# Properties

 Label 700.2.g.g.251.1 Level $700$ Weight $2$ Character 700.251 Analytic conductor $5.590$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$700 = 2^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 700.g (of order $$2$$, degree $$1$$, 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: $$5.58952814149$$ 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: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 140) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 251.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 700.251 Dual form 700.2.g.g.251.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$$ $$q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 + 2.36603i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +0.267949i q^{11} +(3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-2.09808 + 3.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +6.46410i q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} +(0.633975 - 0.169873i) q^{26} +5.19615 q^{27} +(5.00000 + 1.73205i) q^{28} +7.92820 q^{29} +6.00000 q^{31} +(-5.46410 - 1.46410i) q^{32} -0.464102i q^{33} +(8.83013 - 2.36603i) q^{34} +9.46410 q^{37} +(2.19615 + 8.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(3.63397 - 5.36603i) q^{42} -2.00000i q^{43} +(-0.267949 - 0.464102i) q^{44} +(-2.00000 + 0.535898i) q^{46} +1.73205 q^{47} +(-3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} -11.1962i q^{51} +(-0.464102 - 0.803848i) q^{52} -2.00000 q^{53} +(-1.90192 - 7.09808i) q^{54} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(-2.90192 - 10.8301i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(-2.19615 - 8.19615i) q^{62} +8.00000i q^{64} +(-0.633975 + 0.169873i) q^{66} +3.46410i q^{67} +(-6.46410 - 11.1962i) q^{68} +2.53590i q^{69} +7.46410i q^{71} -12.9282i q^{73} +(-3.46410 - 12.9282i) q^{74} +(10.3923 - 6.00000i) q^{76} +(0.535898 - 0.464102i) q^{77} +(-1.09808 + 0.294229i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(-4.73205 + 1.26795i) q^{82} +15.4641 q^{83} +(-8.66025 - 3.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} -13.7321 q^{87} +(-0.535898 + 0.535898i) q^{88} +2.53590i q^{89} +(0.928203 - 0.803848i) q^{91} +(1.46410 + 2.53590i) q^{92} -10.3923 q^{93} +(-0.633975 - 2.36603i) q^{94} +(9.46410 + 2.53590i) q^{96} +13.3923i q^{97} +(9.83013 - 1.16987i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} + 6 q^{6} + 8 q^{8}+O(q^{10})$$ 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8 $$4 q + 2 q^{2} + 6 q^{6} + 8 q^{8} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 24 q^{19} + 12 q^{21} - 2 q^{22} + 6 q^{26} + 20 q^{28} + 4 q^{29} + 24 q^{31} - 8 q^{32} + 18 q^{34} + 24 q^{37} - 12 q^{38} + 18 q^{42} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 12 q^{52} - 8 q^{53} - 18 q^{54} + 16 q^{56} - 22 q^{58} + 12 q^{62} - 6 q^{66} - 12 q^{68} + 16 q^{77} + 6 q^{78} - 36 q^{81} - 12 q^{82} + 48 q^{83} - 4 q^{86} - 48 q^{87} - 16 q^{88} - 24 q^{91} - 8 q^{92} - 6 q^{94} + 24 q^{96} + 22 q^{98}+O(q^{100})$$ 4 * q + 2 * q^2 + 6 * q^6 + 8 * q^8 + 12 * q^12 + 2 * q^14 + 8 * q^16 - 24 * q^19 + 12 * q^21 - 2 * q^22 + 6 * q^26 + 20 * q^28 + 4 * q^29 + 24 * q^31 - 8 * q^32 + 18 * q^34 + 24 * q^37 - 12 * q^38 + 18 * q^42 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 12 * q^52 - 8 * q^53 - 18 * q^54 + 16 * q^56 - 22 * q^58 + 12 * q^62 - 6 * q^66 - 12 * q^68 + 16 * q^77 + 6 * q^78 - 36 * q^81 - 12 * q^82 + 48 * q^83 - 4 * q^86 - 48 * q^87 - 16 * q^88 - 24 * q^91 - 8 * q^92 - 6 * q^94 + 24 * q^96 + 22 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$351$$ $$477$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.366025 1.36603i −0.258819 0.965926i
$$3$$ −1.73205 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 0 0
$$6$$ 0.633975 + 2.36603i 0.258819 + 0.965926i
$$7$$ −1.73205 2.00000i −0.654654 0.755929i
$$8$$ 2.00000 + 2.00000i 0.707107 + 0.707107i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0.267949i 0.0807897i 0.999184 + 0.0403949i $$0.0128616\pi$$
−0.999184 + 0.0403949i $$0.987138\pi$$
$$12$$ 3.00000 1.73205i 0.866025 0.500000i
$$13$$ 0.464102i 0.128719i 0.997927 + 0.0643593i $$0.0205004\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ −2.09808 + 3.09808i −0.560734 + 0.827996i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 6.46410i 1.56777i 0.620903 + 0.783887i $$0.286766\pi$$
−0.620903 + 0.783887i $$0.713234\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ 3.00000 + 3.46410i 0.654654 + 0.755929i
$$22$$ 0.366025 0.0980762i 0.0780369 0.0209099i
$$23$$ 1.46410i 0.305286i −0.988281 0.152643i $$-0.951221\pi$$
0.988281 0.152643i $$-0.0487785\pi$$
$$24$$ −3.46410 3.46410i −0.707107 0.707107i
$$25$$ 0 0
$$26$$ 0.633975 0.169873i 0.124333 0.0333148i
$$27$$ 5.19615 1.00000
$$28$$ 5.00000 + 1.73205i 0.944911 + 0.327327i
$$29$$ 7.92820 1.47223 0.736115 0.676856i $$-0.236658\pi$$
0.736115 + 0.676856i $$0.236658\pi$$
$$30$$ 0 0
$$31$$ 6.00000 1.07763 0.538816 0.842424i $$-0.318872\pi$$
0.538816 + 0.842424i $$0.318872\pi$$
$$32$$ −5.46410 1.46410i −0.965926 0.258819i
$$33$$ 0.464102i 0.0807897i
$$34$$ 8.83013 2.36603i 1.51435 0.405770i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 9.46410 1.55589 0.777944 0.628333i $$-0.216263\pi$$
0.777944 + 0.628333i $$0.216263\pi$$
$$38$$ 2.19615 + 8.19615i 0.356263 + 1.32959i
$$39$$ 0.803848i 0.128719i
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 3.63397 5.36603i 0.560734 0.827996i
$$43$$ 2.00000i 0.304997i −0.988304 0.152499i $$-0.951268\pi$$
0.988304 0.152499i $$-0.0487319\pi$$
$$44$$ −0.267949 0.464102i −0.0403949 0.0699660i
$$45$$ 0 0
$$46$$ −2.00000 + 0.535898i −0.294884 + 0.0790139i
$$47$$ 1.73205 0.252646 0.126323 0.991989i $$-0.459682\pi$$
0.126323 + 0.991989i $$0.459682\pi$$
$$48$$ −3.46410 + 6.00000i −0.500000 + 0.866025i
$$49$$ −1.00000 + 6.92820i −0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 11.1962i 1.56777i
$$52$$ −0.464102 0.803848i −0.0643593 0.111474i
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ −1.90192 7.09808i −0.258819 0.965926i
$$55$$ 0 0
$$56$$ 0.535898 7.46410i 0.0716124 0.997433i
$$57$$ 10.3923 1.37649
$$58$$ −2.90192 10.8301i −0.381041 1.42207i
$$59$$ 3.46410 0.450988 0.225494 0.974245i $$-0.427600\pi$$
0.225494 + 0.974245i $$0.427600\pi$$
$$60$$ 0 0
$$61$$ 9.46410i 1.21175i 0.795558 + 0.605877i $$0.207178\pi$$
−0.795558 + 0.605877i $$0.792822\pi$$
$$62$$ −2.19615 8.19615i −0.278912 1.04091i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ −0.633975 + 0.169873i −0.0780369 + 0.0209099i
$$67$$ 3.46410i 0.423207i 0.977356 + 0.211604i $$0.0678686\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ −6.46410 11.1962i −0.783887 1.35773i
$$69$$ 2.53590i 0.305286i
$$70$$ 0 0
$$71$$ 7.46410i 0.885826i 0.896565 + 0.442913i $$0.146055\pi$$
−0.896565 + 0.442913i $$0.853945\pi$$
$$72$$ 0 0
$$73$$ 12.9282i 1.51313i −0.653917 0.756566i $$-0.726876\pi$$
0.653917 0.756566i $$-0.273124\pi$$
$$74$$ −3.46410 12.9282i −0.402694 1.50287i
$$75$$ 0 0
$$76$$ 10.3923 6.00000i 1.19208 0.688247i
$$77$$ 0.535898 0.464102i 0.0610713 0.0528893i
$$78$$ −1.09808 + 0.294229i −0.124333 + 0.0333148i
$$79$$ 14.6603i 1.64941i 0.565565 + 0.824704i $$0.308658\pi$$
−0.565565 + 0.824704i $$0.691342\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ −4.73205 + 1.26795i −0.522568 + 0.140022i
$$83$$ 15.4641 1.69741 0.848703 0.528870i $$-0.177384\pi$$
0.848703 + 0.528870i $$0.177384\pi$$
$$84$$ −8.66025 3.00000i −0.944911 0.327327i
$$85$$ 0 0
$$86$$ −2.73205 + 0.732051i −0.294605 + 0.0789391i
$$87$$ −13.7321 −1.47223
$$88$$ −0.535898 + 0.535898i −0.0571270 + 0.0571270i
$$89$$ 2.53590i 0.268805i 0.990927 + 0.134402i $$0.0429115\pi$$
−0.990927 + 0.134402i $$0.957089\pi$$
$$90$$ 0 0
$$91$$ 0.928203 0.803848i 0.0973021 0.0842661i
$$92$$ 1.46410 + 2.53590i 0.152643 + 0.264386i
$$93$$ −10.3923 −1.07763
$$94$$ −0.633975 2.36603i −0.0653895 0.244037i
$$95$$ 0 0
$$96$$ 9.46410 + 2.53590i 0.965926 + 0.258819i
$$97$$ 13.3923i 1.35978i 0.733313 + 0.679891i $$0.237973\pi$$
−0.733313 + 0.679891i $$0.762027\pi$$
$$98$$ 9.83013 1.16987i 0.992993 0.118175i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 15.4641i 1.53874i −0.638806 0.769368i $$-0.720571\pi$$
0.638806 0.769368i $$-0.279429\pi$$
$$102$$ −15.2942 + 4.09808i −1.51435 + 0.405770i
$$103$$ −6.80385 −0.670403 −0.335202 0.942146i $$-0.608804\pi$$
−0.335202 + 0.942146i $$0.608804\pi$$
$$104$$ −0.928203 + 0.928203i −0.0910178 + 0.0910178i
$$105$$ 0 0
$$106$$ 0.732051 + 2.73205i 0.0711031 + 0.265360i
$$107$$ 2.39230i 0.231273i 0.993292 + 0.115636i $$0.0368907\pi$$
−0.993292 + 0.115636i $$0.963109\pi$$
$$108$$ −9.00000 + 5.19615i −0.866025 + 0.500000i
$$109$$ 2.07180 0.198442 0.0992211 0.995065i $$-0.468365\pi$$
0.0992211 + 0.995065i $$0.468365\pi$$
$$110$$ 0 0
$$111$$ −16.3923 −1.55589
$$112$$ −10.3923 + 2.00000i −0.981981 + 0.188982i
$$113$$ −5.46410 −0.514019 −0.257010 0.966409i $$-0.582737\pi$$
−0.257010 + 0.966409i $$0.582737\pi$$
$$114$$ −3.80385 14.1962i −0.356263 1.32959i
$$115$$ 0 0
$$116$$ −13.7321 + 7.92820i −1.27499 + 0.736115i
$$117$$ 0 0
$$118$$ −1.26795 4.73205i −0.116724 0.435621i
$$119$$ 12.9282 11.1962i 1.18513 1.02635i
$$120$$ 0 0
$$121$$ 10.9282 0.993473
$$122$$ 12.9282 3.46410i 1.17046 0.313625i
$$123$$ 6.00000i 0.541002i
$$124$$ −10.3923 + 6.00000i −0.933257 + 0.538816i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 15.4641i 1.37222i 0.727499 + 0.686109i $$0.240683\pi$$
−0.727499 + 0.686109i $$0.759317\pi$$
$$128$$ 10.9282 2.92820i 0.965926 0.258819i
$$129$$ 3.46410i 0.304997i
$$130$$ 0 0
$$131$$ −2.53590 −0.221562 −0.110781 0.993845i $$-0.535335\pi$$
−0.110781 + 0.993845i $$0.535335\pi$$
$$132$$ 0.464102 + 0.803848i 0.0403949 + 0.0699660i
$$133$$ 10.3923 + 12.0000i 0.901127 + 1.04053i
$$134$$ 4.73205 1.26795i 0.408787 0.109534i
$$135$$ 0 0
$$136$$ −12.9282 + 12.9282i −1.10858 + 1.10858i
$$137$$ −20.3923 −1.74223 −0.871116 0.491077i $$-0.836603\pi$$
−0.871116 + 0.491077i $$0.836603\pi$$
$$138$$ 3.46410 0.928203i 0.294884 0.0790139i
$$139$$ −6.92820 −0.587643 −0.293821 0.955860i $$-0.594927\pi$$
−0.293821 + 0.955860i $$0.594927\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 10.1962 2.73205i 0.855642 0.229269i
$$143$$ −0.124356 −0.0103991
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −17.6603 + 4.73205i −1.46157 + 0.391627i
$$147$$ 1.73205 12.0000i 0.142857 0.989743i
$$148$$ −16.3923 + 9.46410i −1.34744 + 0.777944i
$$149$$ 3.07180 0.251651 0.125826 0.992052i $$-0.459842\pi$$
0.125826 + 0.992052i $$0.459842\pi$$
$$150$$ 0 0
$$151$$ 15.1962i 1.23665i 0.785924 + 0.618323i $$0.212188\pi$$
−0.785924 + 0.618323i $$0.787812\pi$$
$$152$$ −12.0000 12.0000i −0.973329 0.973329i
$$153$$ 0 0
$$154$$ −0.830127 0.562178i −0.0668935 0.0453016i
$$155$$ 0 0
$$156$$ 0.803848 + 1.39230i 0.0643593 + 0.111474i
$$157$$ 7.85641i 0.627009i −0.949587 0.313505i $$-0.898497\pi$$
0.949587 0.313505i $$-0.101503\pi$$
$$158$$ 20.0263 5.36603i 1.59321 0.426898i
$$159$$ 3.46410 0.274721
$$160$$ 0 0
$$161$$ −2.92820 + 2.53590i −0.230775 + 0.199857i
$$162$$ 3.29423 + 12.2942i 0.258819 + 0.965926i
$$163$$ 20.7846i 1.62798i 0.580881 + 0.813988i $$0.302708\pi$$
−0.580881 + 0.813988i $$0.697292\pi$$
$$164$$ 3.46410 + 6.00000i 0.270501 + 0.468521i
$$165$$ 0 0
$$166$$ −5.66025 21.1244i −0.439321 1.63957i
$$167$$ −5.19615 −0.402090 −0.201045 0.979582i $$-0.564434\pi$$
−0.201045 + 0.979582i $$0.564434\pi$$
$$168$$ −0.928203 + 12.9282i −0.0716124 + 0.997433i
$$169$$ 12.7846 0.983432
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ 14.3205i 1.08877i 0.838836 + 0.544384i $$0.183237\pi$$
−0.838836 + 0.544384i $$0.816763\pi$$
$$174$$ 5.02628 + 18.7583i 0.381041 + 1.42207i
$$175$$ 0 0
$$176$$ 0.928203 + 0.535898i 0.0699660 + 0.0403949i
$$177$$ −6.00000 −0.450988
$$178$$ 3.46410 0.928203i 0.259645 0.0695718i
$$179$$ 6.39230i 0.477783i −0.971046 0.238892i $$-0.923216\pi$$
0.971046 0.238892i $$-0.0767841\pi$$
$$180$$ 0 0
$$181$$ 0.928203i 0.0689928i −0.999405 0.0344964i $$-0.989017\pi$$
0.999405 0.0344964i $$-0.0109827\pi$$
$$182$$ −1.43782 0.973721i −0.106578 0.0721770i
$$183$$ 16.3923i 1.21175i
$$184$$ 2.92820 2.92820i 0.215870 0.215870i
$$185$$ 0 0
$$186$$ 3.80385 + 14.1962i 0.278912 + 1.04091i
$$187$$ −1.73205 −0.126660
$$188$$ −3.00000 + 1.73205i −0.218797 + 0.126323i
$$189$$ −9.00000 10.3923i −0.654654 0.755929i
$$190$$ 0 0
$$191$$ 7.19615i 0.520695i 0.965515 + 0.260348i $$0.0838372\pi$$
−0.965515 + 0.260348i $$0.916163\pi$$
$$192$$ 13.8564i 1.00000i
$$193$$ 9.46410 0.681241 0.340620 0.940201i $$-0.389363\pi$$
0.340620 + 0.940201i $$0.389363\pi$$
$$194$$ 18.2942 4.90192i 1.31345 0.351938i
$$195$$ 0 0
$$196$$ −5.19615 13.0000i −0.371154 0.928571i
$$197$$ 13.3205 0.949047 0.474523 0.880243i $$-0.342620\pi$$
0.474523 + 0.880243i $$0.342620\pi$$
$$198$$ 0 0
$$199$$ −3.46410 −0.245564 −0.122782 0.992434i $$-0.539182\pi$$
−0.122782 + 0.992434i $$0.539182\pi$$
$$200$$ 0 0
$$201$$ 6.00000i 0.423207i
$$202$$ −21.1244 + 5.66025i −1.48630 + 0.398254i
$$203$$ −13.7321 15.8564i −0.963801 1.11290i
$$204$$ 11.1962 + 19.3923i 0.783887 + 1.35773i
$$205$$ 0 0
$$206$$ 2.49038 + 9.29423i 0.173513 + 0.647560i
$$207$$ 0 0
$$208$$ 1.60770 + 0.928203i 0.111474 + 0.0643593i
$$209$$ 1.60770i 0.111207i
$$210$$ 0 0
$$211$$ 3.19615i 0.220032i 0.993930 + 0.110016i $$0.0350902\pi$$
−0.993930 + 0.110016i $$0.964910\pi$$
$$212$$ 3.46410 2.00000i 0.237915 0.137361i
$$213$$ 12.9282i 0.885826i
$$214$$ 3.26795 0.875644i 0.223392 0.0598578i
$$215$$ 0 0
$$216$$ 10.3923 + 10.3923i 0.707107 + 0.707107i
$$217$$ −10.3923 12.0000i −0.705476 0.814613i
$$218$$ −0.758330 2.83013i −0.0513606 0.191680i
$$219$$ 22.3923i 1.51313i
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ 6.00000 + 22.3923i 0.402694 + 1.50287i
$$223$$ −13.7321 −0.919566 −0.459783 0.888031i $$-0.652073\pi$$
−0.459783 + 0.888031i $$0.652073\pi$$
$$224$$ 6.53590 + 13.4641i 0.436698 + 0.899608i
$$225$$ 0 0
$$226$$ 2.00000 + 7.46410i 0.133038 + 0.496505i
$$227$$ 20.6603 1.37127 0.685635 0.727946i $$-0.259525\pi$$
0.685635 + 0.727946i $$0.259525\pi$$
$$228$$ −18.0000 + 10.3923i −1.19208 + 0.688247i
$$229$$ 8.53590i 0.564068i −0.959404 0.282034i $$-0.908991\pi$$
0.959404 0.282034i $$-0.0910091\pi$$
$$230$$ 0 0
$$231$$ −0.928203 + 0.803848i −0.0610713 + 0.0528893i
$$232$$ 15.8564 + 15.8564i 1.04102 + 1.04102i
$$233$$ 9.07180 0.594313 0.297157 0.954829i $$-0.403962\pi$$
0.297157 + 0.954829i $$0.403962\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −6.00000 + 3.46410i −0.390567 + 0.225494i
$$237$$ 25.3923i 1.64941i
$$238$$ −20.0263 13.5622i −1.29811 0.879105i
$$239$$ 23.9808i 1.55119i −0.631233 0.775593i $$-0.717451\pi$$
0.631233 0.775593i $$-0.282549\pi$$
$$240$$ 0 0
$$241$$ 16.3923i 1.05592i 0.849269 + 0.527961i $$0.177043\pi$$
−0.849269 + 0.527961i $$0.822957\pi$$
$$242$$ −4.00000 14.9282i −0.257130 0.959621i
$$243$$ 0 0
$$244$$ −9.46410 16.3923i −0.605877 1.04941i
$$245$$ 0 0
$$246$$ 8.19615 2.19615i 0.522568 0.140022i
$$247$$ 2.78461i 0.177180i
$$248$$ 12.0000 + 12.0000i 0.762001 + 0.762001i
$$249$$ −26.7846 −1.69741
$$250$$ 0 0
$$251$$ 25.8564 1.63204 0.816021 0.578022i $$-0.196175\pi$$
0.816021 + 0.578022i $$0.196175\pi$$
$$252$$ 0 0
$$253$$ 0.392305 0.0246640
$$254$$ 21.1244 5.66025i 1.32546 0.355156i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 6.00000i 0.374270i −0.982334 0.187135i $$-0.940080\pi$$
0.982334 0.187135i $$-0.0599201\pi$$
$$258$$ 4.73205 1.26795i 0.294605 0.0789391i
$$259$$ −16.3923 18.9282i −1.01857 1.17614i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0.928203 + 3.46410i 0.0573446 + 0.214013i
$$263$$ 11.4641i 0.706907i 0.935452 + 0.353453i $$0.114993\pi$$
−0.935452 + 0.353453i $$0.885007\pi$$
$$264$$ 0.928203 0.928203i 0.0571270 0.0571270i
$$265$$ 0 0
$$266$$ 12.5885 18.5885i 0.771848 1.13973i
$$267$$ 4.39230i 0.268805i
$$268$$ −3.46410 6.00000i −0.211604 0.366508i
$$269$$ 12.0000i 0.731653i −0.930683 0.365826i $$-0.880786\pi$$
0.930683 0.365826i $$-0.119214\pi$$
$$270$$ 0 0
$$271$$ −9.46410 −0.574903 −0.287452 0.957795i $$-0.592808\pi$$
−0.287452 + 0.957795i $$0.592808\pi$$
$$272$$ 22.3923 + 12.9282i 1.35773 + 0.783887i
$$273$$ −1.60770 + 1.39230i −0.0973021 + 0.0842661i
$$274$$ 7.46410 + 27.8564i 0.450923 + 1.68287i
$$275$$ 0 0
$$276$$ −2.53590 4.39230i −0.152643 0.264386i
$$277$$ −16.7846 −1.00849 −0.504245 0.863561i $$-0.668229\pi$$
−0.504245 + 0.863561i $$0.668229\pi$$
$$278$$ 2.53590 + 9.46410i 0.152093 + 0.567619i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7.92820 −0.472957 −0.236478 0.971637i $$-0.575993\pi$$
−0.236478 + 0.971637i $$0.575993\pi$$
$$282$$ 1.09808 + 4.09808i 0.0653895 + 0.244037i
$$283$$ 12.1244 0.720718 0.360359 0.932814i $$-0.382654\pi$$
0.360359 + 0.932814i $$0.382654\pi$$
$$284$$ −7.46410 12.9282i −0.442913 0.767148i
$$285$$ 0 0
$$286$$ 0.0455173 + 0.169873i 0.00269150 + 0.0100448i
$$287$$ −6.92820 + 6.00000i −0.408959 + 0.354169i
$$288$$ 0 0
$$289$$ −24.7846 −1.45792
$$290$$ 0 0
$$291$$ 23.1962i 1.35978i
$$292$$ 12.9282 + 22.3923i 0.756566 + 1.31041i
$$293$$ 20.3205i 1.18714i −0.804784 0.593568i $$-0.797719\pi$$
0.804784 0.593568i $$-0.202281\pi$$
$$294$$ −17.0263 + 2.02628i −0.992993 + 0.118175i
$$295$$ 0 0
$$296$$ 18.9282 + 18.9282i 1.10018 + 1.10018i
$$297$$ 1.39230i 0.0807897i
$$298$$ −1.12436 4.19615i −0.0651322 0.243077i
$$299$$ 0.679492 0.0392960
$$300$$ 0 0
$$301$$ −4.00000 + 3.46410i −0.230556 + 0.199667i
$$302$$ 20.7583 5.56218i 1.19451 0.320067i
$$303$$ 26.7846i 1.53874i
$$304$$ −12.0000 + 20.7846i −0.688247 + 1.19208i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.73205 0.0988534 0.0494267 0.998778i $$-0.484261\pi$$
0.0494267 + 0.998778i $$0.484261\pi$$
$$308$$ −0.464102 + 1.33975i −0.0264446 + 0.0763391i
$$309$$ 11.7846 0.670403
$$310$$ 0 0
$$311$$ −7.85641 −0.445496 −0.222748 0.974876i $$-0.571503\pi$$
−0.222748 + 0.974876i $$0.571503\pi$$
$$312$$ 1.60770 1.60770i 0.0910178 0.0910178i
$$313$$ 17.5359i 0.991188i 0.868554 + 0.495594i $$0.165050\pi$$
−0.868554 + 0.495594i $$0.834950\pi$$
$$314$$ −10.7321 + 2.87564i −0.605645 + 0.162282i
$$315$$ 0 0
$$316$$ −14.6603 25.3923i −0.824704 1.42843i
$$317$$ 3.07180 0.172529 0.0862646 0.996272i $$-0.472507\pi$$
0.0862646 + 0.996272i $$0.472507\pi$$
$$318$$ −1.26795 4.73205i −0.0711031 0.265360i
$$319$$ 2.12436i 0.118941i
$$320$$ 0 0
$$321$$ 4.14359i 0.231273i
$$322$$ 4.53590 + 3.07180i 0.252776 + 0.171185i
$$323$$ 38.7846i 2.15803i
$$324$$ 15.5885 9.00000i 0.866025 0.500000i
$$325$$ 0 0
$$326$$ 28.3923 7.60770i 1.57250 0.421351i
$$327$$ −3.58846 −0.198442
$$328$$ 6.92820 6.92820i 0.382546 0.382546i
$$329$$ −3.00000 3.46410i −0.165395 0.190982i
$$330$$ 0 0
$$331$$ 26.3923i 1.45065i −0.688405 0.725326i $$-0.741689\pi$$
0.688405 0.725326i $$-0.258311\pi$$
$$332$$ −26.7846 + 15.4641i −1.47000 + 0.848703i
$$333$$ 0 0
$$334$$ 1.90192 + 7.09808i 0.104069 + 0.388389i
$$335$$ 0 0
$$336$$ 18.0000 3.46410i 0.981981 0.188982i
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ −4.67949 17.4641i −0.254531 0.949922i
$$339$$ 9.46410 0.514019
$$340$$ 0 0
$$341$$ 1.60770i 0.0870616i
$$342$$ 0 0
$$343$$ 15.5885 10.0000i 0.841698 0.539949i
$$344$$ 4.00000 4.00000i 0.215666 0.215666i
$$345$$ 0 0
$$346$$ 19.5622 5.24167i 1.05167 0.281794i
$$347$$ 34.2487i 1.83857i −0.393596 0.919284i $$-0.628769\pi$$
0.393596 0.919284i $$-0.371231\pi$$
$$348$$ 23.7846 13.7321i 1.27499 0.736115i
$$349$$ 5.32051i 0.284800i −0.989809 0.142400i $$-0.954518\pi$$
0.989809 0.142400i $$-0.0454820\pi$$
$$350$$ 0 0
$$351$$ 2.41154i 0.128719i
$$352$$ 0.392305 1.46410i 0.0209099 0.0780369i
$$353$$ 7.39230i 0.393453i 0.980458 + 0.196726i $$0.0630311\pi$$
−0.980458 + 0.196726i $$0.936969\pi$$
$$354$$ 2.19615 + 8.19615i 0.116724 + 0.435621i
$$355$$ 0 0
$$356$$ −2.53590 4.39230i −0.134402 0.232792i
$$357$$ −22.3923 + 19.3923i −1.18513 + 1.02635i
$$358$$ −8.73205 + 2.33975i −0.461503 + 0.123659i
$$359$$ 25.3205i 1.33637i 0.743997 + 0.668183i $$0.232928\pi$$
−0.743997 + 0.668183i $$0.767072\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ −1.26795 + 0.339746i −0.0666419 + 0.0178567i
$$363$$ −18.9282 −0.993473
$$364$$ −0.803848 + 2.32051i −0.0421331 + 0.121628i
$$365$$ 0 0
$$366$$ −22.3923 + 6.00000i −1.17046 + 0.313625i
$$367$$ 11.8756 0.619904 0.309952 0.950752i $$-0.399687\pi$$
0.309952 + 0.950752i $$0.399687\pi$$
$$368$$ −5.07180 2.92820i −0.264386 0.152643i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 3.46410 + 4.00000i 0.179847 + 0.207670i
$$372$$ 18.0000 10.3923i 0.933257 0.538816i
$$373$$ 3.60770 0.186799 0.0933997 0.995629i $$-0.470227\pi$$
0.0933997 + 0.995629i $$0.470227\pi$$
$$374$$ 0.633975 + 2.36603i 0.0327820 + 0.122344i
$$375$$ 0 0
$$376$$ 3.46410 + 3.46410i 0.178647 + 0.178647i
$$377$$ 3.67949i 0.189503i
$$378$$ −10.9019 + 16.0981i −0.560734 + 0.827996i
$$379$$ 5.60770i 0.288048i 0.989574 + 0.144024i $$0.0460042\pi$$
−0.989574 + 0.144024i $$0.953996\pi$$
$$380$$ 0 0
$$381$$ 26.7846i 1.37222i
$$382$$ 9.83013 2.63397i 0.502953 0.134766i
$$383$$ 27.4641 1.40335 0.701675 0.712497i $$-0.252436\pi$$
0.701675 + 0.712497i $$0.252436\pi$$
$$384$$ −18.9282 + 5.07180i −0.965926 + 0.258819i
$$385$$ 0 0
$$386$$ −3.46410 12.9282i −0.176318 0.658028i
$$387$$ 0 0
$$388$$ −13.3923 23.1962i −0.679891 1.17761i
$$389$$ −20.8564 −1.05746 −0.528731 0.848790i $$-0.677332\pi$$
−0.528731 + 0.848790i $$0.677332\pi$$
$$390$$ 0 0
$$391$$ 9.46410 0.478620
$$392$$ −15.8564 + 11.8564i −0.800869 + 0.598839i
$$393$$ 4.39230 0.221562
$$394$$ −4.87564 18.1962i −0.245631 0.916709i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 12.4641i 0.625555i −0.949826 0.312778i $$-0.898741\pi$$
0.949826 0.312778i $$-0.101259\pi$$
$$398$$ 1.26795 + 4.73205i 0.0635566 + 0.237196i
$$399$$ −18.0000 20.7846i −0.901127 1.04053i
$$400$$ 0 0
$$401$$ −10.0718 −0.502962 −0.251481 0.967862i $$-0.580918\pi$$
−0.251481 + 0.967862i $$0.580918\pi$$
$$402$$ −8.19615 + 2.19615i −0.408787 + 0.109534i
$$403$$ 2.78461i 0.138711i
$$404$$ 15.4641 + 26.7846i 0.769368 + 1.33258i
$$405$$ 0 0
$$406$$ −16.6340 + 24.5622i −0.825530 + 1.21900i
$$407$$ 2.53590i 0.125700i
$$408$$ 22.3923 22.3923i 1.10858 1.10858i
$$409$$ 4.14359i 0.204888i 0.994739 + 0.102444i $$0.0326662\pi$$
−0.994739 + 0.102444i $$0.967334\pi$$
$$410$$ 0 0
$$411$$ 35.3205 1.74223
$$412$$ 11.7846 6.80385i 0.580586 0.335202i
$$413$$ −6.00000 6.92820i −0.295241 0.340915i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0.679492 2.53590i 0.0333148 0.124333i
$$417$$ 12.0000 0.587643
$$418$$ −2.19615 + 0.588457i −0.107417 + 0.0287824i
$$419$$ 24.2487 1.18463 0.592314 0.805708i $$-0.298215\pi$$
0.592314 + 0.805708i $$0.298215\pi$$
$$420$$ 0 0
$$421$$ 19.0000 0.926003 0.463002 0.886357i $$-0.346772\pi$$
0.463002 + 0.886357i $$0.346772\pi$$
$$422$$ 4.36603 1.16987i 0.212535 0.0569485i
$$423$$ 0 0
$$424$$ −4.00000 4.00000i −0.194257 0.194257i
$$425$$ 0 0
$$426$$ −17.6603 + 4.73205i −0.855642 + 0.229269i
$$427$$ 18.9282 16.3923i 0.916000 0.793279i
$$428$$ −2.39230 4.14359i −0.115636 0.200288i
$$429$$ 0.215390 0.0103991
$$430$$ 0 0
$$431$$ 13.5885i 0.654533i −0.944932 0.327266i $$-0.893873\pi$$
0.944932 0.327266i $$-0.106127\pi$$
$$432$$ 10.3923 18.0000i 0.500000 0.866025i
$$433$$ 31.8564i 1.53092i 0.643483 + 0.765461i $$0.277489\pi$$
−0.643483 + 0.765461i $$0.722511\pi$$
$$434$$ −12.5885 + 18.5885i −0.604265 + 0.892275i
$$435$$ 0 0
$$436$$ −3.58846 + 2.07180i −0.171856 + 0.0992211i
$$437$$ 8.78461i 0.420225i
$$438$$ 30.5885 8.19615i 1.46157 0.391627i
$$439$$ 39.7128 1.89539 0.947695 0.319179i $$-0.103407\pi$$
0.947695 + 0.319179i $$0.103407\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1.09808 + 4.09808i 0.0522302 + 0.194926i
$$443$$ 26.0000i 1.23530i 0.786454 + 0.617649i $$0.211915\pi$$
−0.786454 + 0.617649i $$0.788085\pi$$
$$444$$ 28.3923 16.3923i 1.34744 0.777944i
$$445$$ 0 0
$$446$$ 5.02628 + 18.7583i 0.238001 + 0.888233i
$$447$$ −5.32051 −0.251651
$$448$$ 16.0000 13.8564i 0.755929 0.654654i
$$449$$ 11.9282 0.562927 0.281463 0.959572i $$-0.409180\pi$$
0.281463 + 0.959572i $$0.409180\pi$$
$$450$$ 0 0
$$451$$ 0.928203 0.0437074
$$452$$ 9.46410 5.46410i 0.445154 0.257010i
$$453$$ 26.3205i 1.23665i
$$454$$ −7.56218 28.2224i −0.354911 1.32454i
$$455$$ 0 0
$$456$$ 20.7846 + 20.7846i 0.973329 + 0.973329i
$$457$$ −20.5359 −0.960629 −0.480314 0.877096i $$-0.659477\pi$$
−0.480314 + 0.877096i $$0.659477\pi$$
$$458$$ −11.6603 + 3.12436i −0.544848 + 0.145992i
$$459$$ 33.5885i 1.56777i
$$460$$ 0 0
$$461$$ 27.7128i 1.29071i 0.763881 + 0.645357i $$0.223291\pi$$
−0.763881 + 0.645357i $$0.776709\pi$$
$$462$$ 1.43782 + 0.973721i 0.0668935 + 0.0453016i
$$463$$ 16.3923i 0.761815i 0.924613 + 0.380908i $$0.124388\pi$$
−0.924613 + 0.380908i $$0.875612\pi$$
$$464$$ 15.8564 27.4641i 0.736115 1.27499i
$$465$$ 0 0
$$466$$ −3.32051 12.3923i −0.153820 0.574062i
$$467$$ 22.5167 1.04195 0.520973 0.853573i $$-0.325569\pi$$
0.520973 + 0.853573i $$0.325569\pi$$
$$468$$ 0 0
$$469$$ 6.92820 6.00000i 0.319915 0.277054i
$$470$$ 0 0
$$471$$ 13.6077i 0.627009i
$$472$$ 6.92820 + 6.92820i 0.318896 + 0.318896i
$$473$$ 0.535898 0.0246406
$$474$$ −34.6865 + 9.29423i −1.59321 + 0.426898i
$$475$$ 0 0
$$476$$ −11.1962 + 32.3205i −0.513175 + 1.48141i
$$477$$ 0 0
$$478$$ −32.7583 + 8.77757i −1.49833 + 0.401477i
$$479$$ −25.1769 −1.15036 −0.575181 0.818026i $$-0.695068\pi$$
−0.575181 + 0.818026i $$0.695068\pi$$
$$480$$ 0 0
$$481$$ 4.39230i 0.200272i
$$482$$ 22.3923 6.00000i 1.01994 0.273293i
$$483$$ 5.07180 4.39230i 0.230775 0.199857i
$$484$$ −18.9282 + 10.9282i −0.860373 + 0.496737i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 12.7846i 0.579326i 0.957129 + 0.289663i $$0.0935432\pi$$
−0.957129 + 0.289663i $$0.906457\pi$$
$$488$$ −18.9282 + 18.9282i −0.856840 + 0.856840i
$$489$$ 36.0000i 1.62798i
$$490$$ 0 0
$$491$$ 9.87564i 0.445682i −0.974855 0.222841i $$-0.928467\pi$$
0.974855 0.222841i $$-0.0715330\pi$$
$$492$$ −6.00000 10.3923i −0.270501 0.468521i
$$493$$ 51.2487i 2.30813i
$$494$$ −3.80385 + 1.01924i −0.171143 + 0.0458577i
$$495$$ 0 0
$$496$$ 12.0000 20.7846i 0.538816 0.933257i
$$497$$ 14.9282 12.9282i 0.669621 0.579909i
$$498$$ 9.80385 + 36.5885i 0.439321 + 1.63957i
$$499$$ 25.5885i 1.14550i 0.819731 + 0.572748i $$0.194123\pi$$
−0.819731 + 0.572748i $$0.805877\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ −9.46410 35.3205i −0.422404 1.57643i
$$503$$ −15.5885 −0.695055 −0.347527 0.937670i $$-0.612979\pi$$
−0.347527 + 0.937670i $$0.612979\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −0.143594 0.535898i −0.00638351 0.0238236i
$$507$$ −22.1436 −0.983432
$$508$$ −15.4641 26.7846i −0.686109 1.18837i
$$509$$ 25.8564i 1.14607i 0.819533 + 0.573033i $$0.194233\pi$$
−0.819533 + 0.573033i $$0.805767\pi$$
$$510$$ 0 0
$$511$$ −25.8564 + 22.3923i −1.14382 + 0.990577i
$$512$$ −16.0000 + 16.0000i −0.707107 + 0.707107i
$$513$$ −31.1769 −1.37649
$$514$$ −8.19615 + 2.19615i −0.361517 + 0.0968681i
$$515$$ 0 0
$$516$$ −3.46410 6.00000i −0.152499 0.264135i
$$517$$ 0.464102i 0.0204112i
$$518$$ −19.8564 + 29.3205i −0.872440 + 1.28827i
$$519$$ 24.8038i 1.08877i
$$520$$ 0 0
$$521$$ 13.6077i 0.596164i 0.954540 + 0.298082i $$0.0963469\pi$$
−0.954540 + 0.298082i $$0.903653\pi$$
$$522$$ 0 0
$$523$$ −24.2487 −1.06032 −0.530161 0.847897i $$-0.677869\pi$$
−0.530161 + 0.847897i $$0.677869\pi$$
$$524$$ 4.39230 2.53590i 0.191879 0.110781i
$$525$$ 0 0
$$526$$ 15.6603 4.19615i 0.682820 0.182961i
$$527$$ 38.7846i 1.68948i
$$528$$ −1.60770 0.928203i −0.0699660 0.0403949i
$$529$$ 20.8564 0.906800
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −30.0000 10.3923i −1.30066 0.450564i
$$533$$ 1.60770 0.0696370
$$534$$ −6.00000 + 1.60770i −0.259645 + 0.0695718i
$$535$$ 0 0
$$536$$ −6.92820 + 6.92820i −0.299253 + 0.299253i
$$537$$ 11.0718i 0.477783i
$$538$$ −16.3923 + 4.39230i −0.706722 + 0.189366i
$$539$$ −1.85641 0.267949i −0.0799611 0.0115414i
$$540$$ 0 0
$$541$$ 7.78461 0.334687 0.167343 0.985899i $$-0.446481\pi$$
0.167343 + 0.985899i $$0.446481\pi$$
$$542$$ 3.46410 + 12.9282i 0.148796 + 0.555314i
$$543$$ 1.60770i 0.0689928i
$$544$$ 9.46410 35.3205i 0.405770 1.51435i
$$545$$ 0 0
$$546$$ 2.49038 + 1.68653i 0.106578 + 0.0721770i
$$547$$ 21.4641i 0.917739i −0.888504 0.458869i $$-0.848255\pi$$
0.888504 0.458869i $$-0.151745\pi$$
$$548$$ 35.3205 20.3923i 1.50882 0.871116i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −47.5692 −2.02652
$$552$$ −5.07180 + 5.07180i −0.215870 + 0.215870i
$$553$$ 29.3205 25.3923i 1.24683 1.07979i
$$554$$ 6.14359 + 22.9282i 0.261016 + 0.974126i
$$555$$ 0 0
$$556$$ 12.0000 6.92820i 0.508913 0.293821i
$$557$$ 21.8564 0.926086 0.463043 0.886336i $$-0.346758\pi$$
0.463043 + 0.886336i $$0.346758\pi$$
$$558$$ 0 0
$$559$$ 0.928203 0.0392588
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ 2.90192 + 10.8301i 0.122410 + 0.456841i
$$563$$ 19.1769 0.808211 0.404105 0.914712i $$-0.367583\pi$$
0.404105 + 0.914712i $$0.367583\pi$$
$$564$$ 5.19615 3.00000i 0.218797 0.126323i
$$565$$ 0 0
$$566$$ −4.43782 16.5622i −0.186536 0.696160i
$$567$$ 15.5885 + 18.0000i 0.654654 + 0.755929i
$$568$$ −14.9282 + 14.9282i −0.626373 + 0.626373i
$$569$$ 7.07180 0.296465 0.148233 0.988953i $$-0.452642\pi$$
0.148233 + 0.988953i $$0.452642\pi$$
$$570$$ 0 0
$$571$$ 6.67949i 0.279528i −0.990185 0.139764i $$-0.955366\pi$$
0.990185 0.139764i $$-0.0446344\pi$$
$$572$$ 0.215390 0.124356i 0.00900592 0.00519957i
$$573$$ 12.4641i 0.520695i
$$574$$ 10.7321 + 7.26795i 0.447947 + 0.303358i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 19.3923i 0.807312i −0.914911 0.403656i $$-0.867739\pi$$
0.914911 0.403656i $$-0.132261\pi$$
$$578$$ 9.07180 + 33.8564i 0.377337 + 1.40824i
$$579$$ −16.3923 −0.681241
$$580$$ 0 0
$$581$$ −26.7846 30.9282i −1.11121 1.28312i
$$582$$ −31.6865 + 8.49038i −1.31345 + 0.351938i
$$583$$ 0.535898i 0.0221946i
$$584$$ 25.8564 25.8564i 1.06995 1.06995i
$$585$$ 0 0
$$586$$ −27.7583 + 7.43782i −1.14669 + 0.307254i
$$587$$ −20.5359 −0.847607 −0.423804 0.905754i $$-0.639305\pi$$
−0.423804 + 0.905754i $$0.639305\pi$$
$$588$$ 9.00000 + 22.5167i 0.371154 + 0.928571i
$$589$$ −36.0000 −1.48335
$$590$$ 0 0
$$591$$ −23.0718 −0.949047
$$592$$ 18.9282 32.7846i 0.777944 1.34744i
$$593$$ 30.4641i 1.25101i −0.780220 0.625505i $$-0.784893\pi$$
0.780220 0.625505i $$-0.215107\pi$$
$$594$$ 1.90192 0.509619i 0.0780369 0.0209099i
$$595$$ 0 0
$$596$$ −5.32051 + 3.07180i −0.217937 + 0.125826i
$$597$$ 6.00000 0.245564
$$598$$ −0.248711 0.928203i −0.0101706 0.0379571i
$$599$$ 10.1244i 0.413670i −0.978376 0.206835i $$-0.933684\pi$$
0.978376 0.206835i $$-0.0663163\pi$$
$$600$$ 0 0
$$601$$ 14.7846i 0.603077i −0.953454 0.301538i $$-0.902500\pi$$
0.953454 0.301538i $$-0.0975001\pi$$
$$602$$ 6.19615 + 4.19615i 0.252536 + 0.171022i
$$603$$ 0 0
$$604$$ −15.1962 26.3205i −0.618323 1.07097i
$$605$$ 0 0
$$606$$ 36.5885 9.80385i 1.48630 0.398254i
$$607$$ −29.1962 −1.18504 −0.592518 0.805557i $$-0.701866\pi$$
−0.592518 + 0.805557i $$0.701866\pi$$
$$608$$ 32.7846 + 8.78461i 1.32959 + 0.356263i
$$609$$ 23.7846 + 27.4641i 0.963801 + 1.11290i
$$610$$ 0 0
$$611$$ 0.803848i 0.0325202i
$$612$$ 0 0
$$613$$ 10.0000 0.403896 0.201948 0.979396i $$-0.435273\pi$$
0.201948 + 0.979396i $$0.435273\pi$$
$$614$$ −0.633975 2.36603i −0.0255851 0.0954850i
$$615$$ 0 0
$$616$$ 2.00000 + 0.143594i 0.0805823 + 0.00578555i
$$617$$ 22.9282 0.923055 0.461527 0.887126i $$-0.347302\pi$$
0.461527 + 0.887126i $$0.347302\pi$$
$$618$$ −4.31347 16.0981i −0.173513 0.647560i
$$619$$ −0.679492 −0.0273111 −0.0136555 0.999907i $$-0.504347\pi$$
−0.0136555 + 0.999907i $$0.504347\pi$$
$$620$$ 0 0
$$621$$ 7.60770i 0.305286i
$$622$$ 2.87564 + 10.7321i 0.115303 + 0.430316i
$$623$$ 5.07180 4.39230i 0.203197 0.175974i
$$624$$ −2.78461 1.60770i −0.111474 0.0643593i
$$625$$ 0 0
$$626$$ 23.9545 6.41858i 0.957414 0.256538i
$$627$$ 2.78461i 0.111207i
$$628$$ 7.85641 + 13.6077i 0.313505 + 0.543006i
$$629$$ 61.1769i 2.43928i
$$630$$ 0 0
$$631$$ 38.9090i 1.54894i 0.632610 + 0.774471i $$0.281984\pi$$
−0.632610 + 0.774471i $$0.718016\pi$$
$$632$$ −29.3205 + 29.3205i −1.16631 + 1.16631i
$$633$$ 5.53590i 0.220032i
$$634$$ −1.12436 4.19615i −0.0446539 0.166651i
$$635$$ 0 0
$$636$$ −6.00000 + 3.46410i −0.237915 + 0.137361i
$$637$$ −3.21539 0.464102i −0.127398 0.0183884i
$$638$$ 2.90192 0.777568i 0.114888 0.0307842i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.92820 0.352643 0.176321 0.984333i $$-0.443580\pi$$
0.176321 + 0.984333i $$0.443580\pi$$
$$642$$ −5.66025 + 1.51666i −0.223392 + 0.0598578i
$$643$$ 7.05256 0.278126 0.139063 0.990284i $$-0.455591\pi$$
0.139063 + 0.990284i $$0.455591\pi$$
$$644$$ 2.53590 7.32051i 0.0999284 0.288468i
$$645$$ 0 0
$$646$$ −52.9808 + 14.1962i −2.08450 + 0.558540i
$$647$$ −10.3923 −0.408564 −0.204282 0.978912i $$-0.565486\pi$$
−0.204282 + 0.978912i $$0.565486\pi$$
$$648$$ −18.0000 18.0000i −0.707107 0.707107i
$$649$$ 0.928203i 0.0364352i
$$650$$ 0 0
$$651$$ 18.0000 + 20.7846i 0.705476 + 0.814613i
$$652$$ −20.7846 36.0000i −0.813988 1.40987i
$$653$$ −17.6077 −0.689042 −0.344521 0.938779i $$-0.611959\pi$$
−0.344521 + 0.938779i $$0.611959\pi$$
$$654$$ 1.31347 + 4.90192i 0.0513606 + 0.191680i
$$655$$ 0 0
$$656$$ −12.0000 6.92820i −0.468521 0.270501i
$$657$$ 0 0
$$658$$ −3.63397 + 5.36603i −0.141667 + 0.209189i
$$659$$ 31.1962i 1.21523i −0.794232 0.607615i $$-0.792126\pi$$
0.794232 0.607615i $$-0.207874\pi$$
$$660$$ 0 0
$$661$$ 39.7128i 1.54465i 0.635228 + 0.772325i $$0.280906\pi$$
−0.635228 + 0.772325i $$0.719094\pi$$
$$662$$ −36.0526 + 9.66025i −1.40122 + 0.375456i
$$663$$ 5.19615 0.201802
$$664$$ 30.9282 + 30.9282i 1.20025 + 1.20025i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 11.6077i 0.449452i
$$668$$ 9.00000 5.19615i 0.348220 0.201045i
$$669$$ 23.7846 0.919566
$$670$$ 0 0
$$671$$ −2.53590 −0.0978973
$$672$$ −11.3205 23.3205i −0.436698 0.899608i
$$673$$ 13.1769 0.507933 0.253966 0.967213i $$-0.418265\pi$$
0.253966 + 0.967213i $$0.418265\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −22.1436 + 12.7846i −0.851677 + 0.491716i
$$677$$ 25.3923i 0.975906i 0.872870 + 0.487953i $$0.162256\pi$$
−0.872870 + 0.487953i $$0.837744\pi$$
$$678$$ −3.46410 12.9282i −0.133038 0.496505i
$$679$$ 26.7846 23.1962i 1.02790 0.890187i
$$680$$ 0 0
$$681$$ −35.7846 −1.37127
$$682$$ 2.19615 0.588457i 0.0840950 0.0225332i
$$683$$ 7.32051i 0.280111i −0.990144 0.140056i $$-0.955272\pi$$
0.990144 0.140056i $$-0.0447282\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −19.3660 17.6340i −0.739398 0.673268i
$$687$$ 14.7846i 0.564068i
$$688$$ −6.92820 4.00000i −0.264135 0.152499i
$$689$$ 0.928203i 0.0353617i
$$690$$ 0 0
$$691$$ 22.6410 0.861305 0.430652 0.902518i $$-0.358283\pi$$
0.430652 + 0.902518i $$0.358283\pi$$
$$692$$ −14.3205 24.8038i −0.544384 0.942901i
$$693$$ 0 0
$$694$$ −46.7846 + 12.5359i −1.77592 + 0.475856i
$$695$$ 0 0
$$696$$ −27.4641 27.4641i −1.04102 1.04102i
$$697$$ 22.3923 0.848169
$$698$$ −7.26795 + 1.94744i −0.275096 + 0.0737117i
$$699$$ −15.7128 −0.594313
$$700$$ 0 0
$$701$$ −37.7846 −1.42711 −0.713553 0.700602i $$-0.752915\pi$$
−0.713553 + 0.700602i $$0.752915\pi$$
$$702$$ 3.29423 0.882686i 0.124333 0.0333148i
$$703$$ −56.7846 −2.14167
$$704$$ −2.14359 −0.0807897
$$705$$ 0 0
$$706$$ 10.0981 2.70577i 0.380046 0.101833i
$$707$$ −30.9282 + 26.7846i −1.16317 + 1.00734i
$$708$$ 10.3923 6.00000i 0.390567 0.225494i
$$709$$ 21.0000 0.788672 0.394336 0.918966i $$-0.370975\pi$$
0.394336 + 0.918966i $$0.370975\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −5.07180 + 5.07180i −0.190074 + 0.190074i
$$713$$ 8.78461i 0.328986i
$$714$$ 34.6865 + 23.4904i 1.29811 + 0.879105i
$$715$$ 0 0
$$716$$ 6.39230 + 11.0718i 0.238892 + 0.413772i
$$717$$ 41.5359i 1.55119i
$$718$$ 34.5885 9.26795i 1.29083 0.345877i
$$719$$ −38.5359 −1.43715 −0.718573 0.695451i $$-0.755205\pi$$
−0.718573 + 0.695451i $$0.755205\pi$$
$$720$$ 0 0
$$721$$ 11.7846 + 13.6077i 0.438882 + 0.506777i
$$722$$ −6.22243 23.2224i −0.231575 0.864249i
$$723$$ 28.3923i 1.05592i
$$724$$ 0.928203 + 1.60770i 0.0344964 + 0.0597495i
$$725$$ 0 0
$$726$$ 6.92820 + 25.8564i 0.257130 + 0.959621i
$$727$$ −13.6077 −0.504681 −0.252341 0.967638i $$-0.581200\pi$$
−0.252341 + 0.967638i $$0.581200\pi$$
$$728$$ 3.46410 + 0.248711i 0.128388 + 0.00921785i
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 12.9282 0.478167
$$732$$ 16.3923 + 28.3923i 0.605877 + 1.04941i
$$733$$ 11.5359i 0.426088i −0.977043 0.213044i $$-0.931662\pi$$
0.977043 0.213044i $$-0.0683378\pi$$
$$734$$ −4.34679 16.2224i −0.160443 0.598781i
$$735$$ 0 0
$$736$$ −2.14359 + 8.00000i −0.0790139 + 0.294884i
$$737$$ −0.928203 −0.0341908
$$738$$ 0 0
$$739$$ 4.26795i 0.156999i −0.996914 0.0784995i $$-0.974987\pi$$
0.996914 0.0784995i $$-0.0250129\pi$$
$$740$$ 0 0
$$741$$ 4.82309i 0.177180i
$$742$$ 4.19615 6.19615i 0.154046 0.227468i
$$743$$ 30.3923i 1.11499i −0.830182 0.557493i $$-0.811763\pi$$
0.830182 0.557493i $$-0.188237\pi$$
$$744$$ −20.7846 20.7846i −0.762001 0.762001i
$$745$$ 0 0
$$746$$ −1.32051 4.92820i −0.0483472 0.180434i
$$747$$ 0 0
$$748$$ 3.00000 1.73205i 0.109691 0.0633300i
$$749$$ 4.78461 4.14359i 0.174826 0.151404i
$$750$$ 0 0
$$751$$ 25.5885i 0.933736i −0.884327 0.466868i $$-0.845382\pi$$
0.884327 0.466868i $$-0.154618\pi$$
$$752$$ 3.46410 6.00000i 0.126323 0.218797i
$$753$$ −44.7846 −1.63204
$$754$$ 5.02628 1.34679i 0.183046 0.0490471i
$$755$$ 0 0
$$756$$ 25.9808 + 9.00000i 0.944911 + 0.327327i
$$757$$ −37.8564 −1.37591 −0.687957 0.725751i $$-0.741492\pi$$
−0.687957 + 0.725751i $$0.741492\pi$$
$$758$$ 7.66025 2.05256i 0.278233 0.0745523i
$$759$$ −0.679492 −0.0246640
$$760$$ 0 0
$$761$$ 42.2487i 1.53151i −0.643130 0.765757i $$-0.722364\pi$$
0.643130 0.765757i $$-0.277636\pi$$
$$762$$ −36.5885 + 9.80385i −1.32546 + 0.355156i
$$763$$ −3.58846 4.14359i −0.129911 0.150008i
$$764$$ −7.19615 12.4641i −0.260348 0.450935i
$$765$$ 0 0
$$766$$ −10.0526 37.5167i −0.363214 1.35553i
$$767$$ 1.60770i 0.0580505i
$$768$$ 13.8564 + 24.0000i 0.500000 + 0.866025i
$$769$$ 18.0000i 0.649097i 0.945869 + 0.324548i $$0.105212\pi$$
−0.945869 + 0.324548i $$0.894788\pi$$
$$770$$ 0 0
$$771$$ 10.3923i 0.374270i
$$772$$ −16.3923 + 9.46410i −0.589972 + 0.340620i
$$773$$ 5.53590i 0.199112i 0.995032 + 0.0995562i $$0.0317423\pi$$
−0.995032 + 0.0995562i $$0.968258\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −26.7846 + 26.7846i −0.961511 + 0.961511i
$$777$$ 28.3923 + 32.7846i 1.01857 + 1.17614i
$$778$$ 7.63397 + 28.4904i 0.273691 + 1.02143i
$$779$$ 20.7846i 0.744686i
$$780$$ 0 0
$$781$$ −2.00000 −0.0715656