# Properties

 Label 676.2.l.c.19.1 Level $676$ Weight $2$ Character 676.19 Analytic conductor $5.398$ Analytic rank $0$ Dimension $4$ CM discriminant -4 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(19,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("676.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$676 = 2^{2} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 676.l (of order $$12$$, degree $$4$$, not minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$5.39788717664$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 52) Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

## Embedding invariants

 Embedding label 19.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 676.19 Dual form 676.2.l.c.427.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(2.36603 - 2.36603i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(2.36603 - 2.36603i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(4.09808 + 2.36603i) q^{10} +(2.00000 - 3.46410i) q^{16} +(5.13397 - 2.96410i) q^{17} +(3.00000 - 3.00000i) q^{18} +(-1.73205 + 6.46410i) q^{20} -6.19615i q^{25} +(5.33013 - 9.23205i) q^{29} +(5.46410 + 1.46410i) q^{32} +(5.92820 + 5.92820i) q^{34} +(5.19615 + 3.00000i) q^{36} +(-4.86603 + 1.30385i) q^{37} -9.46410 q^{40} +(3.03590 + 11.3301i) q^{41} +(-9.69615 - 2.59808i) q^{45} +(-6.06218 - 3.50000i) q^{49} +(8.46410 - 2.26795i) q^{50} +3.53590 q^{53} +(14.5622 + 3.90192i) q^{58} +(7.69615 + 13.3301i) q^{61} +8.00000i q^{64} +(-5.92820 + 10.2679i) q^{68} +(-2.19615 + 8.19615i) q^{72} +(1.16987 + 1.16987i) q^{73} +(-3.56218 - 6.16987i) q^{74} +(-3.46410 - 12.9282i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-14.3660 + 8.29423i) q^{82} +(5.13397 - 19.1603i) q^{85} +(-4.09808 + 1.09808i) q^{89} -14.1962i q^{90} +(-6.83013 - 1.83013i) q^{97} +(2.56218 - 9.56218i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8 - 6 * q^9 $$4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9} + 6 q^{10} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 4 q^{29} + 8 q^{32} - 4 q^{34} - 16 q^{37} - 24 q^{40} + 26 q^{41} - 18 q^{45} + 20 q^{50} + 28 q^{53} + 34 q^{58} + 10 q^{61} + 4 q^{68} + 12 q^{72} + 22 q^{73} + 10 q^{74} - 18 q^{81} - 54 q^{82} + 24 q^{85} - 6 q^{89} - 10 q^{97} - 14 q^{98}+O(q^{100})$$ 4 * q - 2 * q^2 + 6 * q^5 - 8 * q^8 - 6 * q^9 + 6 * q^10 + 8 * q^16 + 24 * q^17 + 12 * q^18 + 4 * q^29 + 8 * q^32 - 4 * q^34 - 16 * q^37 - 24 * q^40 + 26 * q^41 - 18 * q^45 + 20 * q^50 + 28 * q^53 + 34 * q^58 + 10 * q^61 + 4 * q^68 + 12 * q^72 + 22 * q^73 + 10 * q^74 - 18 * q^81 - 54 * q^82 + 24 * q^85 - 6 * q^89 - 10 * q^97 - 14 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$$.

 $$n$$ $$339$$ $$509$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 2.36603 2.36603i 1.05812 1.05812i 0.0599153 0.998203i $$-0.480917\pi$$
0.998203 0.0599153i $$-0.0190830\pi$$
$$6$$ 0 0
$$7$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ −1.50000 2.59808i −0.500000 0.866025i
$$10$$ 4.09808 + 2.36603i 1.29593 + 0.748203i
$$11$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 5.13397 2.96410i 1.24517 0.718900i 0.275029 0.961436i $$-0.411312\pi$$
0.970143 + 0.242536i $$0.0779791\pi$$
$$18$$ 3.00000 3.00000i 0.707107 0.707107i
$$19$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$20$$ −1.73205 + 6.46410i −0.387298 + 1.44542i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ 6.19615i 1.23923i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 5.33013 9.23205i 0.989780 1.71435i 0.371391 0.928477i $$-0.378881\pi$$
0.618389 0.785872i $$-0.287786\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ 0 0
$$34$$ 5.92820 + 5.92820i 1.01668 + 1.01668i
$$35$$ 0 0
$$36$$ 5.19615 + 3.00000i 0.866025 + 0.500000i
$$37$$ −4.86603 + 1.30385i −0.799970 + 0.214351i −0.635571 0.772043i $$-0.719235\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −9.46410 −1.49641
$$41$$ 3.03590 + 11.3301i 0.474128 + 1.76947i 0.624695 + 0.780869i $$0.285223\pi$$
−0.150567 + 0.988600i $$0.548110\pi$$
$$42$$ 0 0
$$43$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$44$$ 0 0
$$45$$ −9.69615 2.59808i −1.44542 0.387298i
$$46$$ 0 0
$$47$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$48$$ 0 0
$$49$$ −6.06218 3.50000i −0.866025 0.500000i
$$50$$ 8.46410 2.26795i 1.19700 0.320736i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 3.53590 0.485693 0.242846 0.970065i $$-0.421919\pi$$
0.242846 + 0.970065i $$0.421919\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 14.5622 + 3.90192i 1.91211 + 0.512348i
$$59$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$60$$ 0 0
$$61$$ 7.69615 + 13.3301i 0.985391 + 1.70675i 0.640184 + 0.768221i $$0.278858\pi$$
0.345207 + 0.938527i $$0.387809\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$68$$ −5.92820 + 10.2679i −0.718900 + 1.24517i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$72$$ −2.19615 + 8.19615i −0.258819 + 0.965926i
$$73$$ 1.16987 + 1.16987i 0.136923 + 0.136923i 0.772246 0.635323i $$-0.219133\pi$$
−0.635323 + 0.772246i $$0.719133\pi$$
$$74$$ −3.56218 6.16987i −0.414095 0.717233i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ −3.46410 12.9282i −0.387298 1.44542i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −14.3660 + 8.29423i −1.58646 + 0.915944i
$$83$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$84$$ 0 0
$$85$$ 5.13397 19.1603i 0.556858 2.07822i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −4.09808 + 1.09808i −0.434395 + 0.116396i −0.469389 0.882992i $$-0.655526\pi$$
0.0349934 + 0.999388i $$0.488859\pi$$
$$90$$ 14.1962i 1.49641i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −6.83013 1.83013i −0.693494 0.185821i −0.105180 0.994453i $$-0.533542\pi$$
−0.588315 + 0.808632i $$0.700208\pi$$
$$98$$ 2.56218 9.56218i 0.258819 0.965926i
$$99$$ 0 0
$$100$$ 6.19615 + 10.7321i 0.619615 + 1.07321i
$$101$$ −7.16025 4.13397i −0.712472 0.411346i 0.0995037 0.995037i $$-0.468274\pi$$
−0.811976 + 0.583691i $$0.801608\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1.29423 + 4.83013i 0.125707 + 0.469143i
$$107$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 0 0
$$109$$ −7.00000 + 7.00000i −0.670478 + 0.670478i −0.957826 0.287348i $$-0.907226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −10.0622 17.4282i −0.946570 1.63951i −0.752577 0.658505i $$-0.771189\pi$$
−0.193993 0.981003i $$-0.562144\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 21.3205i 1.97956i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 9.52628 5.50000i 0.866025 0.500000i
$$122$$ −15.3923 + 15.3923i −1.39355 + 1.39355i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −2.83013 2.83013i −0.253134 0.253134i
$$126$$ 0 0
$$127$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −16.1962 4.33975i −1.38881 0.372130i
$$137$$ −3.47372 + 12.9641i −0.296780 + 1.10760i 0.643013 + 0.765855i $$0.277684\pi$$
−0.939793 + 0.341743i $$0.888983\pi$$
$$138$$ 0 0
$$139$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −12.0000 −1.00000
$$145$$ −9.23205 34.4545i −0.766680 2.86129i
$$146$$ −1.16987 + 2.02628i −0.0968194 + 0.167696i
$$147$$ 0 0
$$148$$ 7.12436 7.12436i 0.585618 0.585618i
$$149$$ 8.06218 + 2.16025i 0.660479 + 0.176975i 0.573462 0.819232i $$-0.305600\pi$$
0.0870170 + 0.996207i $$0.472267\pi$$
$$150$$ 0 0
$$151$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$152$$ 0 0
$$153$$ −15.4019 8.89230i −1.24517 0.718900i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 13.0526 1.04171 0.520854 0.853646i $$-0.325614\pi$$
0.520854 + 0.853646i $$0.325614\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 16.3923 9.46410i 1.29593 0.748203i
$$161$$ 0 0
$$162$$ −12.2942 3.29423i −0.965926 0.258819i
$$163$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$164$$ −16.5885 16.5885i −1.29534 1.29534i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 28.0526 2.15153
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3.46410 + 2.00000i −0.263371 + 0.152057i −0.625871 0.779926i $$-0.715256\pi$$
0.362500 + 0.931984i $$0.381923\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −3.00000 5.19615i −0.224860 0.389468i
$$179$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$180$$ 19.3923 5.19615i 1.44542 0.387298i
$$181$$ 8.32051i 0.618458i 0.950988 + 0.309229i $$0.100071\pi$$
−0.950988 + 0.309229i $$0.899929\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −8.42820 + 14.5981i −0.619654 + 1.07327i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ 0 0
$$193$$ 25.8923 6.93782i 1.86377 0.499395i 0.863779 0.503871i $$-0.168091\pi$$
0.999990 + 0.00447566i $$0.00142465\pi$$
$$194$$ 10.0000i 0.717958i
$$195$$ 0 0
$$196$$ 14.0000 1.00000
$$197$$ 5.49038 + 20.4904i 0.391173 + 1.45988i 0.828201 + 0.560431i $$0.189365\pi$$
−0.437028 + 0.899448i $$0.643969\pi$$
$$198$$ 0 0
$$199$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$200$$ −12.3923 + 12.3923i −0.876268 + 0.876268i
$$201$$ 0 0
$$202$$ 3.02628 11.2942i 0.212928 0.794659i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 33.9904 + 19.6244i 2.37399 + 1.37062i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ −6.12436 + 3.53590i −0.420622 + 0.242846i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −12.1244 7.00000i −0.821165 0.474100i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$224$$ 0 0
$$225$$ −16.0981 + 9.29423i −1.07321 + 0.619615i
$$226$$ 20.1244 20.1244i 1.33865 1.33865i
$$227$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$228$$ 0 0
$$229$$ −17.0000 17.0000i −1.12339 1.12339i −0.991228 0.132164i $$-0.957808\pi$$
−0.132164 0.991228i $$-0.542192\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −29.1244 + 7.80385i −1.91211 + 0.512348i
$$233$$ 16.0000i 1.04819i 0.851658 + 0.524097i $$0.175597\pi$$
−0.851658 + 0.524097i $$0.824403\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$240$$ 0 0
$$241$$ 0.00961894 0.0358984i 0.000619611 0.00231242i −0.965615 0.259975i $$-0.916286\pi$$
0.966235 + 0.257663i $$0.0829523\pi$$
$$242$$ 11.0000 + 11.0000i 0.707107 + 0.707107i
$$243$$ 0 0
$$244$$ −26.6603 15.3923i −1.70675 0.985391i
$$245$$ −22.6244 + 6.06218i −1.44542 + 0.387298i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 2.83013 4.90192i 0.178993 0.310025i
$$251$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 15.3564 + 8.86603i 0.957906 + 0.553047i 0.895528 0.445005i $$-0.146798\pi$$
0.0623783 + 0.998053i $$0.480131\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −31.9808 −1.97956
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 8.36603 8.36603i 0.513921 0.513921i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.0000 + 17.3205i 0.609711 + 1.05605i 0.991288 + 0.131713i $$0.0420477\pi$$
−0.381577 + 0.924337i $$0.624619\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$272$$ 23.7128i 1.43780i
$$273$$ 0 0
$$274$$ −18.9808 −1.14667
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −25.6244 + 14.7942i −1.53962 + 0.888899i −0.540758 + 0.841178i $$0.681862\pi$$
−0.998861 + 0.0477206i $$0.984804\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 23.6865 + 23.6865i 1.41302 + 1.41302i 0.735554 + 0.677466i $$0.236922\pi$$
0.677466 + 0.735554i $$0.263078\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −4.39230 16.3923i −0.258819 0.965926i
$$289$$ 9.07180 15.7128i 0.533635 0.924283i
$$290$$ 43.6865 25.2224i 2.56536 1.48111i
$$291$$ 0 0
$$292$$ −3.19615 0.856406i −0.187041 0.0501174i
$$293$$ −8.23205 + 30.7224i −0.480922 + 1.79482i 0.116841 + 0.993151i $$0.462723\pi$$
−0.597763 + 0.801673i $$0.703944\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 12.3397 + 7.12436i 0.717233 + 0.414095i
$$297$$ 0 0
$$298$$ 11.8038i 0.683779i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 49.7487 + 13.3301i 2.84860 + 0.763281i
$$306$$ 6.50962 24.2942i 0.372130 1.38881i
$$307$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ −24.0000 −1.35656 −0.678280 0.734803i $$-0.737274\pi$$
−0.678280 + 0.734803i $$0.737274\pi$$
$$314$$ 4.77757 + 17.8301i 0.269614 + 1.00621i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −20.1506 + 20.1506i −1.13177 + 1.13177i −0.141890 + 0.989882i $$0.545318\pi$$
−0.989882 + 0.141890i $$0.954682\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 18.9282 + 18.9282i 1.05812 + 1.05812i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 18.0000i 1.00000i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 16.5885 28.7321i 0.915944 1.58646i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$332$$ 0 0
$$333$$ 10.6865 + 10.6865i 0.585618 + 0.585618i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 36.7128i 1.99987i −0.0112091 0.999937i $$-0.503568\pi$$
0.0112091 0.999937i $$-0.496432\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 10.2679 + 38.3205i 0.556858 + 2.07822i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −4.00000 4.00000i −0.215041 0.215041i
$$347$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$348$$ 0 0
$$349$$ 31.4186 8.41858i 1.68180 0.450636i 0.713545 0.700609i $$-0.247088\pi$$
0.968253 + 0.249973i $$0.0804216\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −1.72243 6.42820i −0.0916758 0.342139i 0.904819 0.425797i $$-0.140006\pi$$
−0.996495 + 0.0836583i $$0.973340\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 6.00000 6.00000i 0.317999 0.317999i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$360$$ 14.1962 + 24.5885i 0.748203 + 1.29593i
$$361$$ 16.4545 + 9.50000i 0.866025 + 0.500000i
$$362$$ −11.3660 + 3.04552i −0.597385 + 0.160069i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 5.53590 0.289762
$$366$$ 0 0
$$367$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$368$$ 0 0
$$369$$ 24.8827 24.8827i 1.29534 1.29534i
$$370$$ −23.0263 6.16987i −1.19708 0.320756i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2.93782 + 5.08846i 0.152115 + 0.263470i 0.932005 0.362446i $$-0.118058\pi$$
−0.779890 + 0.625917i $$0.784725\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 18.9545 + 32.8301i 0.964758 + 1.67101i
$$387$$ 0 0
$$388$$ 13.6603 3.66025i 0.693494 0.185821i
$$389$$ 34.3205i 1.74012i 0.492947 + 0.870059i $$0.335920\pi$$
−0.492947 + 0.870059i $$0.664080\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 5.12436 + 19.1244i 0.258819 + 0.965926i
$$393$$ 0 0
$$394$$ −25.9808 + 15.0000i −1.30889 + 0.755689i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −9.15064 + 34.1506i −0.459257 + 1.71397i 0.216004 + 0.976392i $$0.430698\pi$$
−0.675261 + 0.737579i $$0.735969\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −21.4641 12.3923i −1.07321 0.619615i
$$401$$ 8.13397 2.17949i 0.406191 0.108839i −0.0499376 0.998752i $$-0.515902\pi$$
0.456129 + 0.889914i $$0.349236\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 16.5359 0.822692
$$405$$ 7.79423 + 29.0885i 0.387298 + 1.44542i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 38.8205 + 10.4019i 1.91955 + 0.514342i 0.988936 + 0.148340i $$0.0473931\pi$$
0.930614 + 0.366002i $$0.119274\pi$$
$$410$$ −14.3660 + 53.6147i −0.709487 + 2.64784i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$420$$ 0 0
$$421$$ 15.3660 15.3660i 0.748894 0.748894i −0.225377 0.974272i $$-0.572361\pi$$
0.974272 + 0.225377i $$0.0723615\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ −7.07180 7.07180i −0.343437 0.343437i
$$425$$ −18.3660 31.8109i −0.890883 1.54305i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$432$$ 0 0
$$433$$ 35.8923 20.7224i 1.72487 0.995857i 0.816968 0.576683i $$-0.195653\pi$$
0.907906 0.419173i $$-0.137680\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 5.12436 19.1244i 0.245412 0.915891i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ 0 0
$$441$$ 21.0000i 1.00000i
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ −7.09808 + 12.2942i −0.336481 + 0.582802i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 9.88269 36.8827i 0.466393 1.74060i −0.185837 0.982581i $$-0.559500\pi$$
0.652230 0.758021i $$-0.273834\pi$$
$$450$$ −18.5885 18.5885i −0.876268 0.876268i
$$451$$ 0 0
$$452$$ 34.8564 + 20.1244i 1.63951 + 0.946570i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −9.96410 37.1865i −0.466101 1.73951i −0.653213 0.757174i $$-0.726579\pi$$
0.187112 0.982339i $$-0.440087\pi$$
$$458$$ 17.0000 29.4449i 0.794358 1.37587i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −40.4545 10.8397i −1.88415 0.504857i −0.999235 0.0391109i $$-0.987547\pi$$
−0.884918 0.465746i $$-0.845786\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$464$$ −21.3205 36.9282i −0.989780 1.71435i
$$465$$ 0 0
$$466$$ −21.8564 + 5.85641i −1.01248 + 0.271293i
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −5.30385 9.18653i −0.242846 0.420622i
$$478$$ 0 0
$$479$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.0525589 0.00239399
$$483$$ 0 0
$$484$$ −11.0000 + 19.0526i −0.500000 + 0.866025i
$$485$$ −20.4904 + 11.8301i −0.930420 + 0.537178i
$$486$$ 0 0
$$487$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$488$$ 11.2679 42.0526i 0.510076 1.90363i
$$489$$ 0 0
$$490$$ −16.5622 28.6865i −0.748203 1.29593i
$$491$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$492$$ 0 0
$$493$$ 63.1962i 2.84621i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$500$$ 7.73205 + 2.07180i 0.345788 + 0.0926536i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$504$$ 0 0
$$505$$ −26.7224 + 7.16025i −1.18913 + 0.318627i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −0.447441 1.66987i −0.0198325 0.0740158i 0.955300 0.295637i $$-0.0955319\pi$$
−0.975133 + 0.221621i $$0.928865\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 0 0
$$514$$ −6.49038 + 24.2224i −0.286278 + 1.06841i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 39.0526 1.71092 0.855462 0.517866i $$-0.173273\pi$$
0.855462 + 0.517866i $$0.173273\pi$$
$$522$$ −11.7058 43.6865i −0.512348 1.91211i
$$523$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ 14.4904 + 8.36603i 0.629422 + 0.363397i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −20.0000 + 20.0000i −0.862261 + 0.862261i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −21.3468 21.3468i −0.917770 0.917770i 0.0790969 0.996867i $$-0.474796\pi$$
−0.996867 + 0.0790969i $$0.974796\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 32.3923 8.67949i 1.38881 0.372130i
$$545$$ 33.1244i 1.41889i
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ −6.94744 25.9282i −0.296780 1.10760i
$$549$$ 23.0885 39.9904i 0.985391 1.70675i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −29.5885 29.5885i −1.25709 1.25709i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −35.6244 + 9.54552i −1.50945 + 0.404457i −0.916253 0.400599i $$-0.868802\pi$$
−0.593199 + 0.805056i $$0.702135\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −23.6865 + 41.0263i −0.999156 + 1.73059i
$$563$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$564$$ 0 0
$$565$$ −65.0429 17.4282i −2.73638 0.733210i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −34.6410 20.0000i −1.45223 0.838444i −0.453619 0.891196i $$-0.649867\pi$$
−0.998608 + 0.0527519i $$0.983201\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 20.7846 12.0000i 0.866025 0.500000i
$$577$$ −33.1506 + 33.1506i −1.38008 + 1.38008i −0.535620 + 0.844459i $$0.679922\pi$$
−0.844459 + 0.535620i $$0.820078\pi$$
$$578$$ 24.7846 + 6.64102i 1.03090 + 0.276230i
$$579$$ 0 0
$$580$$ 50.4449 + 50.4449i 2.09461 + 2.09461i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 4.67949i 0.193639i
$$585$$ 0 0
$$586$$ −44.9808 −1.85814
$$587$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −5.21539 + 19.4641i −0.214351 + 0.799970i
$$593$$ −34.3468 34.3468i −1.41045 1.41045i −0.756756 0.653698i $$-0.773217\pi$$
−0.653698 0.756756i $$-0.726783\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −16.1244 + 4.32051i −0.660479 + 0.176975i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −7.66987 + 13.2846i −0.312861 + 0.541891i −0.978980 0.203954i $$-0.934621\pi$$
0.666120 + 0.745845i $$0.267954\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 9.52628 35.5526i 0.387298 1.44542i
$$606$$ 0 0
$$607$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 72.8372i 2.94909i
$$611$$ 0 0
$$612$$ 35.5692 1.43780
$$613$$ 11.2776 + 42.0885i 0.455497 + 1.69994i 0.686624 + 0.727013i $$0.259092\pi$$
−0.231127 + 0.972924i $$0.574241\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −27.4545 7.35641i −1.10528 0.296158i −0.340365 0.940294i $$-0.610551\pi$$
−0.764911 + 0.644136i $$0.777217\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 17.5885 0.703538
$$626$$ −8.78461 32.7846i −0.351104 1.31034i
$$627$$ 0 0
$$628$$ −22.6077 + 13.0526i −0.902145 + 0.520854i
$$629$$ −21.1173 + 21.1173i −0.842002 + 0.842002i
$$630$$ 0 0
$$631$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −34.9019 20.1506i −1.38613 0.800284i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −18.9282 + 32.7846i −0.748203 + 1.29593i
$$641$$ 27.6506 15.9641i 1.09213 0.630544i 0.157991 0.987441i $$-0.449498\pi$$
0.934144 + 0.356897i $$0.116165\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 24.5885 6.58846i 0.965926 0.258819i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −22.0000 + 38.1051i −0.860927 + 1.49117i 0.0101092 + 0.999949i $$0.496782\pi$$
−0.871036 + 0.491220i $$0.836551\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 45.3205 + 12.1436i 1.76947 + 0.474128i
$$657$$ 1.28461 4.79423i 0.0501174 0.187041i
$$658$$ 0 0
$$659$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ 43.6506 11.6962i 1.69781 0.454928i 0.725426 0.688301i $$-0.241643\pi$$
0.972387 + 0.233373i $$0.0749763\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −10.6865 + 18.5096i −0.414095 + 0.717233i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −37.9186 21.8923i −1.46165 0.843886i −0.462566 0.886585i $$-0.653071\pi$$
−0.999088 + 0.0426985i $$0.986405\pi$$
$$674$$ 50.1506 13.4378i 1.93173 0.517606i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 2.00000 0.0768662 0.0384331 0.999261i $$-0.487763\pi$$
0.0384331 + 0.999261i $$0.487763\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −48.5885 + 28.0526i −1.86328 + 1.07577i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$684$$ 0 0
$$685$$ 22.4545 + 38.8923i 0.857942 + 1.48600i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$692$$ 4.00000 6.92820i 0.152057 0.263371i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 49.1699 + 49.1699i 1.86244 + 1.86244i
$$698$$ 23.0000 + 39.8372i 0.870563 + 1.50786i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 10.0000i 0.377695i −0.982006 0.188847i $$-0.939525\pi$$
0.982006 0.188847i $$-0.0604752\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 8.15064 4.70577i 0.306753 0.177104i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 13.0096 48.5526i 0.488586 1.82343i −0.0747503 0.997202i $$-0.523816\pi$$
0.563337 0.826227i $$-0.309517\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 10.3923 + 6.00000i 0.389468 + 0.224860i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$720$$ −28.3923 + 28.3923i −1.05812 + 1.05812i
$$721$$ 0 0
$$722$$ −6.95448 + 25.9545i −0.258819 + 0.965926i
$$723$$ 0 0
$$724$$ −8.32051 14.4115i −0.309229 0.535601i
$$725$$ −57.2032 33.0263i −2.12447 1.22657i
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 2.02628 + 7.56218i 0.0749960 + 0.279889i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −7.15064 + 7.15064i −0.264115 + 0.264115i −0.826723 0.562609i $$-0.809798\pi$$
0.562609 + 0.826723i $$0.309798\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 43.0981 + 24.8827i 1.58646 + 0.915944i
$$739$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$740$$ 33.7128i 1.23931i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$744$$ 0 0
$$745$$ 24.1865 13.9641i 0.886126 0.511605i
$$746$$ −5.87564 + 5.87564i −0.215123 + 0.215123i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −9.00000 + 15.5885i −0.327111 + 0.566572i −0.981937 0.189207i $$-0.939408\pi$$
0.654827 + 0.755779i $$0.272742\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.366025 1.36603i 0.0132684 0.0495184i −0.958974 0.283493i $$-0.908507\pi$$
0.972243 + 0.233975i $$0.0751733\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −57.4808 + 15.4019i −2.07822 + 0.556858i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −13.5429 50.5429i −0.488371 1.82263i −0.564376 0.825518i $$-0.690883\pi$$
0.0760054 0.997107i $$-0.475783\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −37.9090 + 37.9090i −1.36437 + 1.36437i
$$773$$ −6.83013 1.83013i −0.245663 0.0658251i 0.133887 0.990997i $$-0.457254\pi$$
−0.379549 + 0.925172i $$0.623921\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 10.0000 + 17.3205i 0.358979 + 0.621770i
$$777$$ 0 0
$$778$$ −46.8827 + 12.5622i −1.68083 + 0.450376i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −24.2487 + 14.0000i −0.866025 + 0.500000i
$$785$$ 30.8827 30.8827i 1.10225 1.10225i
$$786$$ 0 0
$$787$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$788$$ −30.0000 30.0000i −1.06871 1.06871i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −50.0000 −1.77443
$$795$$ 0 0
$$796$$ 0