# Properties

 Label 475.2.e.f.26.5 Level $475$ Weight $2$ Character 475.26 Analytic conductor $3.793$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$475 = 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 475.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$3.79289409601$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1$$ x^12 - 3*x^11 + 17*x^10 - 18*x^9 + 109*x^8 - 93*x^7 + 484*x^6 - 147*x^5 + 1009*x^4 - 552*x^3 + 1107*x^2 + 33*x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 26.5 Root $$-0.928369 + 1.60798i$$ of defining polynomial Character $$\chi$$ $$=$$ 475.26 Dual form 475.2.e.f.201.5

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.740597 + 1.28275i) q^{2} +(-1.42837 - 2.47401i) q^{3} +(-0.0969683 + 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 + 4.46952i) q^{9} +O(q^{10})$$ $$q+(0.740597 + 1.28275i) q^{2} +(-1.42837 - 2.47401i) q^{3} +(-0.0969683 + 0.167954i) q^{4} +(2.11569 - 3.66449i) q^{6} +3.78541 q^{7} +2.67513 q^{8} +(-2.58048 + 4.46952i) q^{9} -5.59460 q^{11} +0.554026 q^{12} +(2.45326 - 4.24917i) q^{13} +(2.80346 + 4.85574i) q^{14} +(2.17513 + 3.76744i) q^{16} +(-0.875095 - 1.51571i) q^{17} -7.64438 q^{18} +(0.636061 - 4.31224i) q^{19} +(-5.40696 - 9.36514i) q^{21} +(-4.14335 - 7.17648i) q^{22} +(0.290768 - 0.503625i) q^{23} +(-3.82107 - 6.61830i) q^{24} +7.26750 q^{26} +6.17328 q^{27} +(-0.367065 + 0.635775i) q^{28} +(-0.832153 + 1.44133i) q^{29} +7.01680 q^{31} +(-0.546661 + 0.946844i) q^{32} +(7.99116 + 13.8411i) q^{33} +(1.29619 - 2.24506i) q^{34} +(-0.500449 - 0.866803i) q^{36} -2.36322 q^{37} +(6.00260 - 2.37773i) q^{38} -14.0166 q^{39} +(-0.417676 - 0.723435i) q^{41} +(8.00877 - 13.8716i) q^{42} +(-0.535664 - 0.927797i) q^{43} +(0.542499 - 0.939635i) q^{44} +0.861369 q^{46} +(1.93378 - 3.34941i) q^{47} +(6.21378 - 10.7626i) q^{48} +7.32934 q^{49} +(-2.49992 + 4.32999i) q^{51} +(0.475776 + 0.824069i) q^{52} +(-3.39842 + 5.88624i) q^{53} +(4.57192 + 7.91879i) q^{54} +10.1265 q^{56} +(-11.5771 + 4.58585i) q^{57} -2.46516 q^{58} +(0.204282 + 0.353827i) q^{59} +(-6.98016 + 12.0900i) q^{61} +(5.19662 + 9.00081i) q^{62} +(-9.76817 + 16.9190i) q^{63} +7.08110 q^{64} +(-11.8365 + 20.5013i) q^{66} +(0.390703 - 0.676717i) q^{67} +0.339426 q^{68} -1.66130 q^{69} +(-3.18919 - 5.52384i) q^{71} +(-6.90312 + 11.9565i) q^{72} +(1.44458 + 2.50208i) q^{73} +(-1.75019 - 3.03142i) q^{74} +(0.662580 + 0.524980i) q^{76} -21.1779 q^{77} +(-10.3807 - 17.9799i) q^{78} +(6.25135 + 10.8276i) q^{79} +(-1.07630 - 1.86420i) q^{81} +(0.618659 - 1.07155i) q^{82} +10.3903 q^{83} +2.09722 q^{84} +(0.793422 - 1.37425i) q^{86} +4.75449 q^{87} -14.9663 q^{88} +(-8.92106 + 15.4517i) q^{89} +(9.28659 - 16.0848i) q^{91} +(0.0563906 + 0.0976714i) q^{92} +(-10.0226 - 17.3596i) q^{93} +5.72861 q^{94} +3.12333 q^{96} +(5.49995 + 9.52619i) q^{97} +(5.42809 + 9.40172i) q^{98} +(14.4367 - 25.0052i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10})$$ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 $$12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100})$$ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.740597 + 1.28275i 0.523681 + 0.907043i 0.999620 + 0.0275641i $$0.00877505\pi$$
−0.475939 + 0.879478i $$0.657892\pi$$
$$3$$ −1.42837 2.47401i −0.824669 1.42837i −0.902172 0.431377i $$-0.858028\pi$$
0.0775023 0.996992i $$-0.475305\pi$$
$$4$$ −0.0969683 + 0.167954i −0.0484841 + 0.0839770i
$$5$$ 0 0
$$6$$ 2.11569 3.66449i 0.863728 1.49602i
$$7$$ 3.78541 1.43075 0.715375 0.698740i $$-0.246256\pi$$
0.715375 + 0.698740i $$0.246256\pi$$
$$8$$ 2.67513 0.945802
$$9$$ −2.58048 + 4.46952i −0.860159 + 1.48984i
$$10$$ 0 0
$$11$$ −5.59460 −1.68684 −0.843418 0.537258i $$-0.819460\pi$$
−0.843418 + 0.537258i $$0.819460\pi$$
$$12$$ 0.554026 0.159934
$$13$$ 2.45326 4.24917i 0.680411 1.17851i −0.294444 0.955669i $$-0.595134\pi$$
0.974855 0.222838i $$-0.0715322\pi$$
$$14$$ 2.80346 + 4.85574i 0.749257 + 1.29775i
$$15$$ 0 0
$$16$$ 2.17513 + 3.76744i 0.543783 + 0.941859i
$$17$$ −0.875095 1.51571i −0.212242 0.367614i 0.740174 0.672415i $$-0.234743\pi$$
−0.952416 + 0.304802i $$0.901410\pi$$
$$18$$ −7.64438 −1.80180
$$19$$ 0.636061 4.31224i 0.145922 0.989296i
$$20$$ 0 0
$$21$$ −5.40696 9.36514i −1.17990 2.04364i
$$22$$ −4.14335 7.17648i −0.883364 1.53003i
$$23$$ 0.290768 0.503625i 0.0606294 0.105013i −0.834118 0.551587i $$-0.814023\pi$$
0.894747 + 0.446574i $$0.147356\pi$$
$$24$$ −3.82107 6.61830i −0.779974 1.35095i
$$25$$ 0 0
$$26$$ 7.26750 1.42527
$$27$$ 6.17328 1.18805
$$28$$ −0.367065 + 0.635775i −0.0693687 + 0.120150i
$$29$$ −0.832153 + 1.44133i −0.154527 + 0.267649i −0.932887 0.360170i $$-0.882719\pi$$
0.778360 + 0.627819i $$0.216052\pi$$
$$30$$ 0 0
$$31$$ 7.01680 1.26025 0.630127 0.776492i $$-0.283003\pi$$
0.630127 + 0.776492i $$0.283003\pi$$
$$32$$ −0.546661 + 0.946844i −0.0966369 + 0.167380i
$$33$$ 7.99116 + 13.8411i 1.39108 + 2.40942i
$$34$$ 1.29619 2.24506i 0.222294 0.385025i
$$35$$ 0 0
$$36$$ −0.500449 0.866803i −0.0834082 0.144467i
$$37$$ −2.36322 −0.388510 −0.194255 0.980951i $$-0.562229\pi$$
−0.194255 + 0.980951i $$0.562229\pi$$
$$38$$ 6.00260 2.37773i 0.973750 0.385718i
$$39$$ −14.0166 −2.24446
$$40$$ 0 0
$$41$$ −0.417676 0.723435i −0.0652300 0.112982i 0.831566 0.555426i $$-0.187445\pi$$
−0.896796 + 0.442444i $$0.854111\pi$$
$$42$$ 8.00877 13.8716i 1.23578 2.14043i
$$43$$ −0.535664 0.927797i −0.0816880 0.141488i 0.822287 0.569073i $$-0.192698\pi$$
−0.903975 + 0.427585i $$0.859364\pi$$
$$44$$ 0.542499 0.939635i 0.0817848 0.141655i
$$45$$ 0 0
$$46$$ 0.861369 0.127002
$$47$$ 1.93378 3.34941i 0.282071 0.488561i −0.689824 0.723977i $$-0.742312\pi$$
0.971895 + 0.235416i $$0.0756453\pi$$
$$48$$ 6.21378 10.7626i 0.896882 1.55345i
$$49$$ 7.32934 1.04705
$$50$$ 0 0
$$51$$ −2.49992 + 4.32999i −0.350059 + 0.606319i
$$52$$ 0.475776 + 0.824069i 0.0659783 + 0.114278i
$$53$$ −3.39842 + 5.88624i −0.466809 + 0.808537i −0.999281 0.0379106i $$-0.987930\pi$$
0.532472 + 0.846448i $$0.321263\pi$$
$$54$$ 4.57192 + 7.91879i 0.622159 + 1.07761i
$$55$$ 0 0
$$56$$ 10.1265 1.35321
$$57$$ −11.5771 + 4.58585i −1.53342 + 0.607411i
$$58$$ −2.46516 −0.323691
$$59$$ 0.204282 + 0.353827i 0.0265953 + 0.0460643i 0.879017 0.476791i $$-0.158200\pi$$
−0.852421 + 0.522855i $$0.824867\pi$$
$$60$$ 0 0
$$61$$ −6.98016 + 12.0900i −0.893718 + 1.54796i −0.0583341 + 0.998297i $$0.518579\pi$$
−0.835384 + 0.549667i $$0.814754\pi$$
$$62$$ 5.19662 + 9.00081i 0.659971 + 1.14310i
$$63$$ −9.76817 + 16.9190i −1.23067 + 2.13159i
$$64$$ 7.08110 0.885138
$$65$$ 0 0
$$66$$ −11.8365 + 20.5013i −1.45697 + 2.52354i
$$67$$ 0.390703 0.676717i 0.0477319 0.0826742i −0.841172 0.540767i $$-0.818134\pi$$
0.888904 + 0.458093i $$0.151467\pi$$
$$68$$ 0.339426 0.0411614
$$69$$ −1.66130 −0.199997
$$70$$ 0 0
$$71$$ −3.18919 5.52384i −0.378487 0.655559i 0.612355 0.790583i $$-0.290222\pi$$
−0.990842 + 0.135024i $$0.956889\pi$$
$$72$$ −6.90312 + 11.9565i −0.813540 + 1.40909i
$$73$$ 1.44458 + 2.50208i 0.169075 + 0.292846i 0.938095 0.346378i $$-0.112589\pi$$
−0.769020 + 0.639225i $$0.779255\pi$$
$$74$$ −1.75019 3.03142i −0.203456 0.352395i
$$75$$ 0 0
$$76$$ 0.662580 + 0.524980i 0.0760032 + 0.0602193i
$$77$$ −21.1779 −2.41344
$$78$$ −10.3807 17.9799i −1.17538 2.03582i
$$79$$ 6.25135 + 10.8276i 0.703331 + 1.21821i 0.967290 + 0.253672i $$0.0816383\pi$$
−0.263959 + 0.964534i $$0.585028\pi$$
$$80$$ 0 0
$$81$$ −1.07630 1.86420i −0.119589 0.207133i
$$82$$ 0.618659 1.07155i 0.0683194 0.118333i
$$83$$ 10.3903 1.14048 0.570240 0.821478i $$-0.306850\pi$$
0.570240 + 0.821478i $$0.306850\pi$$
$$84$$ 2.09722 0.228825
$$85$$ 0 0
$$86$$ 0.793422 1.37425i 0.0855569 0.148189i
$$87$$ 4.75449 0.509735
$$88$$ −14.9663 −1.59541
$$89$$ −8.92106 + 15.4517i −0.945631 + 1.63788i −0.191148 + 0.981561i $$0.561221\pi$$
−0.754483 + 0.656320i $$0.772112\pi$$
$$90$$ 0 0
$$91$$ 9.28659 16.0848i 0.973499 1.68615i
$$92$$ 0.0563906 + 0.0976714i 0.00587913 + 0.0101829i
$$93$$ −10.0226 17.3596i −1.03929 1.80011i
$$94$$ 5.72861 0.590861
$$95$$ 0 0
$$96$$ 3.12333 0.318774
$$97$$ 5.49995 + 9.52619i 0.558435 + 0.967238i 0.997627 + 0.0688448i $$0.0219313\pi$$
−0.439192 + 0.898393i $$0.644735\pi$$
$$98$$ 5.42809 + 9.40172i 0.548319 + 0.949717i
$$99$$ 14.4367 25.0052i 1.45095 2.51311i
$$100$$ 0 0
$$101$$ −2.57944 + 4.46772i −0.256664 + 0.444555i −0.965346 0.260973i $$-0.915957\pi$$
0.708682 + 0.705528i $$0.249290\pi$$
$$102$$ −7.40573 −0.733277
$$103$$ 7.75851 0.764469 0.382235 0.924065i $$-0.375155\pi$$
0.382235 + 0.924065i $$0.375155\pi$$
$$104$$ 6.56279 11.3671i 0.643534 1.11463i
$$105$$ 0 0
$$106$$ −10.0674 −0.977837
$$107$$ 12.6521 1.22313 0.611564 0.791195i $$-0.290541\pi$$
0.611564 + 0.791195i $$0.290541\pi$$
$$108$$ −0.598613 + 1.03683i −0.0576015 + 0.0997688i
$$109$$ 4.09697 + 7.09616i 0.392418 + 0.679689i 0.992768 0.120049i $$-0.0383052\pi$$
−0.600350 + 0.799738i $$0.704972\pi$$
$$110$$ 0 0
$$111$$ 3.37554 + 5.84661i 0.320392 + 0.554936i
$$112$$ 8.23376 + 14.2613i 0.778018 + 1.34757i
$$113$$ 12.5551 1.18108 0.590541 0.807007i $$-0.298914\pi$$
0.590541 + 0.807007i $$0.298914\pi$$
$$114$$ −14.4564 11.4542i −1.35397 1.07279i
$$115$$ 0 0
$$116$$ −0.161385 0.279527i −0.0149842 0.0259534i
$$117$$ 12.6612 + 21.9298i 1.17052 + 2.02741i
$$118$$ −0.302581 + 0.524086i −0.0278549 + 0.0482461i
$$119$$ −3.31260 5.73758i −0.303665 0.525963i
$$120$$ 0 0
$$121$$ 20.2996 1.84541
$$122$$ −20.6779 −1.87209
$$123$$ −1.19319 + 2.06667i −0.107586 + 0.186345i
$$124$$ −0.680407 + 1.17850i −0.0611023 + 0.105832i
$$125$$ 0 0
$$126$$ −28.9371 −2.57792
$$127$$ −4.07957 + 7.06602i −0.362003 + 0.627007i −0.988290 0.152585i $$-0.951240\pi$$
0.626287 + 0.779592i $$0.284574\pi$$
$$128$$ 6.33757 + 10.9770i 0.560167 + 0.970238i
$$129$$ −1.53025 + 2.65047i −0.134731 + 0.233361i
$$130$$ 0 0
$$131$$ −9.62491 16.6708i −0.840932 1.45654i −0.889108 0.457698i $$-0.848674\pi$$
0.0481757 0.998839i $$-0.484659\pi$$
$$132$$ −3.09955 −0.269782
$$133$$ 2.40775 16.3236i 0.208779 1.41544i
$$134$$ 1.15741 0.0999853
$$135$$ 0 0
$$136$$ −2.34099 4.05472i −0.200739 0.347689i
$$137$$ −0.785955 + 1.36131i −0.0671487 + 0.116305i −0.897645 0.440719i $$-0.854724\pi$$
0.830496 + 0.557024i $$0.188057\pi$$
$$138$$ −1.23035 2.13103i −0.104735 0.181406i
$$139$$ 1.02459 1.77464i 0.0869047 0.150523i −0.819297 0.573370i $$-0.805636\pi$$
0.906201 + 0.422847i $$0.138969\pi$$
$$140$$ 0 0
$$141$$ −11.0486 −0.930461
$$142$$ 4.72381 8.18188i 0.396413 0.686608i
$$143$$ −13.7250 + 23.7724i −1.14774 + 1.98795i
$$144$$ −22.4515 −1.87096
$$145$$ 0 0
$$146$$ −2.13970 + 3.70607i −0.177083 + 0.306716i
$$147$$ −10.4690 18.1328i −0.863468 1.49557i
$$148$$ 0.229157 0.396911i 0.0188366 0.0326259i
$$149$$ 0.737839 + 1.27797i 0.0604461 + 0.104696i 0.894665 0.446738i $$-0.147414\pi$$
−0.834219 + 0.551434i $$0.814081\pi$$
$$150$$ 0 0
$$151$$ 6.42543 0.522894 0.261447 0.965218i $$-0.415800\pi$$
0.261447 + 0.965218i $$0.415800\pi$$
$$152$$ 1.70155 11.5358i 0.138014 0.935678i
$$153$$ 9.03266 0.730247
$$154$$ −15.6843 27.1659i −1.26387 2.18909i
$$155$$ 0 0
$$156$$ 1.35917 2.35415i 0.108821 0.188483i
$$157$$ −11.1445 19.3028i −0.889425 1.54053i −0.840556 0.541724i $$-0.817772\pi$$
−0.0488688 0.998805i $$-0.515562\pi$$
$$158$$ −9.25946 + 16.0379i −0.736643 + 1.27590i
$$159$$ 19.4168 1.53985
$$160$$ 0 0
$$161$$ 1.10068 1.90643i 0.0867455 0.150248i
$$162$$ 1.59420 2.76124i 0.125253 0.216944i
$$163$$ −15.0321 −1.17741 −0.588703 0.808350i $$-0.700361\pi$$
−0.588703 + 0.808350i $$0.700361\pi$$
$$164$$ 0.162005 0.0126505
$$165$$ 0 0
$$166$$ 7.69500 + 13.3281i 0.597248 + 1.03446i
$$167$$ −4.79928 + 8.31260i −0.371380 + 0.643249i −0.989778 0.142616i $$-0.954449\pi$$
0.618398 + 0.785865i $$0.287782\pi$$
$$168$$ −14.4643 25.0530i −1.11595 1.93288i
$$169$$ −5.53695 9.59028i −0.425919 0.737714i
$$170$$ 0 0
$$171$$ 17.6323 + 13.9705i 1.34838 + 1.06835i
$$172$$ 0.207770 0.0158423
$$173$$ 4.41611 + 7.64894i 0.335751 + 0.581538i 0.983629 0.180207i $$-0.0576766\pi$$
−0.647878 + 0.761744i $$0.724343\pi$$
$$174$$ 3.52116 + 6.09883i 0.266938 + 0.462351i
$$175$$ 0 0
$$176$$ −12.1690 21.0773i −0.917272 1.58876i
$$177$$ 0.583580 1.01079i 0.0438646 0.0759757i
$$178$$ −26.4277 −1.98084
$$179$$ 10.8178 0.808564 0.404282 0.914634i $$-0.367522\pi$$
0.404282 + 0.914634i $$0.367522\pi$$
$$180$$ 0 0
$$181$$ −5.37359 + 9.30733i −0.399416 + 0.691808i −0.993654 0.112481i $$-0.964120\pi$$
0.594238 + 0.804289i $$0.297454\pi$$
$$182$$ 27.5105 2.03921
$$183$$ 39.8810 2.94809
$$184$$ 0.777843 1.34726i 0.0573434 0.0993216i
$$185$$ 0 0
$$186$$ 14.8454 25.7130i 1.08852 1.88537i
$$187$$ 4.89581 + 8.47979i 0.358017 + 0.620104i
$$188$$ 0.375031 + 0.649573i 0.0273519 + 0.0473750i
$$189$$ 23.3684 1.69980
$$190$$ 0 0
$$191$$ −6.28362 −0.454667 −0.227334 0.973817i $$-0.573001\pi$$
−0.227334 + 0.973817i $$0.573001\pi$$
$$192$$ −10.1144 17.5187i −0.729946 1.26430i
$$193$$ −8.91459 15.4405i −0.641686 1.11143i −0.985056 0.172233i $$-0.944902\pi$$
0.343370 0.939200i $$-0.388431\pi$$
$$194$$ −8.14649 + 14.1101i −0.584884 + 1.01305i
$$195$$ 0 0
$$196$$ −0.710713 + 1.23099i −0.0507652 + 0.0879279i
$$197$$ −16.9925 −1.21066 −0.605332 0.795973i $$-0.706959\pi$$
−0.605332 + 0.795973i $$0.706959\pi$$
$$198$$ 42.7672 3.03934
$$199$$ −8.22212 + 14.2411i −0.582850 + 1.00953i 0.412289 + 0.911053i $$0.364729\pi$$
−0.995140 + 0.0984735i $$0.968604\pi$$
$$200$$ 0 0
$$201$$ −2.23227 −0.157452
$$202$$ −7.64131 −0.537641
$$203$$ −3.15004 + 5.45603i −0.221090 + 0.382938i
$$204$$ −0.484826 0.839743i −0.0339446 0.0587937i
$$205$$ 0 0
$$206$$ 5.74593 + 9.95225i 0.400338 + 0.693406i
$$207$$ 1.50064 + 2.59919i 0.104302 + 0.180656i
$$208$$ 21.3446 1.47998
$$209$$ −3.55851 + 24.1253i −0.246147 + 1.66878i
$$210$$ 0 0
$$211$$ −7.79632 13.5036i −0.536721 0.929628i −0.999078 0.0429343i $$-0.986329\pi$$
0.462357 0.886694i $$-0.347004\pi$$
$$212$$ −0.659078 1.14156i −0.0452657 0.0784024i
$$213$$ −9.11068 + 15.7802i −0.624253 + 1.08124i
$$214$$ 9.37013 + 16.2295i 0.640529 + 1.10943i
$$215$$ 0 0
$$216$$ 16.5143 1.12366
$$217$$ 26.5615 1.80311
$$218$$ −6.06841 + 10.5108i −0.411004 + 0.711880i
$$219$$ 4.12678 7.14779i 0.278862 0.483003i
$$220$$ 0 0
$$221$$ −8.58734 −0.577647
$$222$$ −4.99984 + 8.65997i −0.335567 + 0.581219i
$$223$$ −3.90313 6.76042i −0.261373 0.452711i 0.705234 0.708974i $$-0.250842\pi$$
−0.966607 + 0.256263i $$0.917509\pi$$
$$224$$ −2.06933 + 3.58419i −0.138263 + 0.239479i
$$225$$ 0 0
$$226$$ 9.29826 + 16.1051i 0.618511 + 1.07129i
$$227$$ 16.8511 1.11845 0.559223 0.829017i $$-0.311100\pi$$
0.559223 + 0.829017i $$0.311100\pi$$
$$228$$ 0.352394 2.38909i 0.0233379 0.158222i
$$229$$ −0.251385 −0.0166120 −0.00830600 0.999966i $$-0.502644\pi$$
−0.00830600 + 0.999966i $$0.502644\pi$$
$$230$$ 0 0
$$231$$ 30.2498 + 52.3942i 1.99029 + 3.44729i
$$232$$ −2.22612 + 3.85575i −0.146152 + 0.253142i
$$233$$ −11.6014 20.0943i −0.760035 1.31642i −0.942832 0.333269i $$-0.891848\pi$$
0.182797 0.983151i $$-0.441485\pi$$
$$234$$ −18.7536 + 32.4822i −1.22596 + 2.12343i
$$235$$ 0 0
$$236$$ −0.0792355 −0.00515779
$$237$$ 17.8585 30.9318i 1.16003 2.00923i
$$238$$ 4.90660 8.49848i 0.318047 0.550874i
$$239$$ −7.58778 −0.490813 −0.245406 0.969420i $$-0.578921\pi$$
−0.245406 + 0.969420i $$0.578921\pi$$
$$240$$ 0 0
$$241$$ 2.75808 4.77714i 0.177664 0.307723i −0.763416 0.645907i $$-0.776479\pi$$
0.941080 + 0.338184i $$0.109813\pi$$
$$242$$ 15.0338 + 26.0393i 0.966409 + 1.67387i
$$243$$ 6.18523 10.7131i 0.396783 0.687248i
$$244$$ −1.35371 2.34469i −0.0866623 0.150103i
$$245$$ 0 0
$$246$$ −3.53469 −0.225364
$$247$$ −16.7630 13.2818i −1.06661 0.845099i
$$248$$ 18.7708 1.19195
$$249$$ −14.8411 25.7056i −0.940519 1.62903i
$$250$$ 0 0
$$251$$ 9.32933 16.1589i 0.588862 1.01994i −0.405520 0.914086i $$-0.632910\pi$$
0.994382 0.105852i $$-0.0337571\pi$$
$$252$$ −1.89441 3.28121i −0.119336 0.206697i
$$253$$ −1.62673 + 2.81758i −0.102272 + 0.177140i
$$254$$ −12.0853 −0.758297
$$255$$ 0 0
$$256$$ −2.30606 + 3.99422i −0.144129 + 0.249639i
$$257$$ −0.346352 + 0.599899i −0.0216048 + 0.0374207i −0.876626 0.481173i $$-0.840211\pi$$
0.855021 + 0.518594i $$0.173544\pi$$
$$258$$ −4.53320 −0.282225
$$259$$ −8.94574 −0.555861
$$260$$ 0 0
$$261$$ −4.29470 7.43865i −0.265836 0.460441i
$$262$$ 14.2564 24.6927i 0.880761 1.52552i
$$263$$ −5.81338 10.0691i −0.358468 0.620885i 0.629237 0.777214i $$-0.283368\pi$$
−0.987705 + 0.156328i $$0.950034\pi$$
$$264$$ 21.3774 + 37.0267i 1.31569 + 2.27884i
$$265$$ 0 0
$$266$$ 22.7223 9.00067i 1.39319 0.551866i
$$267$$ 50.9703 3.11933
$$268$$ 0.0757716 + 0.131240i 0.00462849 + 0.00801677i
$$269$$ 11.8057 + 20.4481i 0.719809 + 1.24675i 0.961075 + 0.276286i $$0.0891038\pi$$
−0.241267 + 0.970459i $$0.577563\pi$$
$$270$$ 0 0
$$271$$ 3.81995 + 6.61635i 0.232046 + 0.401915i 0.958410 0.285395i $$-0.0921248\pi$$
−0.726364 + 0.687310i $$0.758791\pi$$
$$272$$ 3.80689 6.59373i 0.230827 0.399804i
$$273$$ −53.0587 −3.21126
$$274$$ −2.32830 −0.140658
$$275$$ 0 0
$$276$$ 0.161093 0.279022i 0.00969667 0.0167951i
$$277$$ −18.6537 −1.12079 −0.560397 0.828224i $$-0.689352\pi$$
−0.560397 + 0.828224i $$0.689352\pi$$
$$278$$ 3.03524 0.182041
$$279$$ −18.1067 + 31.3617i −1.08402 + 1.87758i
$$280$$ 0 0
$$281$$ −6.99489 + 12.1155i −0.417280 + 0.722750i −0.995665 0.0930139i $$-0.970350\pi$$
0.578385 + 0.815764i $$0.303683\pi$$
$$282$$ −8.18257 14.1726i −0.487265 0.843968i
$$283$$ 12.3334 + 21.3620i 0.733143 + 1.26984i 0.955533 + 0.294884i $$0.0952809\pi$$
−0.222390 + 0.974958i $$0.571386\pi$$
$$284$$ 1.23700 0.0734025
$$285$$ 0 0
$$286$$ −40.6588 −2.40420
$$287$$ −1.58107 2.73850i −0.0933278 0.161649i
$$288$$ −2.82129 4.88662i −0.166246 0.287947i
$$289$$ 6.96842 12.0697i 0.409907 0.709979i
$$290$$ 0 0
$$291$$ 15.7119 27.2138i 0.921049 1.59530i
$$292$$ −0.560312 −0.0327898
$$293$$ 10.5784 0.617994 0.308997 0.951063i $$-0.400007\pi$$
0.308997 + 0.951063i $$0.400007\pi$$
$$294$$ 15.5066 26.8583i 0.904365 1.56641i
$$295$$ 0 0
$$296$$ −6.32191 −0.367454
$$297$$ −34.5371 −2.00404
$$298$$ −1.09288 + 1.89293i −0.0633090 + 0.109654i
$$299$$ −1.42666 2.47105i −0.0825058 0.142904i
$$300$$ 0 0
$$301$$ −2.02771 3.51209i −0.116875 0.202434i
$$302$$ 4.75866 + 8.24223i 0.273830 + 0.474287i
$$303$$ 14.7376 0.846652
$$304$$ 17.6296 6.98337i 1.01113 0.400524i
$$305$$ 0 0
$$306$$ 6.68956 + 11.5867i 0.382417 + 0.662365i
$$307$$ 6.41222 + 11.1063i 0.365965 + 0.633870i 0.988931 0.148379i $$-0.0474057\pi$$
−0.622966 + 0.782249i $$0.714072\pi$$
$$308$$ 2.05358 3.55691i 0.117014 0.202674i
$$309$$ −11.0820 19.1946i −0.630434 1.09194i
$$310$$ 0 0
$$311$$ 3.42706 0.194331 0.0971655 0.995268i $$-0.469022\pi$$
0.0971655 + 0.995268i $$0.469022\pi$$
$$312$$ −37.4963 −2.12281
$$313$$ −1.42224 + 2.46339i −0.0803896 + 0.139239i −0.903417 0.428762i $$-0.858950\pi$$
0.823028 + 0.568001i $$0.192283\pi$$
$$314$$ 16.5071 28.5912i 0.931551 1.61349i
$$315$$ 0 0
$$316$$ −2.42473 −0.136402
$$317$$ −2.33072 + 4.03693i −0.130907 + 0.226737i −0.924026 0.382329i $$-0.875122\pi$$
0.793120 + 0.609066i $$0.208455\pi$$
$$318$$ 14.3800 + 24.9069i 0.806392 + 1.39671i
$$319$$ 4.65556 8.06367i 0.260662 0.451479i
$$320$$ 0 0
$$321$$ −18.0719 31.3015i −1.00868 1.74708i
$$322$$ 3.26063 0.181708
$$323$$ −7.09272 + 2.80954i −0.394649 + 0.156327i
$$324$$ 0.417467 0.0231926
$$325$$ 0 0
$$326$$ −11.1327 19.2825i −0.616585 1.06796i
$$327$$ 11.7040 20.2719i 0.647231 1.12104i
$$328$$ −1.11734 1.93528i −0.0616946 0.106858i
$$329$$ 7.32016 12.6789i 0.403573 0.699010i
$$330$$ 0 0
$$331$$ −7.00260 −0.384898 −0.192449 0.981307i $$-0.561643\pi$$
−0.192449 + 0.981307i $$0.561643\pi$$
$$332$$ −1.00753 + 1.74509i −0.0552952 + 0.0957741i
$$333$$ 6.09822 10.5624i 0.334181 0.578818i
$$334$$ −14.2173 −0.777938
$$335$$ 0 0
$$336$$ 23.5217 40.7408i 1.28321 2.22259i
$$337$$ −6.76881 11.7239i −0.368721 0.638643i 0.620645 0.784092i $$-0.286871\pi$$
−0.989366 + 0.145449i $$0.953537\pi$$
$$338$$ 8.20130 14.2051i 0.446092 0.772654i
$$339$$ −17.9333 31.0614i −0.974003 1.68702i
$$340$$ 0 0
$$341$$ −39.2562 −2.12584
$$342$$ −4.86229 + 32.9644i −0.262923 + 1.78251i
$$343$$ 1.24667 0.0673140
$$344$$ −1.43297 2.48198i −0.0772606 0.133819i
$$345$$ 0 0
$$346$$ −6.54112 + 11.3296i −0.351653 + 0.609081i
$$347$$ 10.9817 + 19.0208i 0.589527 + 1.02109i 0.994294 + 0.106671i $$0.0340190\pi$$
−0.404768 + 0.914420i $$0.632648\pi$$
$$348$$ −0.461034 + 0.798535i −0.0247140 + 0.0428060i
$$349$$ −22.1930 −1.18796 −0.593981 0.804479i $$-0.702445\pi$$
−0.593981 + 0.804479i $$0.702445\pi$$
$$350$$ 0 0
$$351$$ 15.1447 26.2313i 0.808362 1.40012i
$$352$$ 3.05835 5.29721i 0.163010 0.282342i
$$353$$ 0.679013 0.0361402 0.0180701 0.999837i $$-0.494248\pi$$
0.0180701 + 0.999837i $$0.494248\pi$$
$$354$$ 1.72879 0.0918843
$$355$$ 0 0
$$356$$ −1.73012 2.99666i −0.0916962 0.158822i
$$357$$ −9.46322 + 16.3908i −0.500847 + 0.867492i
$$358$$ 8.01166 + 13.8766i 0.423430 + 0.733402i
$$359$$ 12.6627 + 21.9325i 0.668314 + 1.15755i 0.978375 + 0.206837i $$0.0663170\pi$$
−0.310062 + 0.950716i $$0.600350\pi$$
$$360$$ 0 0
$$361$$ −18.1909 5.48570i −0.957413 0.288721i
$$362$$ −15.9187 −0.836666
$$363$$ −28.9953 50.2213i −1.52186 2.63593i
$$364$$ 1.80101 + 3.11944i 0.0943985 + 0.163503i
$$365$$ 0 0
$$366$$ 29.5357 + 51.1574i 1.54386 + 2.67404i
$$367$$ 5.83153 10.1005i 0.304404 0.527243i −0.672725 0.739893i $$-0.734876\pi$$
0.977128 + 0.212650i $$0.0682095\pi$$
$$368$$ 2.52984 0.131877
$$369$$ 4.31121 0.224433
$$370$$ 0 0
$$371$$ −12.8644 + 22.2818i −0.667887 + 1.15681i
$$372$$ 3.88749 0.201557
$$373$$ 13.0913 0.677843 0.338921 0.940815i $$-0.389938\pi$$
0.338921 + 0.940815i $$0.389938\pi$$
$$374$$ −7.25164 + 12.5602i −0.374974 + 0.649473i
$$375$$ 0 0
$$376$$ 5.17312 8.96010i 0.266783 0.462082i
$$377$$ 4.08297 + 7.07192i 0.210284 + 0.364222i
$$378$$ 17.3066 + 29.9759i 0.890155 + 1.54179i
$$379$$ −32.7566 −1.68259 −0.841297 0.540573i $$-0.818208\pi$$
−0.841297 + 0.540573i $$0.818208\pi$$
$$380$$ 0 0
$$381$$ 23.3085 1.19413
$$382$$ −4.65363 8.06033i −0.238101 0.412402i
$$383$$ −12.8227 22.2096i −0.655211 1.13486i −0.981841 0.189707i $$-0.939246\pi$$
0.326630 0.945152i $$-0.394087\pi$$
$$384$$ 18.1048 31.3584i 0.923905 1.60025i
$$385$$ 0 0
$$386$$ 13.2042 22.8704i 0.672078 1.16407i
$$387$$ 5.52907 0.281059
$$388$$ −2.13328 −0.108301
$$389$$ 9.27329 16.0618i 0.470174 0.814366i −0.529244 0.848470i $$-0.677524\pi$$
0.999418 + 0.0341039i $$0.0108577\pi$$
$$390$$ 0 0
$$391$$ −1.01780 −0.0514723
$$392$$ 19.6069 0.990300
$$393$$ −27.4958 + 47.6242i −1.38698 + 2.40232i
$$394$$ −12.5846 21.7971i −0.634002 1.09812i
$$395$$ 0 0
$$396$$ 2.79981 + 4.84942i 0.140696 + 0.243692i
$$397$$ 7.69806 + 13.3334i 0.386355 + 0.669186i 0.991956 0.126582i $$-0.0404007\pi$$
−0.605601 + 0.795768i $$0.707067\pi$$
$$398$$ −24.3571 −1.22091
$$399$$ −43.8239 + 17.3593i −2.19394 + 0.869054i
$$400$$ 0 0
$$401$$ 10.2956 + 17.8326i 0.514140 + 0.890517i 0.999865 + 0.0164054i $$0.00522222\pi$$
−0.485725 + 0.874112i $$0.661444\pi$$
$$402$$ −1.65321 2.86345i −0.0824548 0.142816i
$$403$$ 17.2140 29.8155i 0.857491 1.48522i
$$404$$ −0.500248 0.866455i −0.0248883 0.0431078i
$$405$$ 0 0
$$406$$ −9.33165 −0.463122
$$407$$ 13.2212 0.655353
$$408$$ −6.68761 + 11.5833i −0.331086 + 0.573458i
$$409$$ 0.811919 1.40629i 0.0401468 0.0695363i −0.845254 0.534365i $$-0.820551\pi$$
0.885401 + 0.464829i $$0.153884\pi$$
$$410$$ 0 0
$$411$$ 4.49054 0.221502
$$412$$ −0.752330 + 1.30307i −0.0370646 + 0.0641978i
$$413$$ 0.773292 + 1.33938i 0.0380512 + 0.0659066i
$$414$$ −2.22274 + 3.84990i −0.109242 + 0.189212i
$$415$$ 0 0
$$416$$ 2.68220 + 4.64570i 0.131506 + 0.227774i
$$417$$ −5.85398 −0.286671
$$418$$ −33.5822 + 13.3024i −1.64256 + 0.650643i
$$419$$ 16.8087 0.821161 0.410580 0.911824i $$-0.365326\pi$$
0.410580 + 0.911824i $$0.365326\pi$$
$$420$$ 0 0
$$421$$ −10.4718 18.1377i −0.510365 0.883977i −0.999928 0.0120096i $$-0.996177\pi$$
0.489563 0.871968i $$-0.337156\pi$$
$$422$$ 11.5479 20.0015i 0.562142 0.973658i
$$423$$ 9.98016 + 17.2861i 0.485252 + 0.840481i
$$424$$ −9.09122 + 15.7465i −0.441509 + 0.764716i
$$425$$ 0 0
$$426$$ −26.9894 −1.30764
$$427$$ −26.4228 + 45.7656i −1.27869 + 2.21475i
$$428$$ −1.22686 + 2.12498i −0.0593023 + 0.102715i
$$429$$ 78.4175 3.78603
$$430$$ 0 0
$$431$$ −16.8908 + 29.2557i −0.813600 + 1.40920i 0.0967292 + 0.995311i $$0.469162\pi$$
−0.910329 + 0.413885i $$0.864171\pi$$
$$432$$ 13.4277 + 23.2575i 0.646041 + 1.11898i
$$433$$ 7.51443 13.0154i 0.361120 0.625479i −0.627025 0.778999i $$-0.715728\pi$$
0.988146 + 0.153520i $$0.0490610\pi$$
$$434$$ 19.6713 + 34.0718i 0.944254 + 1.63550i
$$435$$ 0 0
$$436$$ −1.58910 −0.0761043
$$437$$ −1.98681 1.57420i −0.0950419 0.0753042i
$$438$$ 12.2251 0.584139
$$439$$ −18.8607 32.6677i −0.900173 1.55915i −0.827269 0.561807i $$-0.810106\pi$$
−0.0729045 0.997339i $$-0.523227\pi$$
$$440$$ 0 0
$$441$$ −18.9132 + 32.7586i −0.900628 + 1.55993i
$$442$$ −6.35976 11.0154i −0.302503 0.523950i
$$443$$ −6.55722 + 11.3574i −0.311543 + 0.539608i −0.978697 0.205312i $$-0.934179\pi$$
0.667154 + 0.744920i $$0.267512\pi$$
$$444$$ −1.30928 −0.0621358
$$445$$ 0 0
$$446$$ 5.78129 10.0135i 0.273752 0.474153i
$$447$$ 2.10781 3.65084i 0.0996961 0.172679i
$$448$$ 26.8049 1.26641
$$449$$ 11.6905 0.551711 0.275855 0.961199i $$-0.411039\pi$$
0.275855 + 0.961199i $$0.411039\pi$$
$$450$$ 0 0
$$451$$ 2.33673 + 4.04733i 0.110032 + 0.190581i
$$452$$ −1.21744 + 2.10868i −0.0572638 + 0.0991838i
$$453$$ −9.17789 15.8966i −0.431215 0.746886i
$$454$$ 12.4799 + 21.6158i 0.585709 + 1.01448i
$$455$$ 0 0
$$456$$ −30.9701 + 12.2678i −1.45031 + 0.574490i
$$457$$ −21.4290 −1.00240 −0.501202 0.865330i $$-0.667109\pi$$
−0.501202 + 0.865330i $$0.667109\pi$$
$$458$$ −0.186175 0.322465i −0.00869939 0.0150678i
$$459$$ −5.40221 9.35691i −0.252154 0.436743i
$$460$$ 0 0
$$461$$ 4.82920 + 8.36442i 0.224918 + 0.389570i 0.956295 0.292404i $$-0.0944551\pi$$
−0.731377 + 0.681974i $$0.761122\pi$$
$$462$$ −44.8058 + 77.6060i −2.08456 + 3.61056i
$$463$$ 1.24981 0.0580838 0.0290419 0.999578i $$-0.490754\pi$$
0.0290419 + 0.999578i $$0.490754\pi$$
$$464$$ −7.24017 −0.336116
$$465$$ 0 0
$$466$$ 17.1840 29.7635i 0.796032 1.37877i
$$467$$ −31.3476 −1.45059 −0.725296 0.688437i $$-0.758297\pi$$
−0.725296 + 0.688437i $$0.758297\pi$$
$$468$$ −4.91092 −0.227007
$$469$$ 1.47897 2.56165i 0.0682925 0.118286i
$$470$$ 0 0
$$471$$ −31.8368 + 55.1430i −1.46696 + 2.54085i
$$472$$ 0.546481 + 0.946533i 0.0251538 + 0.0435677i
$$473$$ 2.99682 + 5.19065i 0.137794 + 0.238666i
$$474$$ 52.9037 2.42995
$$475$$ 0 0
$$476$$ 1.28487 0.0588918
$$477$$ −17.5391 30.3786i −0.803060 1.39094i
$$478$$ −5.61949 9.73324i −0.257029 0.445188i
$$479$$ −2.37730 + 4.11760i −0.108622 + 0.188138i −0.915212 0.402973i $$-0.867977\pi$$
0.806591 + 0.591111i $$0.201310\pi$$
$$480$$ 0 0
$$481$$ −5.79758 + 10.0417i −0.264347 + 0.457862i
$$482$$ 8.17052 0.372157
$$483$$ −6.28870 −0.286146
$$484$$ −1.96841 + 3.40939i −0.0894733 + 0.154972i
$$485$$ 0 0
$$486$$ 18.3230 0.831150
$$487$$ 17.0491 0.772569 0.386285 0.922380i $$-0.373758\pi$$
0.386285 + 0.922380i $$0.373758\pi$$
$$488$$ −18.6728 + 32.3423i −0.845280 + 1.46407i
$$489$$ 21.4714 + 37.1896i 0.970970 + 1.68177i
$$490$$ 0 0
$$491$$ 2.14031 + 3.70713i 0.0965910 + 0.167301i 0.910272 0.414012i $$-0.135873\pi$$
−0.813680 + 0.581312i $$0.802539\pi$$
$$492$$ −0.231403 0.400802i −0.0104325 0.0180696i
$$493$$ 2.91285 0.131188
$$494$$ 4.62258 31.3392i 0.207980 1.41002i
$$495$$ 0 0
$$496$$ 15.2624 + 26.4353i 0.685304 + 1.18698i
$$497$$ −12.0724 20.9100i −0.541521 0.937942i
$$498$$ 21.9826 38.0750i 0.985064 1.70618i
$$499$$ 2.41284 + 4.17916i 0.108013 + 0.187085i 0.914965 0.403532i $$-0.132218\pi$$
−0.806952 + 0.590617i $$0.798884\pi$$
$$500$$ 0 0
$$501$$ 27.4206 1.22506
$$502$$ 27.6371 1.23350
$$503$$ 12.1368 21.0215i 0.541153 0.937304i −0.457685 0.889114i $$-0.651321\pi$$
0.998838 0.0481900i $$-0.0153453\pi$$
$$504$$ −26.1311 + 45.2604i −1.16397 + 2.01606i
$$505$$ 0 0
$$506$$ −4.81901 −0.214231
$$507$$ −15.8176 + 27.3969i −0.702485 + 1.21674i
$$508$$ −0.791177 1.37036i −0.0351028 0.0607998i
$$509$$ 5.05690 8.75880i 0.224143 0.388227i −0.731919 0.681392i $$-0.761375\pi$$
0.956062 + 0.293165i $$0.0947084\pi$$
$$510$$ 0 0
$$511$$ 5.46831 + 9.47140i 0.241904 + 0.418990i
$$512$$ 18.5188 0.818423
$$513$$ 3.92659 26.6207i 0.173363 1.17533i
$$514$$ −1.02603 −0.0452562
$$515$$ 0 0
$$516$$ −0.296772 0.514024i −0.0130646 0.0226286i
$$517$$ −10.8187 + 18.7386i −0.475807 + 0.824123i
$$518$$ −6.62519 11.4752i −0.291094 0.504190i
$$519$$ 12.6157 21.8510i 0.553767 0.959153i
$$520$$ 0 0
$$521$$ 29.3729 1.28685 0.643426 0.765508i $$-0.277513\pi$$
0.643426 + 0.765508i $$0.277513\pi$$
$$522$$ 6.36129 11.0181i 0.278426 0.482248i
$$523$$ 5.59998 9.69944i 0.244870 0.424127i −0.717225 0.696842i $$-0.754588\pi$$
0.962095 + 0.272714i $$0.0879214\pi$$
$$524$$ 3.73324 0.163087
$$525$$ 0 0
$$526$$ 8.61074 14.9142i 0.375446 0.650292i
$$527$$ −6.14037 10.6354i −0.267479 0.463286i
$$528$$ −34.7636 + 60.2124i −1.51289 + 2.62041i
$$529$$ 11.3309 + 19.6257i 0.492648 + 0.853292i
$$530$$ 0 0
$$531$$ −2.10858 −0.0915046
$$532$$ 2.50814 + 1.98726i 0.108742 + 0.0861588i
$$533$$ −4.09866 −0.177533
$$534$$ 37.7485 + 65.3822i 1.63354 + 2.82937i
$$535$$ 0 0
$$536$$ 1.04518 1.81031i 0.0451450 0.0781934i
$$537$$ −15.4519 26.7634i −0.666798 1.15493i
$$538$$ −17.4866 + 30.2877i −0.753901 + 1.30579i
$$539$$ −41.0047 −1.76620
$$540$$ 0 0
$$541$$ −2.84691 + 4.93100i −0.122398 + 0.212000i −0.920713 0.390241i $$-0.872392\pi$$
0.798315 + 0.602241i $$0.205725\pi$$
$$542$$ −5.65809 + 9.80010i −0.243036 + 0.420950i
$$543$$ 30.7019 1.31754
$$544$$ 1.91352 0.0820415
$$545$$ 0 0
$$546$$ −39.2951 68.0612i −1.68168 2.91275i
$$547$$ −5.99088 + 10.3765i −0.256151 + 0.443667i −0.965208 0.261485i $$-0.915788\pi$$
0.709056 + 0.705152i $$0.249121\pi$$
$$548$$ −0.152425 0.264009i −0.00651129 0.0112779i
$$549$$ −36.0243 62.3959i −1.53748 2.66299i
$$550$$ 0 0
$$551$$ 5.68607 + 4.50522i 0.242235 + 0.191929i
$$552$$ −4.44419 −0.189157
$$553$$ 23.6639 + 40.9871i 1.00629 + 1.74295i
$$554$$ −13.8149 23.9281i −0.586939 1.01661i
$$555$$ 0 0
$$556$$ 0.198706 + 0.344168i 0.00842700 + 0.0145960i
$$557$$ 17.2786 29.9275i 0.732119 1.26807i −0.223857 0.974622i $$-0.571865\pi$$
0.955976 0.293446i $$-0.0948019\pi$$
$$558$$ −53.6390 −2.27072
$$559$$ −5.25649 −0.222326
$$560$$ 0 0
$$561$$ 13.9860 24.2245i 0.590491 1.02276i
$$562$$ −20.7216 −0.874087
$$563$$ 24.8817 1.04864 0.524318 0.851522i $$-0.324320\pi$$
0.524318 + 0.851522i $$0.324320\pi$$
$$564$$ 1.07137 1.85566i 0.0451126 0.0781374i
$$565$$ 0 0
$$566$$ −18.2681 + 31.6413i −0.767867 + 1.32998i
$$567$$ −4.07422 7.05676i −0.171101 0.296356i
$$568$$ −8.53150 14.7770i −0.357974 0.620029i
$$569$$ −38.7345 −1.62384 −0.811918 0.583771i $$-0.801577\pi$$
−0.811918 + 0.583771i $$0.801577\pi$$
$$570$$ 0 0
$$571$$ −4.53514 −0.189790 −0.0948948 0.995487i $$-0.530251\pi$$
−0.0948948 + 0.995487i $$0.530251\pi$$
$$572$$ −2.66178 4.61034i −0.111295 0.192768i
$$573$$ 8.97534 + 15.5457i 0.374950 + 0.649433i
$$574$$ 2.34188 4.05625i 0.0977481 0.169305i
$$575$$ 0 0
$$576$$ −18.2726 + 31.6491i −0.761359 + 1.31871i
$$577$$ 21.9514 0.913847 0.456923 0.889506i $$-0.348951\pi$$
0.456923 + 0.889506i $$0.348951\pi$$
$$578$$ 20.6432 0.858642
$$579$$ −25.4666 + 44.1095i −1.05836 + 1.83313i
$$580$$ 0 0
$$581$$ 39.3314 1.63174
$$582$$ 46.5448 1.92934
$$583$$ 19.0128 32.9311i 0.787430 1.36387i
$$584$$ 3.86443 + 6.69339i 0.159911 + 0.276974i
$$585$$ 0 0
$$586$$ 7.83430 + 13.5694i 0.323632 + 0.560547i
$$587$$ −20.5232 35.5472i −0.847084 1.46719i −0.883799 0.467866i $$-0.845023\pi$$
0.0367158 0.999326i $$-0.488310\pi$$
$$588$$ 4.06064 0.167458
$$589$$ 4.46311 30.2581i 0.183899 1.24676i
$$590$$ 0 0
$$591$$ 24.2715 + 42.0395i 0.998397 + 1.72927i
$$592$$ −5.14030 8.90327i −0.211265 0.365922i
$$593$$ −4.85982 + 8.41745i −0.199569 + 0.345663i −0.948389 0.317110i $$-0.897287\pi$$
0.748820 + 0.662774i $$0.230621\pi$$
$$594$$ −25.5780 44.3025i −1.04948 1.81775i
$$595$$ 0 0
$$596$$ −0.286188 −0.0117227
$$597$$ 46.9769 1.92264
$$598$$ 2.11316 3.66010i 0.0864135 0.149673i
$$599$$ 15.2247 26.3700i 0.622065 1.07745i −0.367036 0.930207i $$-0.619627\pi$$
0.989101 0.147241i $$-0.0470392\pi$$
$$600$$ 0 0
$$601$$ 24.5483 1.00135 0.500673 0.865637i $$-0.333086\pi$$
0.500673 + 0.865637i $$0.333086\pi$$
$$602$$ 3.00343 5.20209i 0.122411 0.212021i
$$603$$ 2.01640 + 3.49251i 0.0821142 + 0.142226i
$$604$$ −0.623063 + 1.07918i −0.0253521 + 0.0439111i
$$605$$ 0 0
$$606$$ 10.9146 + 18.9047i 0.443376 + 0.767949i
$$607$$ −39.0162 −1.58362 −0.791810 0.610767i $$-0.790861\pi$$
−0.791810 + 0.610767i $$0.790861\pi$$
$$608$$ 3.73531 + 2.95958i 0.151487 + 0.120027i
$$609$$ 17.9977 0.729303
$$610$$ 0 0
$$611$$ −9.48813 16.4339i −0.383849 0.664845i
$$612$$ −0.875881 + 1.51707i −0.0354054 + 0.0613239i
$$613$$ 2.48708 + 4.30775i 0.100452 + 0.173988i 0.911871 0.410477i $$-0.134638\pi$$
−0.811419 + 0.584465i $$0.801304\pi$$
$$614$$ −9.49775 + 16.4506i −0.383298 + 0.663891i
$$615$$ 0 0
$$616$$ −56.6536 −2.28264
$$617$$ −19.3210 + 33.4649i −0.777834 + 1.34725i 0.155354 + 0.987859i $$0.450348\pi$$
−0.933188 + 0.359389i $$0.882985\pi$$
$$618$$ 16.4146 28.4310i 0.660293 1.14366i
$$619$$ −27.9053 −1.12161 −0.560804 0.827949i $$-0.689508\pi$$
−0.560804 + 0.827949i $$0.689508\pi$$
$$620$$ 0 0
$$621$$ 1.79500 3.10902i 0.0720307 0.124761i
$$622$$ 2.53807 + 4.39607i 0.101767 + 0.176266i
$$623$$ −33.7699 + 58.4912i −1.35296 + 2.34340i
$$624$$ −30.4880 52.8068i −1.22050 2.11396i
$$625$$ 0 0
$$626$$ −4.21322 −0.168394
$$627$$ 64.7690 25.6560i 2.58662 1.02460i
$$628$$ 4.32264 0.172492
$$629$$ 2.06804 + 3.58195i 0.0824581 + 0.142822i
$$630$$ 0 0
$$631$$ 6.62012 11.4664i 0.263543 0.456469i −0.703638 0.710559i $$-0.748442\pi$$
0.967181 + 0.254089i $$0.0817757\pi$$
$$632$$ 16.7232 + 28.9654i 0.665212 + 1.15218i
$$633$$ −22.2721 + 38.5763i −0.885235 + 1.53327i
$$634$$ −6.90451 −0.274213
$$635$$ 0 0
$$636$$ −1.88281 + 3.26113i −0.0746584 + 0.129312i
$$637$$ 17.9808 31.1436i 0.712423 1.23395i
$$638$$ 13.7916 0.546014
$$639$$ 32.9185 1.30224
$$640$$ 0 0
$$641$$ −18.7555 32.4854i −0.740796 1.28310i −0.952133 0.305684i $$-0.901115\pi$$
0.211337 0.977413i $$-0.432218\pi$$
$$642$$ 26.7680 46.3636i 1.05645 1.82982i
$$643$$ −12.1969 21.1257i −0.481000 0.833117i 0.518762 0.854919i $$-0.326393\pi$$
−0.999762 + 0.0218020i $$0.993060\pi$$
$$644$$ 0.213462 + 0.369726i 0.00841157 + 0.0145693i
$$645$$ 0 0
$$646$$ −8.85679 7.01746i −0.348466 0.276098i
$$647$$ −8.05266 −0.316583 −0.158291 0.987392i $$-0.550599\pi$$
−0.158291 + 0.987392i $$0.550599\pi$$
$$648$$ −2.87923 4.98698i −0.113107 0.195907i
$$649$$ −1.14288 1.97952i −0.0448618 0.0777030i
$$650$$ 0 0
$$651$$ −37.9396 65.7133i −1.48697 2.57551i
$$652$$ 1.45764 2.52470i 0.0570855 0.0988750i
$$653$$ 19.9890 0.782228 0.391114 0.920342i $$-0.372090\pi$$
0.391114 + 0.920342i $$0.372090\pi$$
$$654$$ 34.6717 1.35577
$$655$$ 0 0
$$656$$ 1.81700 3.14713i 0.0709419 0.122875i
$$657$$ −14.9108 −0.581725
$$658$$ 21.6852 0.845375
$$659$$ 16.2197 28.0933i 0.631829 1.09436i −0.355349 0.934734i $$-0.615638\pi$$
0.987178 0.159626i $$-0.0510287\pi$$
$$660$$ 0 0
$$661$$ 17.7771 30.7908i 0.691448 1.19762i −0.279915 0.960025i $$-0.590306\pi$$
0.971363 0.237599i $$-0.0763603\pi$$
$$662$$ −5.18610 8.98260i −0.201564 0.349118i
$$663$$ 12.2659 + 21.2451i 0.476368 + 0.825093i
$$664$$ 27.7953 1.07867
$$665$$ 0 0
$$666$$ 18.0653 0.700017
$$667$$ 0.483927 + 0.838187i 0.0187377 + 0.0324547i
$$668$$ −0.930757 1.61212i −0.0360121 0.0623747i
$$669$$ −11.1502 + 19.3127i −0.431092 + 0.746674i
$$670$$ 0 0
$$671$$ 39.0512 67.6387i 1.50755 2.61116i
$$672$$ 11.8231 0.456086
$$673$$ −27.5963 −1.06376 −0.531880 0.846820i $$-0.678514\pi$$
−0.531880 + 0.846820i $$0.678514\pi$$
$$674$$ 10.0259 17.3654i 0.386184 0.668891i
$$675$$ 0 0
$$676$$ 2.14763 0.0826013
$$677$$ −21.2114 −0.815221 −0.407610 0.913156i $$-0.633638\pi$$
−0.407610 + 0.913156i $$0.633638\pi$$
$$678$$ 26.5627 46.0079i 1.02013 1.76692i
$$679$$ 20.8196 + 36.0605i 0.798981 + 1.38388i
$$680$$ 0 0
$$681$$ −24.0696 41.6897i −0.922348 1.59755i
$$682$$ −29.0730 50.3559i −1.11326 1.92823i
$$683$$ −19.3626 −0.740891 −0.370446 0.928854i $$-0.620795\pi$$
−0.370446 + 0.928854i $$0.620795\pi$$
$$684$$ −4.05618 + 1.60672i −0.155092 + 0.0614344i
$$685$$ 0 0
$$686$$ 0.923282 + 1.59917i 0.0352511 + 0.0610567i
$$687$$ 0.359071 + 0.621929i 0.0136994 + 0.0237281i
$$688$$ 2.33028 4.03616i 0.0888410 0.153877i
$$689$$ 16.6744 + 28.8809i 0.635244 + 1.10028i
$$690$$ 0 0
$$691$$ −1.28081 −0.0487241 −0.0243621 0.999703i $$-0.507755\pi$$
−0.0243621 + 0.999703i $$0.507755\pi$$
$$692$$ −1.71289 −0.0651144
$$693$$ 54.6490 94.6548i 2.07594 3.59564i
$$694$$ −16.2660 + 28.1735i −0.617448 + 1.06945i
$$695$$ 0 0
$$696$$ 12.7189 0.482108
$$697$$ −0.731012 + 1.26615i −0.0276891 + 0.0479588i
$$698$$ −16.4361 28.4681i −0.622114 1.07753i
$$699$$ −33.1423 + 57.4041i −1.25356 + 2.17122i
$$700$$ 0 0
$$701$$ 18.5649 + 32.1553i 0.701185 + 1.21449i 0.968051 + 0.250754i $$0.0806787\pi$$
−0.266866 + 0.963734i $$0.585988\pi$$
$$702$$ 44.8644 1.69330
$$703$$ −1.50315 + 10.1908i −0.0566924 + 0.384352i
$$704$$ −39.6159 −1.49308
$$705$$ 0 0
$$706$$ 0.502875 + 0.871005i 0.0189260 + 0.0327807i
$$707$$ −9.76425 + 16.9122i −0.367222 + 0.636048i
$$708$$ 0.113178 + 0.196029i 0.00425347 + 0.00736723i
$$709$$ −6.57886 + 11.3949i −0.247074 + 0.427945i −0.962713 0.270526i $$-0.912802\pi$$
0.715638 + 0.698471i $$0.246136\pi$$
$$710$$ 0 0
$$711$$ −64.5258 −2.41991
$$712$$ −23.8650 + 41.3354i −0.894379 + 1.54911i
$$713$$ 2.04026 3.53384i 0.0764084 0.132343i
$$714$$ −28.0337 −1.04914
$$715$$ 0 0
$$716$$ −1.04899 + 1.81690i −0.0392025 + 0.0679007i
$$717$$ 10.8382 + 18.7722i 0.404758 + 0.701062i
$$718$$ −18.7560 + 32.4863i −0.699967 + 1.21238i
$$719$$ −7.27853 12.6068i −0.271443 0.470153i 0.697788 0.716304i $$-0.254168\pi$$
−0.969232 + 0.246150i $$0.920834\pi$$
$$720$$ 0 0
$$721$$ 29.3692 1.09376
$$722$$ −6.43530 27.3970i −0.239497 1.01961i
$$723$$ −15.7583 −0.586056
$$724$$ −1.04214 1.80503i −0.0387306 0.0670834i
$$725$$ 0 0
$$726$$ 42.9476 74.3874i 1.59394 2.76078i
$$727$$ 4.48581 + 7.76966i 0.166370 + 0.288161i 0.937141 0.348951i $$-0.113462\pi$$
−0.770771 + 0.637112i $$0.780129\pi$$
$$728$$ 24.8428 43.0291i 0.920737 1.59476i
$$729$$ −41.7969 −1.54803
$$730$$ 0 0
$$731$$ −0.937514 + 1.62382i −0.0346752 + 0.0600592i
$$732$$ −3.86719 + 6.69817i −0.142935 + 0.247571i
$$733$$ −24.7325 −0.913516 −0.456758 0.889591i $$-0.650990\pi$$
−0.456758 + 0.889591i $$0.650990\pi$$
$$734$$ 17.2753 0.637642
$$735$$ 0 0
$$736$$ 0.317903 + 0.550624i 0.0117181 + 0.0202963i
$$737$$ −2.18583 + 3.78596i −0.0805159 + 0.139458i
$$738$$ 3.19287 + 5.53021i 0.117531 + 0.203570i
$$739$$ 0.784588 + 1.35895i 0.0288615 + 0.0499896i 0.880095 0.474797i $$-0.157478\pi$$
−0.851234 + 0.524787i $$0.824145\pi$$
$$740$$ 0 0
$$741$$ −8.91543 + 60.4431i −0.327517 + 2.22043i
$$742$$ −38.1094 −1.39904
$$743$$ −12.1463 21.0380i −0.445604 0.771808i 0.552490 0.833519i $$-0.313678\pi$$
−0.998094 + 0.0617109i $$0.980344\pi$$
$$744$$ −26.8117 46.4392i −0.982965 1.70254i
$$745$$ 0 0
$$746$$ 9.69539 + 16.7929i 0.354974 + 0.614832i
$$747$$ −26.8119 + 46.4395i −0.980994 + 1.69913i
$$748$$ −1.89895 −0.0694326
$$749$$ 47.8935 1.74999
$$750$$ 0 0
$$751$$ −17.4771 + 30.2712i −0.637748 + 1.10461i 0.348178 + 0.937429i $$0.386801\pi$$
−0.985926 + 0.167184i $$0.946533\pi$$
$$752$$ 16.8249 0.613541
$$753$$ −53.3029 −1.94247
$$754$$ −6.04768 + 10.4749i −0.220243 + 0.381473i
$$755$$ 0 0
$$756$$ −2.26600 + 3.92482i −0.0824135 + 0.142744i
$$757$$ −1.61043 2.78935i −0.0585321 0.101381i 0.835275 0.549833i $$-0.185309\pi$$
−0.893807 + 0.448452i $$0.851975\pi$$
$$758$$ −24.2595 42.0186i −0.881143 1.52619i
$$759$$ 9.29430 0.337362
$$760$$ 0 0
$$761$$ 3.72402 0.134996 0.0674979 0.997719i $$-0.478498\pi$$
0.0674979 + 0.997719i $$0.478498\pi$$
$$762$$ 17.2622 + 29.8990i 0.625344 + 1.08313i
$$763$$ 15.5087 + 26.8619i 0.561453 + 0.972465i
$$764$$ 0.609312 1.05536i 0.0220441 0.0381816i
$$765$$ 0 0
$$766$$ 18.9930 32.8968i 0.686244 1.18861i
$$767$$ 2.00463 0.0723829
$$768$$ 13.1756 0.475435
$$769$$ 16.1032 27.8915i 0.580695 1.00579i −0.414702 0.909957i $$-0.636114\pi$$
0.995397 0.0958365i $$-0.0305526\pi$$
$$770$$ 0 0
$$771$$ 1.97887 0.0712674
$$772$$ 3.45773 0.124446
$$773$$ 10.3416 17.9122i 0.371963 0.644259i −0.617904 0.786253i $$-0.712018\pi$$
0.989867 + 0.141994i $$0.0453515\pi$$
$$774$$ 4.09482 + 7.09243i 0.147185 + 0.254932i
$$775$$ 0 0
$$776$$ 14.7131 + 25.4838i 0.528169 + 0.914815i
$$777$$ 12.7778 + 22.1318i 0.458402 + 0.793975i
$$778$$ 27.4711