# Properties

 Label 225.2.k.c.49.8 Level $225$ Weight $2$ Character 225.49 Analytic conductor $1.797$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 225.k (of order $$6$$, degree $$2$$, 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: $$1.79663404548$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81$$ x^16 - 12*x^14 + 102*x^12 - 406*x^10 + 1167*x^8 - 1842*x^6 + 2023*x^4 - 441*x^2 + 81 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.8 Root $$2.28087 - 1.31686i$$ of defining polynomial Character $$\chi$$ $$=$$ 225.49 Dual form 225.2.k.c.124.8

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(2.28087 - 1.31686i) q^{2} +(0.238330 + 1.71558i) q^{3} +(2.46825 - 4.27513i) q^{4} +(2.80278 + 3.59916i) q^{6} +(-1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 + 0.817746i) q^{9} +O(q^{10})$$ $$q+(2.28087 - 1.31686i) q^{2} +(0.238330 + 1.71558i) q^{3} +(2.46825 - 4.27513i) q^{4} +(2.80278 + 3.59916i) q^{6} +(-1.55662 + 0.898714i) q^{7} -7.73393i q^{8} +(-2.88640 + 0.817746i) q^{9} +(-0.904062 - 1.56588i) q^{11} +(7.92257 + 3.21558i) q^{12} +(1.70765 + 0.985914i) q^{13} +(-2.36696 + 4.09970i) q^{14} +(-5.24801 - 9.08982i) q^{16} +4.80812i q^{17} +(-5.50664 + 5.66616i) q^{18} -2.96467 q^{19} +(-1.91280 - 2.45630i) q^{21} +(-4.12410 - 2.38105i) q^{22} +(-1.50162 - 0.866963i) q^{23} +(13.2681 - 1.84323i) q^{24} +5.19325 q^{26} +(-2.09082 - 4.75694i) q^{27} +8.87300i q^{28} +(-3.68382 - 6.38057i) q^{29} +(1.31151 - 2.27161i) q^{31} +(-10.5445 - 6.08789i) q^{32} +(2.47092 - 1.92418i) q^{33} +(6.33163 + 10.9667i) q^{34} +(-3.62838 + 14.3581i) q^{36} +11.6351i q^{37} +(-6.76203 + 3.90406i) q^{38} +(-1.28442 + 3.16458i) q^{39} +(1.23324 - 2.13603i) q^{41} +(-7.59746 - 3.08362i) q^{42} +(6.30306 - 3.63907i) q^{43} -8.92580 q^{44} -4.56668 q^{46} +(5.44910 - 3.14604i) q^{47} +(14.3435 - 11.1697i) q^{48} +(-1.88463 + 3.26427i) q^{49} +(-8.24870 + 1.14592i) q^{51} +(8.42983 - 4.86696i) q^{52} -1.72540i q^{53} +(-11.0331 - 8.09664i) q^{54} +(6.95059 + 12.0388i) q^{56} +(-0.706570 - 5.08612i) q^{57} +(-16.8047 - 9.70218i) q^{58} +(5.51300 - 9.54880i) q^{59} +(6.33521 + 10.9729i) q^{61} -6.90833i q^{62} +(3.75810 - 3.86696i) q^{63} -11.0756 q^{64} +(3.10197 - 7.64268i) q^{66} +(-7.88407 - 4.55187i) q^{67} +(20.5554 + 11.8676i) q^{68} +(1.12946 - 2.78277i) q^{69} +1.27460 q^{71} +(6.32439 + 22.3232i) q^{72} +3.58770i q^{73} +(15.3218 + 26.5382i) q^{74} +(-7.31755 + 12.6744i) q^{76} +(2.81456 + 1.62499i) q^{77} +(1.23771 + 8.90941i) q^{78} +(1.05545 + 1.82809i) q^{79} +(7.66258 - 4.72068i) q^{81} -6.49602i q^{82} +(-0.951614 + 0.549415i) q^{83} +(-15.2223 + 2.11470i) q^{84} +(9.58431 - 16.6005i) q^{86} +(10.0684 - 7.84056i) q^{87} +(-12.1104 + 6.99195i) q^{88} +13.2935 q^{89} -3.54422 q^{91} +(-7.41277 + 4.27976i) q^{92} +(4.20969 + 1.70861i) q^{93} +(8.28580 - 14.3514i) q^{94} +(7.93115 - 19.5409i) q^{96} +(-3.31926 + 1.91638i) q^{97} +9.92718i q^{98} +(3.88998 + 3.78046i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10})$$ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 $$16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100})$$ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.28087 1.31686i 1.61282 0.931162i 0.624107 0.781339i $$-0.285463\pi$$
0.988713 0.149823i $$-0.0478703\pi$$
$$3$$ 0.238330 + 1.71558i 0.137600 + 0.990488i
$$4$$ 2.46825 4.27513i 1.23412 2.13757i
$$5$$ 0 0
$$6$$ 2.80278 + 3.59916i 1.14423 + 1.46935i
$$7$$ −1.55662 + 0.898714i −0.588346 + 0.339682i −0.764443 0.644691i $$-0.776986\pi$$
0.176097 + 0.984373i $$0.443653\pi$$
$$8$$ 7.73393i 2.73436i
$$9$$ −2.88640 + 0.817746i −0.962133 + 0.272582i
$$10$$ 0 0
$$11$$ −0.904062 1.56588i −0.272585 0.472131i 0.696938 0.717131i $$-0.254545\pi$$
−0.969523 + 0.245000i $$0.921212\pi$$
$$12$$ 7.92257 + 3.21558i 2.28705 + 0.928257i
$$13$$ 1.70765 + 0.985914i 0.473618 + 0.273443i 0.717753 0.696298i $$-0.245171\pi$$
−0.244135 + 0.969741i $$0.578504\pi$$
$$14$$ −2.36696 + 4.09970i −0.632598 + 1.09569i
$$15$$ 0 0
$$16$$ −5.24801 9.08982i −1.31200 2.27246i
$$17$$ 4.80812i 1.16614i 0.812421 + 0.583071i $$0.198149\pi$$
−0.812421 + 0.583071i $$0.801851\pi$$
$$18$$ −5.50664 + 5.66616i −1.29793 + 1.33553i
$$19$$ −2.96467 −0.680142 −0.340071 0.940400i $$-0.610451\pi$$
−0.340071 + 0.940400i $$0.610451\pi$$
$$20$$ 0 0
$$21$$ −1.91280 2.45630i −0.417407 0.536010i
$$22$$ −4.12410 2.38105i −0.879261 0.507641i
$$23$$ −1.50162 0.866963i −0.313110 0.180774i 0.335207 0.942144i $$-0.391194\pi$$
−0.648317 + 0.761370i $$0.724527\pi$$
$$24$$ 13.2681 1.84323i 2.70835 0.376247i
$$25$$ 0 0
$$26$$ 5.19325 1.01848
$$27$$ −2.09082 4.75694i −0.402379 0.915473i
$$28$$ 8.87300i 1.67684i
$$29$$ −3.68382 6.38057i −0.684069 1.18484i −0.973728 0.227713i $$-0.926875\pi$$
0.289659 0.957130i $$-0.406458\pi$$
$$30$$ 0 0
$$31$$ 1.31151 2.27161i 0.235555 0.407993i −0.723879 0.689927i $$-0.757643\pi$$
0.959434 + 0.281934i $$0.0909760\pi$$
$$32$$ −10.5445 6.08789i −1.86403 1.07620i
$$33$$ 2.47092 1.92418i 0.430132 0.334957i
$$34$$ 6.33163 + 10.9667i 1.08587 + 1.88078i
$$35$$ 0 0
$$36$$ −3.62838 + 14.3581i −0.604729 + 2.39302i
$$37$$ 11.6351i 1.91280i 0.292063 + 0.956399i $$0.405658\pi$$
−0.292063 + 0.956399i $$0.594342\pi$$
$$38$$ −6.76203 + 3.90406i −1.09695 + 0.633322i
$$39$$ −1.28442 + 3.16458i −0.205673 + 0.506738i
$$40$$ 0 0
$$41$$ 1.23324 2.13603i 0.192600 0.333592i −0.753511 0.657435i $$-0.771641\pi$$
0.946111 + 0.323842i $$0.104975\pi$$
$$42$$ −7.59746 3.08362i −1.17231 0.475813i
$$43$$ 6.30306 3.63907i 0.961207 0.554953i 0.0646628 0.997907i $$-0.479403\pi$$
0.896544 + 0.442954i $$0.146069\pi$$
$$44$$ −8.92580 −1.34562
$$45$$ 0 0
$$46$$ −4.56668 −0.673321
$$47$$ 5.44910 3.14604i 0.794833 0.458897i −0.0468283 0.998903i $$-0.514911\pi$$
0.841661 + 0.540006i $$0.181578\pi$$
$$48$$ 14.3435 11.1697i 2.07031 1.61221i
$$49$$ −1.88463 + 3.26427i −0.269233 + 0.466324i
$$50$$ 0 0
$$51$$ −8.24870 + 1.14592i −1.15505 + 0.160461i
$$52$$ 8.42983 4.86696i 1.16901 0.674926i
$$53$$ 1.72540i 0.237001i −0.992954 0.118501i $$-0.962191\pi$$
0.992954 0.118501i $$-0.0378088\pi$$
$$54$$ −11.0331 8.09664i −1.50142 1.10181i
$$55$$ 0 0
$$56$$ 6.95059 + 12.0388i 0.928811 + 1.60875i
$$57$$ −0.706570 5.08612i −0.0935875 0.673673i
$$58$$ −16.8047 9.70218i −2.20656 1.27396i
$$59$$ 5.51300 9.54880i 0.717732 1.24315i −0.244165 0.969734i $$-0.578514\pi$$
0.961896 0.273414i $$-0.0881529\pi$$
$$60$$ 0 0
$$61$$ 6.33521 + 10.9729i 0.811141 + 1.40494i 0.912066 + 0.410043i $$0.134486\pi$$
−0.100925 + 0.994894i $$0.532180\pi$$
$$62$$ 6.90833i 0.877358i
$$63$$ 3.75810 3.86696i 0.473476 0.487192i
$$64$$ −11.0756 −1.38445
$$65$$ 0 0
$$66$$ 3.10197 7.64268i 0.381826 0.940748i
$$67$$ −7.88407 4.55187i −0.963193 0.556100i −0.0660386 0.997817i $$-0.521036\pi$$
−0.897154 + 0.441717i $$0.854369\pi$$
$$68$$ 20.5554 + 11.8676i 2.49271 + 1.43916i
$$69$$ 1.12946 2.78277i 0.135971 0.335006i
$$70$$ 0 0
$$71$$ 1.27460 0.151268 0.0756338 0.997136i $$-0.475902\pi$$
0.0756338 + 0.997136i $$0.475902\pi$$
$$72$$ 6.32439 + 22.3232i 0.745336 + 2.63081i
$$73$$ 3.58770i 0.419908i 0.977711 + 0.209954i $$0.0673315\pi$$
−0.977711 + 0.209954i $$0.932669\pi$$
$$74$$ 15.3218 + 26.5382i 1.78112 + 3.08500i
$$75$$ 0 0
$$76$$ −7.31755 + 12.6744i −0.839380 + 1.45385i
$$77$$ 2.81456 + 1.62499i 0.320749 + 0.185184i
$$78$$ 1.23771 + 8.90941i 0.140143 + 1.00879i
$$79$$ 1.05545 + 1.82809i 0.118747 + 0.205676i 0.919272 0.393624i $$-0.128779\pi$$
−0.800524 + 0.599300i $$0.795445\pi$$
$$80$$ 0 0
$$81$$ 7.66258 4.72068i 0.851398 0.524520i
$$82$$ 6.49602i 0.717366i
$$83$$ −0.951614 + 0.549415i −0.104453 + 0.0603061i −0.551317 0.834296i $$-0.685874\pi$$
0.446863 + 0.894602i $$0.352541\pi$$
$$84$$ −15.2223 + 2.11470i −1.66089 + 0.230733i
$$85$$ 0 0
$$86$$ 9.58431 16.6005i 1.03350 1.79008i
$$87$$ 10.0684 7.84056i 1.07944 0.840596i
$$88$$ −12.1104 + 6.99195i −1.29097 + 0.745344i
$$89$$ 13.2935 1.40910 0.704552 0.709653i $$-0.251148\pi$$
0.704552 + 0.709653i $$0.251148\pi$$
$$90$$ 0 0
$$91$$ −3.54422 −0.371535
$$92$$ −7.41277 + 4.27976i −0.772834 + 0.446196i
$$93$$ 4.20969 + 1.70861i 0.436524 + 0.177174i
$$94$$ 8.28580 14.3514i 0.854615 1.48024i
$$95$$ 0 0
$$96$$ 7.93115 19.5409i 0.809470 1.99438i
$$97$$ −3.31926 + 1.91638i −0.337020 + 0.194579i −0.658954 0.752184i $$-0.729001\pi$$
0.321933 + 0.946762i $$0.395667\pi$$
$$98$$ 9.92718i 1.00280i
$$99$$ 3.88998 + 3.78046i 0.390957 + 0.379951i
$$100$$ 0 0
$$101$$ −3.27618 5.67452i −0.325993 0.564636i 0.655720 0.755004i $$-0.272365\pi$$
−0.981713 + 0.190368i $$0.939032\pi$$
$$102$$ −17.3052 + 13.4761i −1.71347 + 1.33433i
$$103$$ −6.99365 4.03779i −0.689105 0.397855i 0.114172 0.993461i $$-0.463579\pi$$
−0.803277 + 0.595606i $$0.796912\pi$$
$$104$$ 7.62499 13.2069i 0.747691 1.29504i
$$105$$ 0 0
$$106$$ −2.27211 3.93541i −0.220687 0.382241i
$$107$$ 8.97674i 0.867814i −0.900958 0.433907i $$-0.857135\pi$$
0.900958 0.433907i $$-0.142865\pi$$
$$108$$ −25.4972 2.80278i −2.45347 0.269697i
$$109$$ 6.34164 0.607419 0.303710 0.952765i $$-0.401775\pi$$
0.303710 + 0.952765i $$0.401775\pi$$
$$110$$ 0 0
$$111$$ −19.9609 + 2.77299i −1.89460 + 0.263201i
$$112$$ 16.3383 + 9.43292i 1.54382 + 0.891327i
$$113$$ −12.9060 7.45127i −1.21409 0.700957i −0.250444 0.968131i $$-0.580577\pi$$
−0.963648 + 0.267174i $$0.913910\pi$$
$$114$$ −8.30931 10.6703i −0.778238 0.999367i
$$115$$ 0 0
$$116$$ −36.3704 −3.37691
$$117$$ −5.73519 1.44931i −0.530219 0.133989i
$$118$$ 29.0394i 2.67330i
$$119$$ −4.32113 7.48441i −0.396117 0.686095i
$$120$$ 0 0
$$121$$ 3.86534 6.69497i 0.351395 0.608634i
$$122$$ 28.8996 + 16.6852i 2.61645 + 1.51061i
$$123$$ 3.95845 + 1.60663i 0.356921 + 0.144865i
$$124$$ −6.47428 11.2138i −0.581408 1.00703i
$$125$$ 0 0
$$126$$ 3.47948 13.7689i 0.309977 1.22663i
$$127$$ 3.62303i 0.321492i 0.986996 + 0.160746i $$0.0513899\pi$$
−0.986996 + 0.160746i $$0.948610\pi$$
$$128$$ −4.17289 + 2.40922i −0.368835 + 0.212947i
$$129$$ 7.74531 + 9.94607i 0.681936 + 0.875703i
$$130$$ 0 0
$$131$$ −3.64673 + 6.31631i −0.318616 + 0.551859i −0.980200 0.198012i $$-0.936551\pi$$
0.661584 + 0.749871i $$0.269885\pi$$
$$132$$ −2.12729 15.3129i −0.185157 1.33282i
$$133$$ 4.61486 2.66439i 0.400159 0.231032i
$$134$$ −23.9767 −2.07127
$$135$$ 0 0
$$136$$ 37.1857 3.18865
$$137$$ −6.17148 + 3.56310i −0.527265 + 0.304417i −0.739902 0.672715i $$-0.765128\pi$$
0.212637 + 0.977131i $$0.431795\pi$$
$$138$$ −1.08838 7.83449i −0.0926488 0.666916i
$$139$$ −7.35533 + 12.7398i −0.623871 + 1.08058i 0.364887 + 0.931052i $$0.381108\pi$$
−0.988758 + 0.149525i $$0.952226\pi$$
$$140$$ 0 0
$$141$$ 6.69595 + 8.59855i 0.563901 + 0.724128i
$$142$$ 2.90721 1.67848i 0.243967 0.140855i
$$143$$ 3.56531i 0.298146i
$$144$$ 22.5810 + 21.9453i 1.88175 + 1.82878i
$$145$$ 0 0
$$146$$ 4.72450 + 8.18308i 0.391003 + 0.677236i
$$147$$ −6.04927 2.45525i −0.498935 0.202505i
$$148$$ 49.7416 + 28.7183i 4.08873 + 2.36063i
$$149$$ −0.282655 + 0.489572i −0.0231560 + 0.0401073i −0.877371 0.479812i $$-0.840705\pi$$
0.854215 + 0.519920i $$0.174038\pi$$
$$150$$ 0 0
$$151$$ −0.0766925 0.132835i −0.00624115 0.0108100i 0.862888 0.505395i $$-0.168653\pi$$
−0.869129 + 0.494585i $$0.835320\pi$$
$$152$$ 22.9285i 1.85975i
$$153$$ −3.93183 13.8782i −0.317869 1.12198i
$$154$$ 8.55953 0.689746
$$155$$ 0 0
$$156$$ 10.3587 + 13.3021i 0.829362 + 1.06502i
$$157$$ 9.92525 + 5.73035i 0.792121 + 0.457332i 0.840709 0.541487i $$-0.182139\pi$$
−0.0485874 + 0.998819i $$0.515472\pi$$
$$158$$ 4.81469 + 2.77976i 0.383036 + 0.221146i
$$159$$ 2.96005 0.411214i 0.234747 0.0326114i
$$160$$ 0 0
$$161$$ 3.11661 0.245623
$$162$$ 11.2609 20.8578i 0.884738 1.63875i
$$163$$ 22.0595i 1.72783i 0.503637 + 0.863915i $$0.331995\pi$$
−0.503637 + 0.863915i $$0.668005\pi$$
$$164$$ −6.08789 10.5445i −0.475384 0.823389i
$$165$$ 0 0
$$166$$ −1.44701 + 2.50629i −0.112310 + 0.194526i
$$167$$ −14.7817 8.53421i −1.14384 0.660397i −0.196462 0.980511i $$-0.562945\pi$$
−0.947379 + 0.320115i $$0.896279\pi$$
$$168$$ −18.9969 + 14.7935i −1.46564 + 1.14134i
$$169$$ −4.55595 7.89113i −0.350457 0.607010i
$$170$$ 0 0
$$171$$ 8.55722 2.42435i 0.654387 0.185395i
$$172$$ 35.9285i 2.73953i
$$173$$ −10.3444 + 5.97233i −0.786468 + 0.454067i −0.838718 0.544567i $$-0.816694\pi$$
0.0522497 + 0.998634i $$0.483361\pi$$
$$174$$ 12.6398 31.1420i 0.958218 2.36087i
$$175$$ 0 0
$$176$$ −9.48906 + 16.4355i −0.715265 + 1.23887i
$$177$$ 17.6956 + 7.18221i 1.33008 + 0.539848i
$$178$$ 30.3207 17.5056i 2.27263 1.31210i
$$179$$ −8.54921 −0.638998 −0.319499 0.947587i $$-0.603515\pi$$
−0.319499 + 0.947587i $$0.603515\pi$$
$$180$$ 0 0
$$181$$ −10.5524 −0.784351 −0.392176 0.919890i $$-0.628277\pi$$
−0.392176 + 0.919890i $$0.628277\pi$$
$$182$$ −8.08390 + 4.66724i −0.599219 + 0.345959i
$$183$$ −17.3150 + 13.4837i −1.27996 + 0.996744i
$$184$$ −6.70503 + 11.6135i −0.494301 + 0.856155i
$$185$$ 0 0
$$186$$ 11.8518 1.64646i 0.869013 0.120724i
$$187$$ 7.52895 4.34684i 0.550571 0.317873i
$$188$$ 31.0608i 2.26534i
$$189$$ 7.52973 + 5.52569i 0.547708 + 0.401935i
$$190$$ 0 0
$$191$$ 8.66862 + 15.0145i 0.627239 + 1.08641i 0.988103 + 0.153792i $$0.0491485\pi$$
−0.360864 + 0.932618i $$0.617518\pi$$
$$192$$ −2.63964 19.0010i −0.190500 1.37128i
$$193$$ 1.35059 + 0.779763i 0.0972175 + 0.0561286i 0.547821 0.836596i $$-0.315458\pi$$
−0.450603 + 0.892724i $$0.648791\pi$$
$$194$$ −5.04721 + 8.74202i −0.362369 + 0.627641i
$$195$$ 0 0
$$196$$ 9.30346 + 16.1141i 0.664533 + 1.15100i
$$197$$ 17.9767i 1.28079i 0.768046 + 0.640395i $$0.221229\pi$$
−0.768046 + 0.640395i $$0.778771\pi$$
$$198$$ 13.8509 + 3.50019i 0.984339 + 0.248748i
$$199$$ −11.0225 −0.781362 −0.390681 0.920526i $$-0.627760\pi$$
−0.390681 + 0.920526i $$0.627760\pi$$
$$200$$ 0 0
$$201$$ 5.93007 14.6106i 0.418275 1.03055i
$$202$$ −14.9451 8.62856i −1.05153 0.607104i
$$203$$ 11.4686 + 6.62141i 0.804939 + 0.464732i
$$204$$ −15.4609 + 38.0927i −1.08248 + 2.66702i
$$205$$ 0 0
$$206$$ −21.2688 −1.48187
$$207$$ 5.04324 + 1.27445i 0.350529 + 0.0885806i
$$208$$ 20.6964i 1.43503i
$$209$$ 2.68025 + 4.64232i 0.185397 + 0.321116i
$$210$$ 0 0
$$211$$ 11.9643 20.7227i 0.823655 1.42661i −0.0792886 0.996852i $$-0.525265\pi$$
0.902943 0.429760i $$-0.141402\pi$$
$$212$$ −7.37630 4.25871i −0.506606 0.292489i
$$213$$ 0.303776 + 2.18668i 0.0208144 + 0.149829i
$$214$$ −11.8211 20.4748i −0.808076 1.39963i
$$215$$ 0 0
$$216$$ −36.7898 + 16.1703i −2.50323 + 1.10025i
$$217$$ 4.71470i 0.320055i
$$218$$ 14.4645 8.35107i 0.979658 0.565606i
$$219$$ −6.15497 + 0.855056i −0.415914 + 0.0577793i
$$220$$ 0 0
$$221$$ −4.74040 + 8.21061i −0.318874 + 0.552305i
$$222$$ −41.8766 + 32.6106i −2.81057 + 2.18868i
$$223$$ −18.8020 + 10.8553i −1.25907 + 0.726927i −0.972895 0.231249i $$-0.925719\pi$$
−0.286180 + 0.958176i $$0.592385\pi$$
$$224$$ 21.8851 1.46226
$$225$$ 0 0
$$226$$ −39.2492 −2.61082
$$227$$ 12.2111 7.05010i 0.810481 0.467932i −0.0366416 0.999328i $$-0.511666\pi$$
0.847123 + 0.531397i $$0.178333\pi$$
$$228$$ −23.4878 9.53312i −1.55552 0.631347i
$$229$$ 1.83879 3.18488i 0.121511 0.210463i −0.798853 0.601526i $$-0.794559\pi$$
0.920364 + 0.391064i $$0.127893\pi$$
$$230$$ 0 0
$$231$$ −2.11699 + 5.21587i −0.139288 + 0.343179i
$$232$$ −49.3469 + 28.4904i −3.23978 + 1.87049i
$$233$$ 5.34164i 0.349943i 0.984574 + 0.174971i $$0.0559833\pi$$
−0.984574 + 0.174971i $$0.944017\pi$$
$$234$$ −14.9898 + 4.24676i −0.979913 + 0.277619i
$$235$$ 0 0
$$236$$ −27.2149 47.1376i −1.77154 3.06840i
$$237$$ −2.88469 + 2.24639i −0.187380 + 0.145919i
$$238$$ −19.7119 11.3807i −1.27773 0.737698i
$$239$$ −11.0167 + 19.0815i −0.712613 + 1.23428i 0.251260 + 0.967920i $$0.419155\pi$$
−0.963873 + 0.266362i $$0.914178\pi$$
$$240$$ 0 0
$$241$$ 9.32358 + 16.1489i 0.600585 + 1.04024i 0.992733 + 0.120341i $$0.0383988\pi$$
−0.392148 + 0.919902i $$0.628268\pi$$
$$242$$ 20.3605i 1.30882i
$$243$$ 9.92491 + 12.0207i 0.636683 + 0.771126i
$$244$$ 62.5475 4.00420
$$245$$ 0 0
$$246$$ 11.1444 1.54820i 0.710542 0.0987095i
$$247$$ −5.06263 2.92291i −0.322127 0.185980i
$$248$$ −17.5684 10.1431i −1.11560 0.644091i
$$249$$ −1.16936 1.50162i −0.0741052 0.0951616i
$$250$$ 0 0
$$251$$ 14.6929 0.927407 0.463704 0.885990i $$-0.346520\pi$$
0.463704 + 0.885990i $$0.346520\pi$$
$$252$$ −7.25586 25.6110i −0.457076 1.61334i
$$253$$ 3.13515i 0.197105i
$$254$$ 4.77103 + 8.26366i 0.299361 + 0.518508i
$$255$$ 0 0
$$256$$ 4.73035 8.19320i 0.295647 0.512075i
$$257$$ −19.2335 11.1045i −1.19975 0.692678i −0.239253 0.970957i $$-0.576902\pi$$
−0.960500 + 0.278280i $$0.910236\pi$$
$$258$$ 30.7637 + 12.4862i 1.91526 + 0.777357i
$$259$$ −10.4566 18.1114i −0.649743 1.12539i
$$260$$ 0 0
$$261$$ 15.8507 + 15.4044i 0.981132 + 0.953510i
$$262$$ 19.2089i 1.18673i
$$263$$ −4.97100 + 2.87001i −0.306525 + 0.176972i −0.645370 0.763870i $$-0.723297\pi$$
0.338846 + 0.940842i $$0.389964\pi$$
$$264$$ −14.8815 19.1099i −0.915892 1.17613i
$$265$$ 0 0
$$266$$ 7.01727 12.1543i 0.430256 0.745226i
$$267$$ 3.16823 + 22.8059i 0.193892 + 1.39570i
$$268$$ −38.9197 + 22.4703i −2.37740 + 1.37259i
$$269$$ 15.6162 0.952139 0.476070 0.879408i $$-0.342061\pi$$
0.476070 + 0.879408i $$0.342061\pi$$
$$270$$ 0 0
$$271$$ −6.75315 −0.410225 −0.205112 0.978738i $$-0.565756\pi$$
−0.205112 + 0.978738i $$0.565756\pi$$
$$272$$ 43.7050 25.2331i 2.65000 1.52998i
$$273$$ −0.844693 6.08037i −0.0511232 0.368001i
$$274$$ −9.38423 + 16.2540i −0.566922 + 0.981938i
$$275$$ 0 0
$$276$$ −9.10894 11.6972i −0.548294 0.704087i
$$277$$ 26.2376 15.1483i 1.57646 0.910172i 0.581118 0.813820i $$-0.302616\pi$$
0.995347 0.0963529i $$-0.0307177\pi$$
$$278$$ 38.7438i 2.32370i
$$279$$ −1.92795 + 7.62925i −0.115423 + 0.456751i
$$280$$ 0 0
$$281$$ −9.31755 16.1385i −0.555838 0.962740i −0.997838 0.0657249i $$-0.979064\pi$$
0.441999 0.897015i $$-0.354269\pi$$
$$282$$ 26.5957 + 10.7945i 1.58375 + 0.642805i
$$283$$ −4.91354 2.83683i −0.292079 0.168632i 0.346800 0.937939i $$-0.387268\pi$$
−0.638879 + 0.769307i $$0.720602\pi$$
$$284$$ 3.14604 5.44910i 0.186683 0.323345i
$$285$$ 0 0
$$286$$ −4.69502 8.13201i −0.277622 0.480856i
$$287$$ 4.43332i 0.261690i
$$288$$ 35.4141 + 8.94931i 2.08679 + 0.527343i
$$289$$ −6.11806 −0.359886
$$290$$ 0 0
$$291$$ −4.07877 5.23772i −0.239102 0.307040i
$$292$$ 15.3379 + 8.85533i 0.897582 + 0.518219i
$$293$$ 15.8286 + 9.13867i 0.924720 + 0.533887i 0.885138 0.465329i $$-0.154064\pi$$
0.0395819 + 0.999216i $$0.487397\pi$$
$$294$$ −17.0308 + 2.36594i −0.993257 + 0.137985i
$$295$$ 0 0
$$296$$ 89.9850 5.23027
$$297$$ −5.55857 + 7.57454i −0.322541 + 0.439520i
$$298$$ 1.48887i 0.0862478i
$$299$$ −1.70950 2.96094i −0.0988631 0.171236i
$$300$$ 0 0
$$301$$ −6.54097 + 11.3293i −0.377015 + 0.653009i
$$302$$ −0.349852 0.201987i −0.0201317 0.0116230i
$$303$$ 8.95425 6.97295i 0.514408 0.400585i
$$304$$ 15.5586 + 26.9483i 0.892349 + 1.54559i
$$305$$ 0 0
$$306$$ −27.2436 26.4766i −1.55741 1.51357i
$$307$$ 15.5050i 0.884915i −0.896789 0.442458i $$-0.854107\pi$$
0.896789 0.442458i $$-0.145893\pi$$
$$308$$ 13.8941 8.02174i 0.791688 0.457081i
$$309$$ 5.26033 12.9605i 0.299250 0.737295i
$$310$$ 0 0
$$311$$ −15.2232 + 26.3673i −0.863228 + 1.49515i 0.00556798 + 0.999984i $$0.498228\pi$$
−0.868796 + 0.495170i $$0.835106\pi$$
$$312$$ 24.4746 + 9.93365i 1.38560 + 0.562382i
$$313$$ 6.01832 3.47468i 0.340176 0.196401i −0.320174 0.947359i $$-0.603741\pi$$
0.660350 + 0.750958i $$0.270408\pi$$
$$314$$ 30.1843 1.70340
$$315$$ 0 0
$$316$$ 10.4205 0.586196
$$317$$ −13.9820 + 8.07253i −0.785309 + 0.453398i −0.838308 0.545196i $$-0.816455\pi$$
0.0529995 + 0.998595i $$0.483122\pi$$
$$318$$ 6.20998 4.83590i 0.348238 0.271184i
$$319$$ −6.66081 + 11.5369i −0.372934 + 0.645940i
$$320$$ 0 0
$$321$$ 15.4003 2.13943i 0.859560 0.119411i
$$322$$ 7.10858 4.10414i 0.396146 0.228715i
$$323$$ 14.2545i 0.793142i
$$324$$ −1.26838 44.4104i −0.0704655 2.46724i
$$325$$ 0 0
$$326$$ 29.0493 + 50.3148i 1.60889 + 2.78668i
$$327$$ 1.51140 + 10.8796i 0.0835808 + 0.601642i
$$328$$ −16.5199 9.53779i −0.912160 0.526636i
$$329$$ −5.65478 + 9.79436i −0.311758 + 0.539981i
$$330$$ 0 0
$$331$$ −6.31112 10.9312i −0.346890 0.600832i 0.638805 0.769369i $$-0.279429\pi$$
−0.985695 + 0.168537i $$0.946096\pi$$
$$332$$ 5.42437i 0.297701i
$$333$$ −9.51456 33.5835i −0.521394 1.84037i
$$334$$ −44.9535 −2.45975
$$335$$ 0 0
$$336$$ −12.2890 + 30.2777i −0.670419 + 1.65179i
$$337$$ 5.99324 + 3.46020i 0.326473 + 0.188489i 0.654274 0.756258i $$-0.272974\pi$$
−0.327801 + 0.944747i $$0.606308\pi$$
$$338$$ −20.7831 11.9991i −1.13045 0.652665i
$$339$$ 9.70734 23.9170i 0.527230 1.29900i
$$340$$ 0 0
$$341$$ −4.74276 −0.256835
$$342$$ 16.3254 16.7983i 0.882776 0.908348i
$$343$$ 19.3570i 1.04518i
$$344$$ −28.1443 48.7474i −1.51744 2.62828i
$$345$$ 0 0
$$346$$ −15.7295 + 27.2442i −0.845621 + 1.46466i
$$347$$ −11.9566 6.90317i −0.641866 0.370581i 0.143467 0.989655i $$-0.454175\pi$$
−0.785333 + 0.619074i $$0.787508\pi$$
$$348$$ −8.66816 62.3962i −0.464662 3.34479i
$$349$$ 3.28384 + 5.68778i 0.175780 + 0.304460i 0.940431 0.339985i $$-0.110422\pi$$
−0.764651 + 0.644445i $$0.777089\pi$$
$$350$$ 0 0
$$351$$ 1.11954 10.1846i 0.0597564 0.543612i
$$352$$ 22.0153i 1.17342i
$$353$$ 3.05273 1.76250i 0.162481 0.0938082i −0.416555 0.909111i $$-0.636763\pi$$
0.579035 + 0.815302i $$0.303429\pi$$
$$354$$ 49.8194 6.92097i 2.64787 0.367846i
$$355$$ 0 0
$$356$$ 32.8116 56.8313i 1.73901 3.01205i
$$357$$ 11.8102 9.19698i 0.625063 0.486756i
$$358$$ −19.4996 + 11.2581i −1.03059 + 0.595010i
$$359$$ −22.9285 −1.21012 −0.605061 0.796179i $$-0.706851\pi$$
−0.605061 + 0.796179i $$0.706851\pi$$
$$360$$ 0 0
$$361$$ −10.2107 −0.537407
$$362$$ −24.0686 + 13.8960i −1.26502 + 0.730358i
$$363$$ 12.4070 + 5.03568i 0.651196 + 0.264304i
$$364$$ −8.74801 + 15.1520i −0.458520 + 0.794181i
$$365$$ 0 0
$$366$$ −21.7371 + 53.5560i −1.13621 + 2.79942i
$$367$$ 3.61939 2.08966i 0.188931 0.109079i −0.402551 0.915397i $$-0.631876\pi$$
0.591482 + 0.806318i $$0.298543\pi$$
$$368$$ 18.1993i 0.948706i
$$369$$ −1.81289 + 7.17392i −0.0943751 + 0.373459i
$$370$$ 0 0
$$371$$ 1.55064 + 2.68578i 0.0805051 + 0.139439i
$$372$$ 17.6951 13.7797i 0.917447 0.714444i
$$373$$ 5.92440 + 3.42045i 0.306754 + 0.177104i 0.645473 0.763783i $$-0.276660\pi$$
−0.338719 + 0.940888i $$0.609994\pi$$
$$374$$ 11.4484 19.8292i 0.591982 1.02534i
$$375$$ 0 0
$$376$$ −24.3312 42.1429i −1.25479 2.17336i
$$377$$ 14.5277i 0.748217i
$$378$$ 24.4509 + 2.68776i 1.25762 + 0.138244i
$$379$$ 12.7764 0.656280 0.328140 0.944629i $$-0.393578\pi$$
0.328140 + 0.944629i $$0.393578\pi$$
$$380$$ 0 0
$$381$$ −6.21558 + 0.863476i −0.318434 + 0.0442372i
$$382$$ 39.5440 + 22.8307i 2.02325 + 1.16812i
$$383$$ 6.52515 + 3.76730i 0.333420 + 0.192500i 0.657358 0.753578i $$-0.271674\pi$$
−0.323939 + 0.946078i $$0.605007\pi$$
$$384$$ −5.12773 6.58472i −0.261673 0.336025i
$$385$$ 0 0
$$386$$ 4.10736 0.209059
$$387$$ −15.2173 + 15.6581i −0.773538 + 0.795946i
$$388$$ 18.9204i 0.960538i
$$389$$ 2.72588 + 4.72135i 0.138207 + 0.239382i 0.926818 0.375511i $$-0.122533\pi$$
−0.788611 + 0.614893i $$0.789199\pi$$
$$390$$ 0 0
$$391$$ 4.16847 7.22000i 0.210808 0.365131i
$$392$$ 25.2456 + 14.5756i 1.27510 + 0.736177i
$$393$$ −11.7052 4.75087i −0.590451 0.239649i
$$394$$ 23.6729 + 41.0026i 1.19262 + 2.06568i
$$395$$ 0 0
$$396$$ 25.7634 7.29904i 1.29466 0.366791i
$$397$$ 5.64549i 0.283339i −0.989914 0.141670i $$-0.954753\pi$$
0.989914 0.141670i $$-0.0452470\pi$$
$$398$$ −25.1408 + 14.5151i −1.26020 + 0.727574i
$$399$$ 5.67082 + 7.28214i 0.283896 + 0.364563i
$$400$$ 0 0
$$401$$ 2.75209 4.76676i 0.137433 0.238040i −0.789091 0.614276i $$-0.789448\pi$$
0.926524 + 0.376235i $$0.122782\pi$$
$$402$$ −5.71438 41.1339i −0.285007 2.05157i
$$403$$ 4.47922 2.58608i 0.223126 0.128822i
$$404$$ −32.3458 −1.60926
$$405$$ 0 0
$$406$$ 34.8779 1.73096
$$407$$ 18.2192 10.5188i 0.903091 0.521400i
$$408$$ 8.86246 + 63.7948i 0.438757 + 3.15831i
$$409$$ 16.4265 28.4515i 0.812238 1.40684i −0.0990570 0.995082i $$-0.531583\pi$$
0.911295 0.411755i $$-0.135084\pi$$
$$410$$ 0 0
$$411$$ −7.58362 9.73844i −0.374072 0.480362i
$$412$$ −34.5241 + 19.9325i −1.70088 + 0.982005i
$$413$$ 19.8184i 0.975202i
$$414$$ 13.1813 3.73439i 0.647824 0.183535i
$$415$$ 0 0
$$416$$ −12.0043 20.7920i −0.588558 1.01941i
$$417$$ −23.6091 9.58235i −1.15614 0.469250i
$$418$$ 12.2266 + 7.05903i 0.598022 + 0.345268i
$$419$$ 11.4295 19.7965i 0.558369 0.967124i −0.439264 0.898358i $$-0.644761\pi$$
0.997633 0.0687656i $$-0.0219060\pi$$
$$420$$ 0 0
$$421$$ −8.97071 15.5377i −0.437205 0.757262i 0.560267 0.828312i $$-0.310698\pi$$
−0.997473 + 0.0710498i $$0.977365\pi$$
$$422$$ 63.0212i 3.06782i
$$423$$ −13.1556 + 13.5367i −0.639648 + 0.658177i
$$424$$ −13.3441 −0.648046
$$425$$ 0 0
$$426$$ 3.57243 + 4.58750i 0.173085 + 0.222265i
$$427$$ −19.7230 11.3871i −0.954463 0.551060i
$$428$$ −38.3768 22.1568i −1.85501 1.07099i
$$429$$ 6.11656 0.849720i 0.295310 0.0410249i
$$430$$ 0 0
$$431$$ −6.18871 −0.298100 −0.149050 0.988830i $$-0.547622\pi$$
−0.149050 + 0.988830i $$0.547622\pi$$
$$432$$ −32.2671 + 43.9697i −1.55245 + 2.11549i
$$433$$ 3.11806i 0.149844i 0.997189 + 0.0749221i $$0.0238708\pi$$
−0.997189 + 0.0749221i $$0.976129\pi$$
$$434$$ 6.20861 + 10.7536i 0.298023 + 0.516190i
$$435$$ 0 0
$$436$$ 15.6528 27.1114i 0.749631 1.29840i
$$437$$ 4.45182 + 2.57026i 0.212960 + 0.122952i
$$438$$ −12.9127 + 10.0555i −0.616992 + 0.480471i
$$439$$ 6.75494 + 11.6999i 0.322396 + 0.558406i 0.980982 0.194100i $$-0.0621785\pi$$
−0.658586 + 0.752505i $$0.728845\pi$$
$$440$$ 0 0
$$441$$ 2.77044 10.9631i 0.131926 0.522054i
$$442$$ 24.9698i 1.18769i
$$443$$ 21.0248 12.1387i 0.998918 0.576726i 0.0909904 0.995852i $$-0.470997\pi$$
0.907928 + 0.419126i $$0.137663\pi$$
$$444$$ −37.4135 + 92.1799i −1.77557 + 4.37466i
$$445$$ 0 0
$$446$$ −28.5899 + 49.5192i −1.35377 + 2.34480i
$$447$$ −0.907263 0.368236i −0.0429121 0.0174169i
$$448$$ 17.2404 9.95377i 0.814534 0.470271i
$$449$$ 24.1437 1.13941 0.569705 0.821849i $$-0.307057\pi$$
0.569705 + 0.821849i $$0.307057\pi$$
$$450$$ 0 0
$$451$$ −4.45970 −0.209999
$$452$$ −63.7104 + 36.7832i −2.99668 + 1.73014i
$$453$$ 0.209611 0.163230i 0.00984838 0.00766924i
$$454$$ 18.5680 32.1607i 0.871440 1.50938i
$$455$$ 0 0
$$456$$ −39.3357 + 5.46456i −1.84206 + 0.255902i
$$457$$ −2.44355 + 1.41078i −0.114304 + 0.0659937i −0.556062 0.831141i $$-0.687688\pi$$
0.441758 + 0.897134i $$0.354355\pi$$
$$458$$ 9.68573i 0.452585i
$$459$$ 22.8720 10.0529i 1.06757 0.469230i
$$460$$ 0 0
$$461$$ −10.7286 18.5825i −0.499681 0.865474i 0.500318 0.865841i $$-0.333216\pi$$
−1.00000 0.000367761i $$0.999883\pi$$
$$462$$ 2.03999 + 14.6845i 0.0949090 + 0.683185i
$$463$$ −17.1502 9.90167i −0.797037 0.460170i 0.0453970 0.998969i $$-0.485545\pi$$
−0.842434 + 0.538799i $$0.818878\pi$$
$$464$$ −38.6655 + 66.9706i −1.79500 + 3.10903i
$$465$$ 0 0
$$466$$ 7.03421 + 12.1836i 0.325853 + 0.564395i
$$467$$ 22.7210i 1.05140i 0.850669 + 0.525701i $$0.176197\pi$$
−0.850669 + 0.525701i $$0.823803\pi$$
$$468$$ −20.3519 + 20.9415i −0.940767 + 0.968019i
$$469$$ 16.3633 0.755588
$$470$$ 0 0
$$471$$ −7.46536 + 18.3932i −0.343986 + 0.847516i
$$472$$ −73.8497 42.6372i −3.39921 1.96253i
$$473$$ −11.3967 6.57989i −0.524021 0.302544i
$$474$$ −3.62141 + 8.92247i −0.166337 + 0.409822i
$$475$$ 0 0
$$476$$ −42.6625 −1.95543
$$477$$ 1.41094 + 4.98018i 0.0646023 + 0.228027i
$$478$$ 58.0300i 2.65423i
$$479$$ 10.6440 + 18.4359i 0.486336 + 0.842359i 0.999877 0.0157065i $$-0.00499974\pi$$
−0.513541 + 0.858065i $$0.671666\pi$$
$$480$$ 0 0
$$481$$ −11.4712 + 19.8687i −0.523042 + 0.905935i
$$482$$ 42.5318 + 24.5557i 1.93727 + 1.11848i
$$483$$ 0.742781 + 5.34677i 0.0337977 + 0.243287i
$$484$$ −19.0813 33.0497i −0.867330 1.50226i
$$485$$ 0 0
$$486$$ 38.4670 + 14.3478i 1.74490 + 0.650831i
$$487$$ 9.58690i 0.434424i −0.976124 0.217212i $$-0.930304\pi$$
0.976124 0.217212i $$-0.0696963\pi$$
$$488$$ 84.8637 48.9961i 3.84160 2.21795i
$$489$$ −37.8447 + 5.25743i −1.71140 + 0.237749i
$$490$$ 0 0
$$491$$ 18.9222 32.7742i 0.853945 1.47908i −0.0236745 0.999720i $$-0.507537\pi$$
0.877620 0.479357i $$-0.159130\pi$$
$$492$$ 16.6390 12.9573i 0.750144 0.584160i
$$493$$ 30.6786 17.7123i 1.38169 0.797721i
$$494$$ −15.3963 −0.692711
$$495$$ 0 0
$$496$$ −27.5314 −1.23619
$$497$$ −1.98407 + 1.14550i −0.0889977 + 0.0513829i
$$498$$ −4.64459 1.88513i −0.208129 0.0844745i
$$499$$ 8.46266 14.6577i 0.378840 0.656171i −0.612053 0.790816i $$-0.709656\pi$$
0.990894 + 0.134646i $$0.0429896\pi$$
$$500$$ 0 0
$$501$$ 11.1182 27.3930i 0.496723 1.22383i
$$502$$ 33.5126 19.3485i 1.49574 0.863566i
$$503$$ 40.4168i 1.80210i −0.433719 0.901048i $$-0.642799\pi$$
0.433719 0.901048i $$-0.357201\pi$$
$$504$$ −29.9068 29.0649i −1.33216 1.29465i
$$505$$ 0 0
$$506$$ 4.12856 + 7.15088i 0.183537 + 0.317896i
$$507$$ 12.4520 9.69676i 0.553013 0.430648i
$$508$$ 15.4889 + 8.94253i 0.687210 + 0.396761i
$$509$$ −20.7034 + 35.8593i −0.917660 + 1.58943i −0.114701 + 0.993400i $$0.536591\pi$$
−0.802959 + 0.596034i $$0.796742\pi$$
$$510$$ 0 0
$$511$$ −3.22431 5.58467i −0.142635 0.247051i
$$512$$ 34.5537i 1.52707i
$$513$$ 6.19860 + 14.1028i 0.273675 + 0.622652i
$$514$$ −58.4922 −2.57998
$$515$$ 0 0
$$516$$ 61.6381 8.56285i 2.71347 0.376959i
$$517$$ −9.85265 5.68843i −0.433319 0.250177i
$$518$$ −47.7004 27.5398i −2.09584 1.21003i
$$519$$ −12.7113 16.3232i −0.557966 0.716507i
$$520$$ 0 0
$$521$$ −17.0301 −0.746103 −0.373052 0.927811i $$-0.621689\pi$$
−0.373052 + 0.927811i $$0.621689\pi$$
$$522$$ 56.4389 + 14.2624i 2.47026 + 0.624248i
$$523$$ 9.57651i 0.418751i −0.977835 0.209376i $$-0.932857\pi$$
0.977835 0.209376i $$-0.0671432\pi$$
$$524$$ 18.0021 + 31.1805i 0.786424 + 1.36213i
$$525$$ 0 0
$$526$$ −7.55880 + 13.0922i −0.329579 + 0.570848i
$$527$$ 10.9222 + 6.30592i 0.475777 + 0.274690i
$$528$$ −30.4579 12.3621i −1.32551 0.537992i
$$529$$ −9.99675 17.3149i −0.434641 0.752821i
$$530$$ 0 0
$$531$$ −8.10422 + 32.0699i −0.351693 + 1.39171i
$$532$$ 26.3055i 1.14049i
$$533$$ 4.21189 2.43174i 0.182437 0.105330i
$$534$$ 37.2586 + 47.8452i 1.61234 + 2.07047i
$$535$$ 0 0
$$536$$ −35.2038 + 60.9748i −1.52057 + 2.63371i
$$537$$ −2.03753 14.6668i −0.0879260 0.632920i
$$538$$ 35.6187 20.5644i 1.53563 0.886596i
$$539$$ 6.81528 0.293555
$$540$$ 0 0
$$541$$ −0.833751 −0.0358458 −0.0179229 0.999839i $$-0.505705\pi$$
−0.0179229 + 0.999839i $$0.505705\pi$$
$$542$$ −15.4031 + 8.89297i −0.661619 + 0.381986i
$$543$$ −2.51495 18.1034i −0.107927 0.776891i
$$544$$ 29.2713 50.6994i 1.25500 2.17372i
$$545$$ 0 0
$$546$$ −9.93365 12.7562i −0.425121 0.545915i
$$547$$ −24.5319 + 14.1635i −1.04891 + 0.605587i −0.922343 0.386371i $$-0.873728\pi$$
−0.126565 + 0.991958i $$0.540395\pi$$
$$548$$ 35.1785i 1.50275i
$$549$$ −27.2590 26.4916i −1.16339 1.13063i
$$550$$ 0 0
$$551$$ 10.9213 + 18.9163i 0.465264 + 0.805861i
$$552$$ −21.5218 8.73515i −0.916027 0.371793i
$$553$$ −3.28586 1.89709i −0.139729 0.0806727i
$$554$$ 39.8964 69.1026i 1.69504 2.93589i
$$555$$ 0 0
$$556$$ 36.3096 + 62.8901i 1.53987 + 2.66713i
$$557$$ 11.5042i 0.487448i 0.969845 + 0.243724i $$0.0783690\pi$$
−0.969845 + 0.243724i $$0.921631\pi$$
$$558$$ 5.64926 + 19.9402i 0.239152 + 0.844135i
$$559$$ 14.3512 0.606993
$$560$$ 0 0
$$561$$ 9.25171 + 11.8805i 0.390608 + 0.501595i
$$562$$ −42.5043 24.5398i −1.79293 1.03515i
$$563$$ 28.5840 + 16.5030i 1.20467 + 0.695517i 0.961590 0.274490i $$-0.0885089\pi$$
0.243080 + 0.970006i $$0.421842\pi$$
$$564$$ 53.2872 7.40273i 2.24380 0.311711i
$$565$$ 0 0
$$566$$ −14.9429 −0.628095
$$567$$ −7.68517 + 14.2348i −0.322747 + 0.597804i
$$568$$ 9.85769i 0.413619i
$$569$$ −13.5044 23.3903i −0.566135 0.980574i −0.996943 0.0781305i $$-0.975105\pi$$
0.430809 0.902443i $$-0.358228\pi$$
$$570$$ 0 0
$$571$$ 12.2122 21.1521i 0.511064 0.885189i −0.488854 0.872366i $$-0.662585\pi$$
0.999918 0.0128232i $$-0.00408185\pi$$
$$572$$ −15.2422 8.80007i −0.637307 0.367950i
$$573$$ −23.6925 + 18.4501i −0.989768 + 0.770763i
$$574$$ 5.83807 + 10.1118i 0.243676 + 0.422060i
$$575$$ 0 0
$$576$$ 31.9685 9.05701i 1.33202 0.377375i
$$577$$ 14.7976i 0.616033i 0.951381 + 0.308017i $$0.0996653\pi$$
−0.951381 + 0.308017i $$0.900335\pi$$
$$578$$ −13.9545 + 8.05663i −0.580431 + 0.335112i
$$579$$ −1.01586 + 2.50288i −0.0422175 + 0.104016i
$$580$$ 0 0
$$581$$ 0.987533 1.71046i 0.0409698 0.0709617i
$$582$$ −16.2005 6.57538i −0.671532 0.272558i
$$583$$ −2.70177 + 1.55987i −0.111896 + 0.0646030i
$$584$$ 27.7470 1.14818
$$585$$ 0 0
$$586$$ 48.1375 1.98854
$$587$$ 26.4813 15.2890i 1.09300 0.631044i 0.158626 0.987339i $$-0.449294\pi$$
0.934374 + 0.356295i $$0.115960\pi$$
$$588$$ −25.4276 + 19.8013i −1.04862 + 0.816590i
$$589$$ −3.88821 + 6.73457i −0.160211 + 0.277493i
$$590$$ 0 0
$$591$$ −30.8405 + 4.28440i −1.26861 + 0.176237i
$$592$$ 105.761 61.0611i 4.34675 2.50960i
$$593$$ 5.09990i 0.209428i 0.994502 + 0.104714i $$0.0333927\pi$$
−0.994502 + 0.104714i $$0.966607\pi$$
$$594$$ −2.70376 + 24.5964i −0.110936 + 1.00920i
$$595$$ 0 0
$$596$$ 1.39532 + 2.41677i 0.0571547 + 0.0989949i
$$597$$ −2.62698 18.9099i −0.107515 0.773929i
$$598$$ −7.79831 4.50236i −0.318897 0.184115i
$$599$$ −0.282655 + 0.489572i −0.0115490 + 0.0200034i −0.871742 0.489965i $$-0.837010\pi$$
0.860193 + 0.509968i $$0.170343\pi$$
$$600$$ 0 0
$$601$$ 5.50480 + 9.53459i 0.224546 + 0.388924i 0.956183 0.292770i $$-0.0945769\pi$$
−0.731637 + 0.681694i $$0.761244\pi$$
$$602$$ 34.4542i 1.40425i
$$603$$ 26.4788 + 6.69134i 1.07830 + 0.272492i
$$604$$ −0.757185 −0.0308094
$$605$$ 0 0
$$606$$ 11.2411 27.6959i 0.456638 1.12507i
$$607$$ 16.5396 + 9.54913i 0.671321 + 0.387587i 0.796577 0.604537i $$-0.206642\pi$$
−0.125256 + 0.992124i $$0.539975\pi$$
$$608$$ 31.2611 + 18.0486i 1.26780 + 0.731967i
$$609$$ −8.62621 + 21.2534i −0.349552 + 0.861229i
$$610$$ 0 0
$$611$$ 12.4069 0.501929
$$612$$ −69.0357 17.4457i −2.79060 0.705200i
$$613$$ 9.33918i 0.377206i −0.982053 0.188603i $$-0.939604\pi$$
0.982053 0.188603i $$-0.0603959\pi$$
$$614$$ −20.4179 35.3648i −0.823999 1.42721i
$$615$$ 0 0
$$616$$ 12.5675 21.7676i 0.506360 0.877041i
$$617$$ 21.1444 + 12.2077i 0.851241 + 0.491464i 0.861069 0.508488i $$-0.169795\pi$$
−0.00982861 + 0.999952i $$0.503129\pi$$
$$618$$ −5.06900 36.4883i −0.203905 1.46777i
$$619$$ 19.7431 + 34.1961i 0.793544 + 1.37446i 0.923760 + 0.382973i $$0.125100\pi$$
−0.130216 + 0.991486i $$0.541567\pi$$
$$620$$ 0 0
$$621$$ −0.984464 + 8.95580i −0.0395052 + 0.359384i
$$622$$ 80.1874i 3.21522i
$$623$$ −20.6928 + 11.9470i −0.829040 + 0.478647i
$$624$$ 35.5062 4.93256i 1.42138 0.197461i
$$625$$ 0 0
$$626$$ 9.15135 15.8506i 0.365761 0.633517i
$$627$$ −7.32547 + 5.70457i −0.292551 + 0.227819i
$$628$$ 48.9960 28.2879i 1.95515 1.12881i
$$629$$ −55.9430 −2.23059
$$630$$ 0 0
$$631$$ 42.1634 1.67850 0.839249 0.543747i $$-0.182995\pi$$
0.839249 + 0.543747i $$0.182995\pi$$
$$632$$ 14.1383 8.16277i 0.562393 0.324698i
$$633$$ 38.4029 + 15.5868i 1.52638 + 0.619518i
$$634$$ −21.2608 + 36.8248i −0.844375 + 1.46250i
$$635$$ 0 0
$$636$$ 5.54814 13.6696i 0.219998 0.542034i
$$637$$ −6.43658 + 3.71616i −0.255027 + 0.147240i
$$638$$ 35.0855i 1.38905i
$$639$$ −3.67901 + 1.04230i −0.145539 + 0.0412328i
$$640$$ 0 0
$$641$$ −17.6577 30.5841i −0.697438 1.20800i −0.969352 0.245677i $$-0.920990\pi$$
0.271913 0.962322i $$-0.412344\pi$$
$$642$$ 32.3087 25.1598i 1.27512 0.992978i
$$643$$ 12.2936 + 7.09771i 0.484812 + 0.279906i 0.722420 0.691455i $$-0.243030\pi$$
−0.237608 + 0.971361i $$0.576363\pi$$
$$644$$ 7.69256 13.3239i 0.303129 0.525036i
$$645$$ 0 0
$$646$$ −18.7712 32.5127i −0.738544 1.27919i
$$647$$ 17.4897i 0.687593i 0.939044 + 0.343796i $$0.111713\pi$$
−0.939044 + 0.343796i $$0.888287\pi$$
$$648$$ −36.5094 59.2618i −1.43422 2.32803i
$$649$$ −19.9364 −0.782572
$$650$$ 0 0
$$651$$ −8.08842 + 1.12365i −0.317010 + 0.0440395i
$$652$$ 94.3072 + 54.4483i 3.69335 + 2.13236i
$$653$$ −9.50650 5.48858i −0.372018 0.214785i 0.302322 0.953206i $$-0.402238\pi$$
−0.674340 + 0.738421i $$0.735572\pi$$
$$654$$ 17.7742 + 22.8246i 0.695026 + 0.892512i
$$655$$ 0 0
$$656$$ −25.8882 −1.01077
$$657$$ −2.93383 10.3555i −0.114459 0.404007i
$$658$$ 29.7862i 1.16119i
$$659$$ −7.89381 13.6725i −0.307499 0.532604i 0.670316 0.742076i $$-0.266159\pi$$
−0.977815 + 0.209472i $$0.932825\pi$$
$$660$$ 0 0
$$661$$ −24.9466 + 43.2088i −0.970311 + 1.68063i −0.275697 + 0.961245i $$0.588909\pi$$
−0.694614 + 0.719383i $$0.744425\pi$$
$$662$$ −28.7897 16.6217i −1.11894 0.646022i
$$663$$ −15.2157 6.17567i −0.590929 0.239843i
$$664$$ 4.24913 + 7.35972i 0.164898 + 0.285612i
$$665$$ 0 0
$$666$$ −65.9263 64.0703i −2.55459 2.48267i
$$667$$ 12.7750i 0.494649i
$$668$$ −72.9698 + 42.1291i −2.82328 + 1.63002i
$$669$$ −23.1042 29.6691i −0.893261 1.14707i
$$670$$ 0 0
$$671$$ 11.4549 19.8404i 0.442210 0.765929i
$$672$$ 5.21587 + 37.5455i 0.201207 + 1.44835i
$$673$$ −24.9757 + 14.4197i −0.962743 + 0.555840i −0.897016 0.441998i $$-0.854270\pi$$
−0.0657266 + 0.997838i $$0.520937\pi$$
$$674$$ 18.2264 0.702055
$$675$$ 0 0
$$676$$ −44.9809 −1.73003
$$677$$ 9.06176 5.23181i 0.348272 0.201075i −0.315652 0.948875i $$-0.602223\pi$$
0.663924 + 0.747800i $$0.268890\pi$$
$$678$$ −9.35426 67.3349i −0.359248 2.58598i
$$679$$ 3.44455 5.96614i 0.132190 0.228959i
$$680$$ 0 0
$$681$$ 15.0053 + 19.2689i 0.575003 + 0.738385i
$$682$$ −10.8176 + 6.24556i −0.414228 + 0.239155i
$$683$$ 16.1875i 0.619396i 0.950835 + 0.309698i $$0.100228\pi$$
−0.950835 + 0.309698i $$0.899772\pi$$
$$684$$ 10.7569 42.5672i 0.411302 1.62760i
$$685$$ 0 0
$$686$$ −25.4904 44.1507i −0.973229 1.68568i
$$687$$ 5.90214 + 2.39553i 0.225181 + 0.0913953i
$$688$$ −66.1570 38.1958i −2.52221 1.45620i
$$689$$ 1.70109 2.94638i 0.0648065 0.112248i
$$690$$ 0 0
$$691$$ −4.94181 8.55946i −0.187995 0.325617i 0.756586 0.653894i $$-0.226866\pi$$
−0.944582 + 0.328276i $$0.893532\pi$$
$$692$$ 58.9648i 2.24150i
$$693$$ −9.45276 2.38876i −0.359081 0.0907415i
$$694$$ −36.3621 −1.38029
$$695$$ 0 0
$$696$$ −60.6383 77.8682i −2.29849 2.95158i
$$697$$ 10.2703 + 5.92957i 0.389016 + 0.224598i
$$698$$ 14.9800 + 8.64872i 0.567002 + 0.327359i
$$699$$ −9.16399 + 1.27307i −0.346614 + 0.0481521i
$$700$$ 0 0
$$701$$ 43.9692 1.66069 0.830346 0.557248i $$-0.188143\pi$$
0.830346 + 0.557248i $$0.188143\pi$$
$$702$$ −10.8582 24.7040i −0.409815 0.932391i
$$703$$ 34.4942i 1.30097i
$$704$$ 10.0130 + 17.3430i 0.377379 + 0.653640i
$$705$$ 0 0
$$706$$ 4.64193 8.04005i 0.174701 0.302591i
$$707$$ 10.1995 + 5.88870i 0.383593 + 0.221467i
$$708$$ 74.3820 57.9236i 2.79545 2.17690i
$$709$$ 12.6130 + 21.8464i 0.473692 + 0.820458i 0.999546 0.0301162i $$-0.00958774\pi$$
−0.525855 + 0.850574i $$0.676254\pi$$
$$710$$ 0 0
$$711$$ −4.54136 4.41351i −0.170314 0.165520i
$$712$$ 102.811i 3.85299i
$$713$$ −3.93880 + 2.27407i −0.147509 + 0.0851645i
$$714$$ 14.8264 36.5295i 0.554865 1.36708i
$$715$$ 0 0
$$716$$ −21.1016 + 36.5490i −0.788603 + 1.36590i
$$717$$ −35.3614 14.3523i −1.32060 0.535998i
$$718$$ −52.2971 + 30.1937i −1.95171 + 1.12682i
$$719$$ 36.8600 1.37465 0.687323 0.726352i $$-0.258786\pi$$
0.687323 + 0.726352i $$0.258786\pi$$
$$720$$ 0 0
$$721$$ 14.5153 0.540576
$$722$$ −23.2893 + 13.4461i −0.866740 + 0.500412i
$$723$$ −25.4826 + 19.8441i −0.947708 + 0.738009i
$$724$$ −26.0459 + 45.1128i −0.967988 + 1.67660i
$$725$$ 0 0
$$726$$ 34.9300 4.85252i 1.29637 0.180094i
$$727$$ −33.1213 + 19.1226i −1.22840 + 0.709217i −0.966695 0.255931i $$-0.917618\pi$$
−0.261705 + 0.965148i $$0.584285\pi$$
$$728$$ 27.4107i 1.01591i
$$729$$ −18.2569 + 19.8918i −0.676183 + 0.736734i
$$730$$ 0 0
$$731$$ 17.4971 + 30.3059i 0.647154 + 1.12090i
$$732$$ 14.9070 + 107.305i 0.550977 + 3.96611i
$$733$$ 34.2801 + 19.7916i 1.26616 + 0.731020i 0.974260 0.225428i $$-0.0723781\pi$$
0.291903 + 0.956448i $$0.405711\pi$$
$$734$$ 5.50358 9.53248i 0.203141 0.351850i
$$735$$ 0 0
$$736$$ 10.5559 + 18.2834i 0.389097 + 0.673936i
$$737$$ 16.4607i 0.606338i
$$738$$ 5.31210 + 18.7501i 0.195541 + 0.690201i
$$739$$ 8.24773 0.303398 0.151699 0.988427i $$-0.451526\pi$$
0.151699 + 0.988427i $$0.451526\pi$$
$$740$$ 0 0
$$741$$ 3.80790 9.38194i 0.139887 0.344654i
$$742$$ 7.07361 + 4.08395i 0.259680 + 0.149927i
$$743$$ 1.13292 + 0.654091i 0.0415627 + 0.0239963i 0.520637 0.853778i $$-0.325694\pi$$
−0.479075 + 0.877774i $$0.659028\pi$$
$$744$$ 13.2142 32.5574i 0.484458 1.19361i
$$745$$ 0 0
$$746$$ 18.0171 0.659651
$$747$$ 2.29746 2.36401i 0.0840595 0.0864946i
$$748$$ 42.9164i 1.56918i
$$749$$ 8.06752 + 13.9734i 0.294781 + 0.510575i
$$750$$ 0 0
$$751$$ −14.2234 + 24.6357i −0.519020 + 0.898969i 0.480736 + 0.876866i $$0.340370\pi$$
−0.999756 + 0.0221034i $$0.992964\pi$$
$$752$$ −57.1939 33.0209i −2.08565 1.20415i
$$753$$ 3.50176 + 25.2068i 0.127611 + 0.918585i
$$754$$ −19.1310 33.1359i −0.696711 1.20674i
$$755$$ 0 0
$$756$$ 42.2083 18.5518i 1.53510 0.674724i
$$757$$ 38.2012i 1.38845i −0.719760 0.694223i $$-0.755748\pi$$
0.719760 0.694223i $$-0.244252\pi$$
$$758$$ 29.1414 16.8248i 1.05846 0.611103i
$$759$$ −5.37859 + 0.747201i −0.195231 + 0.0271217i
$$760$$ 0 0
$$761$$ −11.0952 + 19.2174i −0.402200 + 0.696632i −0.993991 0.109460i $$-0.965088\pi$$
0.591791 + 0.806092i $$0.298421\pi$$
$$762$$ −13.0398 + 10.1545i −0.472384 + 0.367860i
$$763$$ −9.87152 + 5.69932i −0.357373 + 0.206329i
$$764$$ 85.5852 3.09637
$$765$$ 0 0
$$766$$ 19.8440 0.716994
$$767$$ 18.8286 10.8707i 0.679861 0.392518i
$$768$$ 15.1834 + 6.16258i 0.547885 + 0.222373i
$$769$$ −8.45652 + 14.6471i −0.304950 + 0.528189i −0.977250 0.212090i $$-0.931973\pi$$
0.672300 + 0.740279i $$0.265306\pi$$
$$770$$ 0 0
$$771$$ 14.4666 35.6431i 0.521003 1.28365i
$$772$$ 6.66718 3.84930i 0.239957 0.138539i
$$773$$ 38.6464i 1.39001i 0.719003 + 0.695007i $$0.244599\pi$$
−0.719003 + 0.695007i $$0.755401\pi$$
$$774$$ −14.0891 + 55.7532i −0.506423 + 2.00401i
$$775$$ 0