0000 + 20.0000i 0.754314 + 0.754314i
$$704$$ 4.24264 0.159901
$$705$$ −6.72792 + 22.2426i −0.253388 + 0.837706i
$$706$$ 4.00000 0.150542
$$707$$ 0 0
$$708$$ 9.65685 1.65685i 0.362927 0.0622684i
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ −1.41421 + 2.82843i −0.0530745 + 0.106149i
$$711$$ −10.0000 28.2843i −0.375029 1.06074i
$$712$$ 5.00000 5.00000i 0.187383 0.187383i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −18.0000 + 36.0000i −0.673162 + 1.34632i
$$716$$ 18.3848i 0.687071i
$$717$$ −3.31371 19.3137i −0.123753 0.721284i
$$718$$ −3.00000 3.00000i −0.111959 0.111959i
$$719$$ 22.6274 0.843860 0.421930 0.906628i $$-0.361353\pi$$
0.421930 + 0.906628i $$0.361353\pi$$
$$720$$ −5.29289 + 4.12132i −0.197254 + 0.153593i
$$721$$ 0 0
$$722$$ 2.12132 + 2.12132i 0.0789474 + 0.0789474i
$$723$$ 6.44365 + 37.5563i 0.239642 + 1.39674i
$$724$$ 10.0000i 0.371647i
$$725$$ −11.3137 + 8.48528i −0.420181 + 0.315135i
$$726$$ 7.00000 9.89949i 0.259794 0.367405i
$$727$$ −14.0000 + 14.0000i −0.519231 + 0.519231i −0.917339 0.398108i $$-0.869667\pi$$
0.398108 + 0.917339i $$0.369667\pi$$
$$728$$ 0 0
$$729$$ −14.1421 + 23.0000i −0.523783 + 0.851852i
$$730$$ −2.00000 6.00000i −0.0740233 0.222070i
$$731$$ 22.6274i 0.836905i
$$732$$ 13.6569 2.34315i 0.504772 0.0866052i
$$733$$ 28.0000 + 28.0000i 1.03420 + 1.03420i 0.999394 + 0.0348096i $$0.0110825\pi$$
0.0348096 + 0.999394i $$0.488918\pi$$
$$734$$ 4.24264 0.156599
$$735$$ 23.8995 12.7990i 0.881546 0.472098i
$$736$$ 0 0
$$737$$ −4.24264 4.24264i −0.156280 0.156280i
$$738$$ 0 0
$$739$$ 20.0000i 0.735712i −0.929883 0.367856i $$-0.880092\pi$$
0.929883 0.367856i $$-0.119908\pi$$
$$740$$ 14.1421 + 7.07107i 0.519875 + 0.259938i
$$741$$ −24.0000 16.9706i −0.881662 0.623429i
$$742$$ 0 0
$$743$$ −16.9706 + 16.9706i −0.622590 + 0.622590i −0.946193 0.323603i $$-0.895106\pi$$
0.323603 + 0.946193i $$0.395106\pi$$
$$744$$ 1.41421 + 1.00000i 0.0518476 + 0.0366618i
$$745$$ 3.00000 1.00000i 0.109911 0.0366372i
$$746$$ 22.6274i 0.828449i
$$747$$ −23.2721 + 48.7279i −0.851481 + 1.78286i
$$748$$ −6.00000 6.00000i −0.219382 0.219382i
$$749$$ 0 0
$$750$$ −6.63604 18.1924i −0.242314 0.664292i
$$751$$ −12.0000 −0.437886 −0.218943 0.975738i $$-0.570261\pi$$
−0.218943 + 0.975738i $$0.570261\pi$$
$$752$$ 4.24264 + 4.24264i 0.154713 + 0.154713i
$$753$$ 36.2132 6.21320i 1.31968 0.226422i
$$754$$ 12.0000i 0.437014i
$$755$$ 33.9411 11.3137i 1.23524 0.411748i
$$756$$ 0 0
$$757$$ −21.0000 + 21.0000i −0.763258 + 0.763258i −0.976910 0.213652i $$-0.931464\pi$$
0.213652 + 0.976910i $$0.431464\pi$$
$$758$$ 4.24264 4.24264i 0.154100 0.154100i
$$759$$ 0 0
$$760$$ −8.00000 4.00000i −0.290191 0.145095i
$$761$$ 18.3848i 0.666448i −0.942848 0.333224i $$-0.891864\pi$$
0.942848 0.333224i $$-0.108136\pi$$
$$762$$ −3.72792 21.7279i −0.135048 0.787120i
$$763$$ 0 0
$$764$$ 1.41421 0.0511645
$$765$$ 13.3137 + 1.65685i 0.481358 + 0.0599037i
$$766$$ 24.0000 0.867155
$$767$$ 16.9706 + 16.9706i 0.612772 + 0.612772i
$$768$$ 0.292893 + 1.70711i 0.0105689 + 0.0615999i
$$769$$ 32.0000i 1.15395i 0.816762 + 0.576975i $$0.195767\pi$$
−0.816762 + 0.576975i $$0.804233\pi$$
$$770$$ 0 0
$$771$$ 6.00000 8.48528i 0.216085 0.305590i
$$772$$ −15.0000 + 15.0000i −0.539862 + 0.539862i
$$773$$ −26.8701 + 26.8701i −0.966449 + 0.966449i −0.999455 0.0330063i $$-0.989492\pi$$
0.0330063 + 0.999455i $$0.489492\pi$$
$$774$$ −11.3137 32.0000i −0.406663 1.15022i
$$775$$ −4.00000 + 3.00000i −0.143684 + 0.107763i
$$776$$