# Properties

 Label 3040.1.cn.a.2469.5 Level $3040$ Weight $1$ Character 3040.2469 Analytic conductor $1.517$ Analytic rank $0$ Dimension $32$ Projective image $D_{32}$ CM discriminant -95 Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3040,1,Mod(189,3040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3040, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3040.189");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3040 = 2^{5} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 3040.cn (of order $$8$$, degree $$4$$, 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: $$1.51715763840$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$8$$ over $$\Q(\zeta_{8})$$ Coefficient field: $$\Q(\zeta_{64})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{32} + 1$$ x^32 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{32}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{32} + \cdots)$$

## Embedding invariants

 Embedding label 2469.5 Root $$0.956940 - 0.290285i$$ of defining polynomial Character $$\chi$$ $$=$$ 3040.2469 Dual form 3040.1.cn.a.1709.5

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.0980171 + 0.995185i) q^{2} +(0.485544 + 1.17221i) q^{3} +(-0.980785 + 0.195090i) q^{4} +(0.923880 + 0.382683i) q^{5} +(-1.11897 + 0.598102i) q^{6} +(-0.290285 - 0.956940i) q^{8} +(-0.431207 + 0.431207i) q^{9} +O(q^{10})$$ $$q+(0.0980171 + 0.995185i) q^{2} +(0.485544 + 1.17221i) q^{3} +(-0.980785 + 0.195090i) q^{4} +(0.923880 + 0.382683i) q^{5} +(-1.11897 + 0.598102i) q^{6} +(-0.290285 - 0.956940i) q^{8} +(-0.431207 + 0.431207i) q^{9} +(-0.290285 + 0.956940i) q^{10} +(-0.636379 + 1.53636i) q^{11} +(-0.704900 - 1.05496i) q^{12} +(1.62958 - 0.674993i) q^{13} +1.26879i q^{15} +(0.923880 - 0.382683i) q^{16} +(-0.471397 - 0.386865i) q^{18} +(-0.923880 + 0.382683i) q^{19} +(-0.980785 - 0.195090i) q^{20} +(-1.59133 - 0.482726i) q^{22} +(0.980785 - 0.804910i) q^{24} +(0.707107 + 0.707107i) q^{25} +(0.831470 + 1.55557i) q^{26} +(0.457372 + 0.189450i) q^{27} +(-1.26268 + 0.124363i) q^{30} +(0.471397 + 0.881921i) q^{32} -2.10991 q^{33} +(0.338797 - 0.507046i) q^{36} +(-1.83886 - 0.761681i) q^{37} +(-0.471397 - 0.881921i) q^{38} +(1.58246 + 1.58246i) q^{39} +(0.0980171 - 0.995185i) q^{40} +(0.324423 - 1.63099i) q^{44} +(-0.563400 + 0.233368i) q^{45} +(0.897168 + 0.897168i) q^{48} +1.00000i q^{49} +(-0.634393 + 0.773010i) q^{50} +(-1.46658 + 0.979938i) q^{52} +(0.591637 - 1.42834i) q^{53} +(-0.143707 + 0.473739i) q^{54} +(-1.17588 + 1.17588i) q^{55} +(-0.897168 - 0.897168i) q^{57} +(-0.247528 - 1.24441i) q^{60} +(-0.425215 - 1.02656i) q^{61} +(-0.831470 + 0.555570i) q^{64} +1.76384 q^{65} +(-0.206808 - 2.09976i) q^{66} +(-0.732410 - 1.76820i) q^{67} +(0.537813 + 0.287467i) q^{72} +(0.577774 - 1.90466i) q^{74} +(-0.485544 + 1.17221i) q^{75} +(0.831470 - 0.555570i) q^{76} +(-1.41973 + 1.72995i) q^{78} +1.00000 q^{80} +1.23794i q^{81} +(1.65493 + 0.162997i) q^{88} +(-0.287467 - 0.537813i) q^{90} -1.00000 q^{95} +(-0.804910 + 0.980785i) q^{96} -0.942793 q^{97} +(-0.995185 + 0.0980171i) q^{98} +(-0.388076 - 0.936899i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32 q+O(q^{10})$$ 32 * q $$32 q - 32 q^{66} + 32 q^{80} - 32 q^{95} - 32 q^{96} - 32 q^{99}+O(q^{100})$$ 32 * q - 32 * q^66 + 32 * q^80 - 32 * q^95 - 32 * q^96 - 32 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3040\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$1217$$ $$1921$$ $$2661$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.0980171 + 0.995185i 0.0980171 + 0.995185i
$$3$$ 0.485544 + 1.17221i 0.485544 + 1.17221i 0.956940 + 0.290285i $$0.0937500\pi$$
−0.471397 + 0.881921i $$0.656250\pi$$
$$4$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$5$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$6$$ −1.11897 + 0.598102i −1.11897 + 0.598102i
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ −0.290285 0.956940i −0.290285 0.956940i
$$9$$ −0.431207 + 0.431207i −0.431207 + 0.431207i
$$10$$ −0.290285 + 0.956940i −0.290285 + 0.956940i
$$11$$ −0.636379 + 1.53636i −0.636379 + 1.53636i 0.195090 + 0.980785i $$0.437500\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$12$$ −0.704900 1.05496i −0.704900 1.05496i
$$13$$ 1.62958 0.674993i 1.62958 0.674993i 0.634393 0.773010i $$-0.281250\pi$$
0.995185 + 0.0980171i $$0.0312500\pi$$
$$14$$ 0 0
$$15$$ 1.26879i 1.26879i
$$16$$ 0.923880 0.382683i 0.923880 0.382683i
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ −0.471397 0.386865i −0.471397 0.386865i
$$19$$ −0.923880 + 0.382683i −0.923880 + 0.382683i
$$20$$ −0.980785 0.195090i −0.980785 0.195090i
$$21$$ 0 0
$$22$$ −1.59133 0.482726i −1.59133 0.482726i
$$23$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$24$$ 0.980785 0.804910i 0.980785 0.804910i
$$25$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$26$$ 0.831470 + 1.55557i 0.831470 + 1.55557i
$$27$$ 0.457372 + 0.189450i 0.457372 + 0.189450i
$$28$$ 0 0
$$29$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$30$$ −1.26268 + 0.124363i −1.26268 + 0.124363i
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0.471397 + 0.881921i 0.471397 + 0.881921i
$$33$$ −2.10991 −2.10991
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0.338797 0.507046i 0.338797 0.507046i
$$37$$ −1.83886 0.761681i −1.83886 0.761681i −0.956940 0.290285i $$-0.906250\pi$$
−0.881921 0.471397i $$-0.843750\pi$$
$$38$$ −0.471397 0.881921i −0.471397 0.881921i
$$39$$ 1.58246 + 1.58246i 1.58246 + 1.58246i
$$40$$ 0.0980171 0.995185i 0.0980171 0.995185i
$$41$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$44$$ 0.324423 1.63099i 0.324423 1.63099i
$$45$$ −0.563400 + 0.233368i −0.563400 + 0.233368i
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0.897168 + 0.897168i 0.897168 + 0.897168i
$$49$$ 1.00000i 1.00000i
$$50$$ −0.634393 + 0.773010i −0.634393 + 0.773010i
$$51$$ 0 0
$$52$$ −1.46658 + 0.979938i −1.46658 + 0.979938i
$$53$$ 0.591637 1.42834i 0.591637 1.42834i −0.290285 0.956940i $$-0.593750\pi$$
0.881921 0.471397i $$-0.156250\pi$$
$$54$$ −0.143707 + 0.473739i −0.143707 + 0.473739i
$$55$$ −1.17588 + 1.17588i −1.17588 + 1.17588i
$$56$$ 0 0
$$57$$ −0.897168 0.897168i −0.897168 0.897168i
$$58$$ 0 0
$$59$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$60$$ −0.247528 1.24441i −0.247528 1.24441i
$$61$$ −0.425215 1.02656i −0.425215 1.02656i −0.980785 0.195090i $$-0.937500\pi$$
0.555570 0.831470i $$-0.312500\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −0.831470 + 0.555570i −0.831470 + 0.555570i
$$65$$ 1.76384 1.76384
$$66$$ −0.206808 2.09976i −0.206808 2.09976i
$$67$$ −0.732410 1.76820i −0.732410 1.76820i −0.634393 0.773010i $$-0.718750\pi$$
−0.0980171 0.995185i $$-0.531250\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$72$$ 0.537813 + 0.287467i 0.537813 + 0.287467i
$$73$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$74$$ 0.577774 1.90466i 0.577774 1.90466i
$$75$$ −0.485544 + 1.17221i −0.485544 + 1.17221i
$$76$$ 0.831470 0.555570i 0.831470 0.555570i
$$77$$ 0 0
$$78$$ −1.41973 + 1.72995i −1.41973 + 1.72995i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 1.00000 1.00000
$$81$$ 1.23794i 1.23794i
$$82$$ 0 0
$$83$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 1.65493 + 0.162997i 1.65493 + 0.162997i
$$89$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$90$$ −0.287467 0.537813i −0.287467 0.537813i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.00000 −1.00000
$$96$$ −0.804910 + 0.980785i −0.804910 + 0.980785i
$$97$$ −0.942793 −0.942793 −0.471397 0.881921i $$-0.656250\pi$$
−0.471397 + 0.881921i $$0.656250\pi$$
$$98$$ −0.995185 + 0.0980171i −0.995185 + 0.0980171i
$$99$$ −0.388076 0.936899i −0.388076 0.936899i
$$100$$ −0.831470 0.555570i −0.831470 0.555570i
$$101$$ 1.53636 + 0.636379i 1.53636 + 0.636379i 0.980785 0.195090i $$-0.0625000\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$102$$ 0 0
$$103$$ 0.138617 + 0.138617i 0.138617 + 0.138617i 0.773010 0.634393i $$-0.218750\pi$$
−0.634393 + 0.773010i $$0.718750\pi$$
$$104$$ −1.11897 1.36347i −1.11897 1.36347i
$$105$$ 0 0
$$106$$ 1.47945 + 0.448786i 1.47945 + 0.448786i
$$107$$ 0.222174 0.536376i 0.222174 0.536376i −0.773010 0.634393i $$-0.781250\pi$$
0.995185 + 0.0980171i $$0.0312500\pi$$
$$108$$ −0.485544 0.0965806i −0.485544 0.0965806i
$$109$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$110$$ −1.28547 1.05496i −1.28547 1.05496i
$$111$$ 2.52535i 2.52535i
$$112$$ 0 0
$$113$$ 1.54602i 1.54602i 0.634393 + 0.773010i $$0.281250\pi$$
−0.634393 + 0.773010i $$0.718750\pi$$
$$114$$ 0.804910 0.980785i 0.804910 0.980785i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −0.411624 + 0.993748i −0.411624 + 0.993748i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 1.21415 0.368309i 1.21415 0.368309i
$$121$$ −1.24830 1.24830i −1.24830 1.24830i
$$122$$ 0.979938 0.523788i 0.979938 0.523788i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$126$$ 0 0
$$127$$ 1.91388 1.91388 0.956940 0.290285i $$-0.0937500\pi$$
0.956940 + 0.290285i $$0.0937500\pi$$
$$128$$ −0.634393 0.773010i −0.634393 0.773010i
$$129$$ 0 0
$$130$$ 0.172887 + 1.75535i 0.172887 + 1.75535i
$$131$$ −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$-0.5\pi$$
$$132$$ 2.06937 0.411624i 2.06937 0.411624i
$$133$$ 0 0
$$134$$ 1.68789 0.902197i 1.68789 0.902197i
$$135$$ 0.350057 + 0.350057i 0.350057 + 0.350057i
$$136$$ 0 0
$$137$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$138$$ 0 0
$$139$$ 0.750661 1.81225i 0.750661 1.81225i 0.195090 0.980785i $$-0.437500\pi$$
0.555570 0.831470i $$-0.312500\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.93316i 2.93316i
$$144$$ −0.233368 + 0.563400i −0.233368 + 0.563400i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −1.17221 + 0.485544i −1.17221 + 0.485544i
$$148$$ 1.95213 + 0.388302i 1.95213 + 0.388302i
$$149$$ −0.750661 + 1.81225i −0.750661 + 1.81225i −0.195090 + 0.980785i $$0.562500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$150$$ −1.21415 0.368309i −1.21415 0.368309i
$$151$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$152$$ 0.634393 + 0.773010i 0.634393 + 0.773010i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.86078 1.24333i −1.86078 1.24333i
$$157$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$158$$ 0 0
$$159$$ 1.96157 1.96157
$$160$$ 0.0980171 + 0.995185i 0.0980171 + 0.995185i
$$161$$ 0 0
$$162$$ −1.23198 + 0.121339i −1.23198 + 0.121339i
$$163$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$164$$ 0 0
$$165$$ −1.94931 0.807429i −1.94931 0.807429i
$$166$$ 0 0
$$167$$ −0.410525 0.410525i −0.410525 0.410525i 0.471397 0.881921i $$-0.343750\pi$$
−0.881921 + 0.471397i $$0.843750\pi$$
$$168$$ 0 0
$$169$$ 1.49280 1.49280i 1.49280 1.49280i
$$170$$ 0 0
$$171$$ 0.233368 0.563400i 0.233368 0.563400i
$$172$$ 0 0
$$173$$ 1.76820 0.732410i 1.76820 0.732410i 0.773010 0.634393i $$-0.218750\pi$$
0.995185 0.0980171i $$-0.0312500\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.66294i 1.66294i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$180$$ 0.507046 0.338797i 0.507046 0.338797i
$$181$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$182$$ 0 0
$$183$$ 0.996879 0.996879i 0.996879 0.996879i
$$184$$ 0 0
$$185$$ −1.40740 1.40740i −1.40740 1.40740i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −0.0980171 0.995185i −0.0980171 0.995185i
$$191$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$192$$ −1.05496 0.704900i −1.05496 0.704900i
$$193$$ 0.580569 0.580569 0.290285 0.956940i $$-0.406250\pi$$
0.290285 + 0.956940i $$0.406250\pi$$
$$194$$ −0.0924099 0.938254i −0.0924099 0.938254i
$$195$$ 0.856422 + 2.06759i 0.856422 + 2.06759i
$$196$$ −0.195090 0.980785i −0.195090 0.980785i
$$197$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$198$$ 0.894350 0.478040i 0.894350 0.478040i
$$199$$ −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i $$-0.375000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$200$$ 0.471397 0.881921i 0.471397 0.881921i
$$201$$ 1.71707 1.71707i 1.71707 1.71707i
$$202$$ −0.482726 + 1.59133i −0.482726 + 1.59133i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −0.124363 + 0.151537i −0.124363 + 0.151537i
$$207$$ 0 0
$$208$$ 1.24723 1.24723i 1.24723 1.24723i
$$209$$ 1.66294i 1.66294i
$$210$$ 0 0
$$211$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$212$$ −0.301614 + 1.51631i −0.301614 + 1.51631i
$$213$$ 0 0
$$214$$ 0.555570 + 0.168530i 0.555570 + 0.168530i
$$215$$ 0 0
$$216$$ 0.0485240 0.492672i 0.0485240 0.492672i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0.923880 1.38268i 0.923880 1.38268i
$$221$$ 0 0
$$222$$ 2.51319 0.247528i 2.51319 0.247528i
$$223$$ 0.942793 0.942793 0.471397 0.881921i $$-0.343750\pi$$
0.471397 + 0.881921i $$0.343750\pi$$
$$224$$ 0 0
$$225$$ −0.609819 −0.609819
$$226$$ −1.53858 + 0.151537i −1.53858 + 0.151537i
$$227$$ −0.360791 0.871028i −0.360791 0.871028i −0.995185 0.0980171i $$-0.968750\pi$$
0.634393 0.773010i $$-0.281250\pi$$
$$228$$ 1.05496 + 0.704900i 1.05496 + 0.704900i
$$229$$ −1.81225 0.750661i −1.81225 0.750661i −0.980785 0.195090i $$-0.937500\pi$$
−0.831470 0.555570i $$-0.812500\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$234$$ −1.02931 0.312238i −1.02931 0.312238i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$240$$ 0.485544 + 1.17221i 0.485544 + 1.17221i
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 1.11994 1.36465i 1.11994 1.36465i
$$243$$ −0.993748 + 0.411624i −0.993748 + 0.411624i
$$244$$ 0.617317 + 0.923880i 0.617317 + 0.923880i
$$245$$ −0.382683 + 0.923880i −0.382683 + 0.923880i
$$246$$ 0 0
$$247$$ −1.24723 + 1.24723i −1.24723 + 1.24723i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −0.881921 + 0.471397i −0.881921 + 0.471397i
$$251$$ 1.30656 + 0.541196i 1.30656 + 0.541196i 0.923880 0.382683i $$-0.125000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0.187593 + 1.90466i 0.187593 + 1.90466i
$$255$$ 0 0
$$256$$ 0.707107 0.707107i 0.707107 0.707107i
$$257$$ −0.580569 −0.580569 −0.290285 0.956940i $$-0.593750\pi$$
−0.290285 + 0.956940i $$0.593750\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −1.72995 + 0.344109i −1.72995 + 0.344109i
$$261$$ 0 0
$$262$$ 1.62958 0.871028i 1.62958 0.871028i
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 0.612476 + 2.01906i 0.612476 + 2.01906i
$$265$$ 1.09320 1.09320i 1.09320 1.09320i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 1.06330 + 1.59133i 1.06330 + 1.59133i
$$269$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$270$$ −0.314060 + 0.382683i −0.314060 + 0.382683i
$$271$$ 1.96157i 1.96157i 0.195090 + 0.980785i $$0.437500\pi$$
−0.195090 + 0.980785i $$0.562500\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.53636 + 0.636379i −1.53636 + 0.636379i
$$276$$ 0 0
$$277$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$278$$ 1.87711 + 0.569414i 1.87711 + 0.569414i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$284$$ 0 0
$$285$$ −0.485544 1.17221i −0.485544 1.17221i
$$286$$ −2.91904 + 0.287500i −2.91904 + 0.287500i
$$287$$ 0 0
$$288$$ −0.583561 0.177021i −0.583561 0.177021i
$$289$$ −1.00000 −1.00000
$$290$$ 0 0
$$291$$ −0.457767 1.10515i −0.457767 1.10515i
$$292$$ 0 0
$$293$$ 0.181112 + 0.0750191i 0.181112 + 0.0750191i 0.471397 0.881921i $$-0.343750\pi$$
−0.290285 + 0.956940i $$0.593750\pi$$
$$294$$ −0.598102 1.11897i −0.598102 1.11897i
$$295$$ 0 0
$$296$$ −0.195090 + 1.98079i −0.195090 + 1.98079i
$$297$$ −0.582124 + 0.582124i −0.582124 + 0.582124i
$$298$$ −1.87711 0.569414i −1.87711 0.569414i
$$299$$ 0 0
$$300$$ 0.247528 1.24441i 0.247528 1.24441i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 2.10991i 2.10991i
$$304$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$305$$ 1.11114i 1.11114i
$$306$$ 0 0
$$307$$ −0.871028 + 0.360791i −0.871028 + 0.360791i −0.773010 0.634393i $$-0.781250\pi$$
−0.0980171 + 0.995185i $$0.531250\pi$$
$$308$$ 0 0
$$309$$ −0.0951832 + 0.229793i −0.0951832 + 0.229793i
$$310$$ 0 0
$$311$$ 0.785695 0.785695i 0.785695 0.785695i −0.195090 0.980785i $$-0.562500\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$312$$ 1.05496 1.97369i 1.05496 1.97369i
$$313$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −0.222174 0.536376i −0.222174 0.536376i 0.773010 0.634393i $$-0.218750\pi$$
−0.995185 + 0.0980171i $$0.968750\pi$$
$$318$$ 0.192268 + 1.95213i 0.192268 + 1.95213i
$$319$$ 0 0
$$320$$ −0.980785 + 0.195090i −0.980785 + 0.195090i
$$321$$ 0.736619 0.736619
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −0.241510 1.21415i −0.241510 1.21415i
$$325$$ 1.62958 + 0.674993i 1.62958 + 0.674993i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0.612476 2.01906i 0.612476 2.01906i
$$331$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$332$$ 0 0
$$333$$ 1.12137 0.464488i 1.12137 0.464488i
$$334$$ 0.368309 0.448786i 0.368309 0.448786i
$$335$$ 1.91388i 1.91388i
$$336$$ 0 0
$$337$$ 1.99037i 1.99037i 0.0980171 + 0.995185i $$0.468750\pi$$
−0.0980171 + 0.995185i $$0.531250\pi$$
$$338$$ 1.63193 + 1.33929i 1.63193 + 1.33929i
$$339$$ −1.81225 + 0.750661i −1.81225 + 0.750661i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.583561 + 0.177021i 0.583561 + 0.177021i
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0.902197 + 1.68789i 0.902197 + 1.68789i
$$347$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$348$$ 0 0
$$349$$ −0.541196 1.30656i −0.541196 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$350$$ 0 0
$$351$$ 0.873201 0.873201
$$352$$ −1.65493 + 0.162997i −1.65493 + 0.162997i
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 1.38704 + 1.38704i 1.38704 + 1.38704i 0.831470 + 0.555570i $$0.187500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$360$$ 0.386865 + 0.471397i 0.386865 + 0.471397i
$$361$$ 0.707107 0.707107i 0.707107 0.707107i
$$362$$ 0 0
$$363$$ 0.857163 2.06937i 0.857163 2.06937i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 1.08979 + 0.894368i 1.08979 + 0.894368i
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 1.26268 1.53858i 1.26268 1.53858i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −0.485544 + 1.17221i −0.485544 + 1.17221i 0.471397 + 0.881921i $$0.343750\pi$$
−0.956940 + 0.290285i $$0.906250\pi$$
$$374$$ 0 0
$$375$$ −0.897168 + 0.897168i −0.897168 + 0.897168i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$380$$ 0.980785 0.195090i 0.980785 0.195090i
$$381$$ 0.929273 + 2.24346i 0.929273 + 2.24346i
$$382$$ −0.0750191 0.761681i −0.0750191 0.761681i
$$383$$ −0.196034 −0.196034 −0.0980171 0.995185i $$-0.531250\pi$$
−0.0980171 + 0.995185i $$0.531250\pi$$
$$384$$ 0.598102 1.11897i 0.598102 1.11897i
$$385$$ 0 0
$$386$$ 0.0569057 + 0.577774i 0.0569057 + 0.577774i
$$387$$ 0 0
$$388$$ 0.924678 0.183930i 0.924678 0.183930i
$$389$$ 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 $$0$$
0.707107 + 0.707107i $$0.250000\pi$$
$$390$$ −1.97369 + 1.05496i −1.97369 + 1.05496i
$$391$$ 0 0
$$392$$ 0.956940 0.290285i 0.956940 0.290285i
$$393$$ 1.65775 1.65775i 1.65775 1.65775i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.563400 + 0.843187i 0.563400 + 0.843187i
$$397$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$398$$ 0.485544 0.591637i 0.485544 0.591637i
$$399$$ 0 0
$$400$$ 0.923880 + 0.382683i 0.923880 + 0.382683i
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 1.87711 + 1.54050i 1.87711 + 1.54050i
$$403$$ 0 0
$$404$$ −1.63099 0.324423i −1.63099 0.324423i
$$405$$ −0.473739 + 1.14371i −0.473739 + 1.14371i
$$406$$ 0 0
$$407$$ 2.34043 2.34043i 2.34043 2.34043i
$$408$$ 0 0
$$409$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −0.162997 0.108911i −0.162997 0.108911i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.36347 + 1.11897i 1.36347 + 1.11897i
$$417$$ 2.48881 2.48881
$$418$$ 1.65493 0.162997i 1.65493 0.162997i
$$419$$ 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 $$0$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ −1.53858 0.151537i −1.53858 0.151537i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.113263 + 0.569414i −0.113263 + 0.569414i
$$429$$ −3.43827 + 1.42418i −3.43827 + 1.42418i
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0.495056 0.495056
$$433$$ 1.26879i 1.26879i −0.773010 0.634393i $$-0.781250\pi$$
0.773010 0.634393i $$-0.218750\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$440$$ 1.46658 + 0.783904i 1.46658 + 0.783904i
$$441$$ −0.431207 0.431207i −0.431207 0.431207i
$$442$$ 0 0
$$443$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$444$$ 0.492672 + 2.47683i 0.492672 + 2.47683i
$$445$$ 0 0
$$446$$ 0.0924099 + 0.938254i 0.0924099 + 0.938254i
$$447$$ −2.48881 −2.48881
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ −0.0597727 0.606883i −0.0597727 0.606883i
$$451$$ 0 0
$$452$$ −0.301614 1.51631i −0.301614 1.51631i
$$453$$ 0 0
$$454$$ 0.831470 0.444430i 0.831470 0.444430i
$$455$$ 0 0
$$456$$ −0.598102 + 1.11897i −0.598102 + 1.11897i
$$457$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$458$$ 0.569414 1.87711i 0.569414 1.87711i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i $$-0.750000\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$468$$ 0.209844 1.05496i 0.209844 1.05496i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −0.923880 0.382683i −0.923880 0.382683i
$$476$$ 0 0
$$477$$ 0.360791 + 0.871028i 0.360791 + 0.871028i
$$478$$ −1.40740 + 0.138617i −1.40740 + 0.138617i
$$479$$ 1.66294 1.66294 0.831470 0.555570i $$-0.187500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$480$$ −1.11897 + 0.598102i −1.11897 + 0.598102i
$$481$$ −3.51070 −3.51070
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.46785 + 0.980785i 1.46785 + 0.980785i
$$485$$ −0.871028 0.360791i −0.871028 0.360791i
$$486$$ −0.507046 0.948617i −0.507046 0.948617i
$$487$$ −1.09320 1.09320i −1.09320 1.09320i −0.995185 0.0980171i $$-0.968750\pi$$
−0.0980171 0.995185i $$-0.531250\pi$$
$$488$$ −0.858923 + 0.704900i −0.858923 + 0.704900i
$$489$$ 0 0
$$490$$ −0.956940 0.290285i −0.956940 0.290285i
$$491$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −1.36347 1.11897i −1.36347 1.11897i
$$495$$ 1.01409i 1.01409i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0.360480 0.149316i 0.360480 0.149316i −0.195090 0.980785i $$-0.562500\pi$$
0.555570 + 0.831470i $$0.312500\pi$$
$$500$$ −0.555570 0.831470i −0.555570 0.831470i
$$501$$ 0.281892 0.680547i 0.281892 0.680547i
$$502$$ −0.410525 + 1.35332i −0.410525 + 1.35332i
$$503$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$504$$ 0 0
$$505$$ 1.17588 + 1.17588i 1.17588 + 1.17588i
$$506$$ 0 0
$$507$$ 2.47469 + 1.02505i 2.47469 + 1.02505i
$$508$$ −1.87711 + 0.373380i −1.87711 + 0.373380i
$$509$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.773010 + 0.634393i 0.773010 + 0.634393i
$$513$$ −0.495056 −0.495056
$$514$$ −0.0569057 0.577774i −0.0569057 0.577774i
$$515$$ 0.0750191 + 0.181112i 0.0750191 + 0.181112i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 1.71707 + 1.71707i 1.71707 + 1.71707i
$$520$$ −0.512016 1.68789i −0.512016 1.68789i
$$521$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$522$$ 0 0
$$523$$ 0.0750191 0.181112i 0.0750191 0.181112i −0.881921 0.471397i $$-0.843750\pi$$
0.956940 + 0.290285i $$0.0937500\pi$$
$$524$$ 1.02656 + 1.53636i 1.02656 + 1.53636i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −1.94931 + 0.807429i −1.94931 + 0.807429i
$$529$$ 1.00000i 1.00000i
$$530$$ 1.19509 + 0.980785i 1.19509 + 0.980785i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0.410525 0.410525i 0.410525 0.410525i
$$536$$ −1.47945 + 1.21415i −1.47945 + 1.21415i
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.53636 0.636379i −1.53636 0.636379i
$$540$$ −0.411624 0.275038i −0.411624 0.275038i
$$541$$ −0.149316 0.360480i −0.149316 0.360480i 0.831470 0.555570i $$-0.187500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$542$$ −1.95213 + 0.192268i −1.95213 + 0.192268i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.761681 + 1.83886i 0.761681 + 1.83886i 0.471397 + 0.881921i $$0.343750\pi$$
0.290285 + 0.956940i $$0.406250\pi$$
$$548$$ 0 0
$$549$$ 0.626016 + 0.259304i 0.626016 + 0.259304i
$$550$$ −0.783904 1.46658i −0.783904 1.46658i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0.966411 2.33312i 0.966411 2.33312i
$$556$$ −0.382683 + 1.92388i −0.382683 + 1.92388i
$$557$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.83886 + 0.761681i −1.83886 + 0.761681i −0.881921 + 0.471397i $$0.843750\pi$$
−0.956940 + 0.290285i $$0.906250\pi$$
$$564$$ 0 0
$$565$$ −0.591637 + 1.42834i −0.591637 + 1.42834i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$570$$ 1.11897 0.598102i 1.11897 0.598102i
$$571$$ −0.360480 0.149316i −0.360480 0.149316i 0.195090 0.980785i $$-0.437500\pi$$
−0.555570 + 0.831470i $$0.687500\pi$$
$$572$$ −0.572232 2.87680i −0.572232 2.87680i
$$573$$ −0.371619 0.897168i −0.371619 0.897168i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0.118970 0.598102i 0.118970 0.598102i
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −0.0980171 0.995185i −0.0980171 0.995185i
$$579$$ 0.281892 + 0.680547i 0.281892 + 0.680547i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 1.05496 0.563887i 1.05496 0.563887i
$$583$$ 1.81793 + 1.81793i 1.81793 + 1.81793i
$$584$$ 0 0
$$585$$ −0.760582 + 0.760582i −0.760582 + 0.760582i
$$586$$ −0.0569057 + 0.187593i −0.0569057 + 0.187593i
$$587$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$588$$ 1.05496 0.704900i 1.05496 0.704900i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.99037 −1.99037
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ −0.636379 0.522263i −0.636379 0.522263i
$$595$$ 0 0
$$596$$ 0.382683 1.92388i 0.382683 1.92388i
$$597$$ 0.371619 0.897168i 0.371619 0.897168i
$$598$$ 0 0
$$599$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$600$$ 1.26268 + 0.124363i 1.26268 + 0.124363i
$$601$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$602$$ 0 0
$$603$$ 1.07828 + 0.446638i 1.07828 + 0.446638i
$$604$$ 0 0
$$605$$ −0.675577 1.63099i −0.675577 1.63099i
$$606$$ −2.09976 + 0.206808i −2.09976 + 0.206808i
$$607$$ −1.54602 −1.54602 −0.773010 0.634393i $$-0.781250\pi$$
−0.773010 + 0.634393i $$0.781250\pi$$
$$608$$ −0.773010 0.634393i −0.773010 0.634393i
$$609$$ 0 0
$$610$$ 1.10579 0.108911i 1.10579 0.108911i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$614$$ −0.444430 0.831470i −0.444430 0.831470i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$618$$ −0.238016 0.0722012i −0.238016 0.0722012i
$$619$$ −0.425215 + 1.02656i −0.425215 + 1.02656i 0.555570 + 0.831470i $$0.312500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0.858923 + 0.704900i 0.858923 + 0.704900i
$$623$$ 0 0
$$624$$ 2.06759 + 0.856422i 2.06759 + 0.856422i
$$625$$ 1.00000i 1.00000i
$$626$$ 0 0
$$627$$ 1.94931 0.807429i 1.94931 0.807429i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0.275899 0.275899i 0.275899 0.275899i −0.555570 0.831470i $$-0.687500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0.512016 0.273678i 0.512016 0.273678i
$$635$$ 1.76820 + 0.732410i 1.76820 + 0.732410i
$$636$$ −1.92388 + 0.382683i −1.92388 + 0.382683i
$$637$$ 0.674993 + 1.62958i 0.674993 + 1.62958i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.290285 0.956940i −0.290285 0.956940i
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0.0722012 + 0.733072i 0.0722012 + 0.733072i
$$643$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$648$$ 1.18463 0.359355i 1.18463 0.359355i
$$649$$ 0 0
$$650$$ −0.512016 + 1.68789i −0.512016 + 1.68789i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$654$$ 0 0
$$655$$ 1.84776i 1.84776i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$660$$ 2.06937 + 0.411624i 2.06937 + 0.411624i
$$661$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0.572165 + 1.07045i 0.572165 + 1.07045i
$$667$$ 0 0
$$668$$ 0.482726 + 0.322547i 0.482726 + 0.322547i
$$669$$ 0.457767 + 1.10515i 0.457767 + 1.10515i
$$670$$ 1.90466 0.187593i 1.90466 0.187593i
$$671$$ 1.84776 1.84776
$$672$$ 0 0
$$673$$ −1.99037 −1.99037 −0.995185 0.0980171i $$-0.968750\pi$$
−0.995185 + 0.0980171i $$0.968750\pi$$
$$674$$ −1.98079 + 0.195090i −1.98079 + 0.195090i
$$675$$ 0.189450 + 0.457372i 0.189450 + 0.457372i
$$676$$ −1.17289 + 1.75535i −1.17289 + 1.75535i
$$677$$ 1.83886 + 0.761681i 1.83886 + 0.761681i 0.956940 + 0.290285i $$0.0937500\pi$$
0.881921 + 0.471397i $$0.156250\pi$$
$$678$$ −0.924678 1.72995i −0.924678 1.72995i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.845844 0.845844i 0.845844 0.845844i
$$682$$ 0 0
$$683$$ 0.761681 1.83886i 0.761681 1.83886i 0.290285 0.956940i $$-0.406250\pi$$
0.471397 0.881921i $$-0.343750\pi$$
$$684$$ −0.118970 + 0.598102i −0.118970 + 0.598102i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 2.48881i 2.48881i
$$688$$ 0 0
$$689$$ 2.72694i 2.72694i
$$690$$ 0 0
$$691$$ 1.02656 0.425215i 1.02656 0.425215i 0.195090 0.980785i $$-0.437500\pi$$
0.831470 + 0.555570i $$0.187500\pi$$
$$692$$ −1.59133 + 1.06330i −1.59133 + 1.06330i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 1.38704 1.38704i 1.38704 1.38704i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.24723 0.666656i 1.24723 0.666656i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0.149316 + 0.360480i 0.149316 + 0.360480i 0.980785 0.195090i $$-0.0625000\pi$$
−0.831470 + 0.555570i $$0.812500\pi$$
$$702$$ 0.0855886 + 0.868996i 0.0855886 + 0.868996i
$$703$$ 1.99037 1.99037
$$704$$ −0.324423 1.63099i −0.324423 1.63099i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −1.30656 0.541196i −1.30656 0.541196i −0.382683 0.923880i $$-0.625000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −1.12247 + 2.70989i −1.12247 + 2.70989i
$$716$$ 0 0
$$717$$ −1.65775 + 0.686662i −1.65775 + 0.686662i
$$718$$ −1.24441 + 1.51631i −1.24441 + 1.51631i
$$719$$ 0.390181i 0.390181i −0.980785 0.195090i $$-0.937500\pi$$
0.980785 0.195090i $$-0.0625000\pi$$
$$720$$ −0.431207 + 0.431207i −0.431207 + 0.431207i
$$721$$ 0 0
$$722$$ 0.773010 + 0.634393i 0.773010 + 0.634393i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 2.14343 + 0.650201i 2.14343 + 0.650201i
$$727$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$728$$ 0 0
$$729$$ −0.0896606 0.0896606i −0.0896606 0.0896606i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ −0.783243 + 1.17221i −0.783243 + 1.17221i
$$733$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$734$$ 0 0
$$735$$ −1.26879 −1.26879
$$736$$ 0 0
$$737$$ 3.18267 3.18267
$$738$$ 0 0
$$739$$ −0.541196 1.30656i −0.541196 1.30656i −0.923880 0.382683i $$-0.875000\pi$$
0.382683 0.923880i $$-0.375000\pi$$
$$740$$ 1.65493 + 1.10579i 1.65493 + 1.10579i
$$741$$ −2.06759 0.856422i −2.06759 0.856422i
$$742$$ 0 0
$$743$$ −1.24723 1.24723i −1.24723 1.24723i −0.956940 0.290285i $$-0.906250\pi$$
−0.290285 0.956940i $$-0.593750\pi$$
$$744$$ 0 0
$$745$$ −1.38704 + 1.38704i −1.38704 + 1.38704i
$$746$$ −1.21415 0.368309i −1.21415 0.368309i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −0.980785 0.804910i −0.980785 0.804910i
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 1.79434i 1.79434i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0.290285 + 0.956940i 0.290285 + 0.956940i
$$761$$ −0.785695 0.785695i −0.785695 0.785695i 0.195090 0.980785i $$-0.437500\pi$$
−0.980785 + 0.195090i $$0.937500\pi$$
$$762$$ −2.14157 + 1.14470i −2.14157 + 1.14470i
$$763$$ 0 0
$$764$$ 0.750661 0.149316i 0.750661 0.149316i
$$765$$ 0 0
$$766$$ −0.0192147 0.195090i −0.0192147 0.195090i
$$767$$ 0 0
$$768$$ 1.17221 + 0.485544i 1.17221 + 0.485544i
$$769$$ 1.96157 1.96157 0.980785 0.195090i $$-0.0625000\pi$$
0.980785 + 0.195090i $$0.0625000\pi$$
$$770$$ 0 0
$$771$$ −0.281892 0.680547i −0.281892 0.680547i
$$772$$ −0.569414 + 0.113263i −0.569414 + 0.113263i
$$773$$ −0.871028 0.360791i −0.871028 0.360791i −0.0980171 0.995185i $$-0.531250\pi$$
−0.773010 + 0.634393i $$0.781250\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0.273678 + 0.902197i 0.273678 + 0.902197i
$$777$$ 0 0
$$778$$ −0.536376 + 1.76820i −0.536376 + 1.76820i
$$779$$ 0 0
$$780$$ −1.24333 1.86078i −1.24333 1.86078i
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.382683 + 0.923880i 0.382683 + 0.923880i
$$785$$ 0 0
$$786$$ 1.81225 + 1.48728i 1.81225 + 1.48728i
$$787$$ −0.181112 + 0.0750191i −0.181112 + 0.0750191i −0.471397 0.881921i $$-0.656250\pi$$
0.290285 + 0.956940i $$0.406250\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0