# Properties

 Label 441.2.e.f.226.2 Level $441$ Weight $2$ Character 441.226 Analytic conductor $3.521$ Analytic rank $0$ Dimension $4$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$, 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: $$3.52140272914$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 147) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 226.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.226 Dual form 441.2.e.f.361.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.70711 + 2.95680i) q^{5} +1.58579 q^{8} +O(q^{10})$$ $$q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-1.70711 + 2.95680i) q^{5} +1.58579 q^{8} +(0.707107 + 1.22474i) q^{10} +(-1.00000 - 1.73205i) q^{11} -2.58579 q^{13} +(-1.50000 + 2.59808i) q^{16} +(1.12132 + 1.94218i) q^{17} +(-1.41421 + 2.44949i) q^{19} -6.24264 q^{20} -0.828427 q^{22} +(-3.82843 + 6.63103i) q^{23} +(-3.32843 - 5.76500i) q^{25} +(-0.535534 + 0.927572i) q^{26} +6.82843 q^{29} +(-0.585786 - 1.01461i) q^{31} +(2.20711 + 3.82282i) q^{32} +0.928932 q^{34} +(2.00000 - 3.46410i) q^{37} +(0.585786 + 1.01461i) q^{38} +(-2.70711 + 4.68885i) q^{40} +6.24264 q^{41} +5.65685 q^{43} +(1.82843 - 3.16693i) q^{44} +(1.58579 + 2.74666i) q^{46} +(1.41421 - 2.44949i) q^{47} -2.75736 q^{50} +(-2.36396 - 4.09450i) q^{52} +(-1.00000 - 1.73205i) q^{53} +6.82843 q^{55} +(1.41421 - 2.44949i) q^{58} +(0.585786 + 1.01461i) q^{59} +(6.12132 - 10.6024i) q^{61} -0.485281 q^{62} -4.17157 q^{64} +(4.41421 - 7.64564i) q^{65} +(2.82843 + 4.89898i) q^{67} +(-2.05025 + 3.55114i) q^{68} -9.31371 q^{71} +(6.94975 + 12.0373i) q^{73} +(-0.828427 - 1.43488i) q^{74} -5.17157 q^{76} +(-6.82843 + 11.8272i) q^{79} +(-5.12132 - 8.87039i) q^{80} +(1.29289 - 2.23936i) q^{82} +7.31371 q^{83} -7.65685 q^{85} +(1.17157 - 2.02922i) q^{86} +(-1.58579 - 2.74666i) q^{88} +(7.12132 - 12.3345i) q^{89} -14.0000 q^{92} +(-0.585786 - 1.01461i) q^{94} +(-4.82843 - 8.36308i) q^{95} -2.58579 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8}+O(q^{10})$$ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 $$4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 6 q^{16} - 4 q^{17} - 8 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 12 q^{26} + 16 q^{29} - 8 q^{31} + 6 q^{32} + 32 q^{34} + 8 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 4 q^{44} + 12 q^{46} - 28 q^{50} + 16 q^{52} - 4 q^{53} + 16 q^{55} + 8 q^{59} + 16 q^{61} + 32 q^{62} - 28 q^{64} + 12 q^{65} - 28 q^{68} + 8 q^{71} + 8 q^{73} + 8 q^{74} - 32 q^{76} - 16 q^{79} - 12 q^{80} + 8 q^{82} - 16 q^{83} - 8 q^{85} + 16 q^{86} - 12 q^{88} + 20 q^{89} - 56 q^{92} - 8 q^{94} - 8 q^{95} - 16 q^{97}+O(q^{100})$$ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 - 4 * q^11 - 16 * q^13 - 6 * q^16 - 4 * q^17 - 8 * q^20 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 12 * q^26 + 16 * q^29 - 8 * q^31 + 6 * q^32 + 32 * q^34 + 8 * q^37 + 8 * q^38 - 8 * q^40 + 8 * q^41 - 4 * q^44 + 12 * q^46 - 28 * q^50 + 16 * q^52 - 4 * q^53 + 16 * q^55 + 8 * q^59 + 16 * q^61 + 32 * q^62 - 28 * q^64 + 12 * q^65 - 28 * q^68 + 8 * q^71 + 8 * q^73 + 8 * q^74 - 32 * q^76 - 16 * q^79 - 12 * q^80 + 8 * q^82 - 16 * q^83 - 8 * q^85 + 16 * q^86 - 12 * q^88 + 20 * q^89 - 56 * q^92 - 8 * q^94 - 8 * q^95 - 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.207107 0.358719i 0.146447 0.253653i −0.783465 0.621436i $$-0.786550\pi$$
0.929912 + 0.367783i $$0.119883\pi$$
$$3$$ 0 0
$$4$$ 0.914214 + 1.58346i 0.457107 + 0.791732i
$$5$$ −1.70711 + 2.95680i −0.763441 + 1.32232i 0.177625 + 0.984098i $$0.443158\pi$$
−0.941067 + 0.338221i $$0.890175\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 1.58579 0.560660
$$9$$ 0 0
$$10$$ 0.707107 + 1.22474i 0.223607 + 0.387298i
$$11$$ −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ 0 0
$$13$$ −2.58579 −0.717168 −0.358584 0.933497i $$-0.616740\pi$$
−0.358584 + 0.933497i $$0.616740\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −1.50000 + 2.59808i −0.375000 + 0.649519i
$$17$$ 1.12132 + 1.94218i 0.271960 + 0.471049i 0.969364 0.245630i $$-0.0789948\pi$$
−0.697404 + 0.716679i $$0.745661\pi$$
$$18$$ 0 0
$$19$$ −1.41421 + 2.44949i −0.324443 + 0.561951i −0.981399 0.191977i $$-0.938510\pi$$
0.656957 + 0.753928i $$0.271843\pi$$
$$20$$ −6.24264 −1.39590
$$21$$ 0 0
$$22$$ −0.828427 −0.176621
$$23$$ −3.82843 + 6.63103i −0.798282 + 1.38267i 0.122452 + 0.992474i $$0.460924\pi$$
−0.920734 + 0.390191i $$0.872409\pi$$
$$24$$ 0 0
$$25$$ −3.32843 5.76500i −0.665685 1.15300i
$$26$$ −0.535534 + 0.927572i −0.105027 + 0.181912i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 6.82843 1.26801 0.634004 0.773330i $$-0.281410\pi$$
0.634004 + 0.773330i $$0.281410\pi$$
$$30$$ 0 0
$$31$$ −0.585786 1.01461i −0.105210 0.182230i 0.808614 0.588340i $$-0.200218\pi$$
−0.913824 + 0.406110i $$0.866885\pi$$
$$32$$ 2.20711 + 3.82282i 0.390165 + 0.675786i
$$33$$ 0 0
$$34$$ 0.928932 0.159311
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i $$-0.726690\pi$$
0.982274 + 0.187453i $$0.0600231\pi$$
$$38$$ 0.585786 + 1.01461i 0.0950271 + 0.164592i
$$39$$ 0 0
$$40$$ −2.70711 + 4.68885i −0.428031 + 0.741372i
$$41$$ 6.24264 0.974937 0.487468 0.873141i $$-0.337920\pi$$
0.487468 + 0.873141i $$0.337920\pi$$
$$42$$ 0 0
$$43$$ 5.65685 0.862662 0.431331 0.902194i $$-0.358044\pi$$
0.431331 + 0.902194i $$0.358044\pi$$
$$44$$ 1.82843 3.16693i 0.275646 0.477432i
$$45$$ 0 0
$$46$$ 1.58579 + 2.74666i 0.233811 + 0.404973i
$$47$$ 1.41421 2.44949i 0.206284 0.357295i −0.744257 0.667893i $$-0.767196\pi$$
0.950541 + 0.310599i $$0.100530\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −2.75736 −0.389949
$$51$$ 0 0
$$52$$ −2.36396 4.09450i −0.327822 0.567805i
$$53$$ −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i $$-0.210529\pi$$
−0.926497 + 0.376303i $$0.877195\pi$$
$$54$$ 0 0
$$55$$ 6.82843 0.920745
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.41421 2.44949i 0.185695 0.321634i
$$59$$ 0.585786 + 1.01461i 0.0762629 + 0.132091i 0.901635 0.432498i $$-0.142368\pi$$
−0.825372 + 0.564589i $$0.809035\pi$$
$$60$$ 0 0
$$61$$ 6.12132 10.6024i 0.783755 1.35750i −0.145985 0.989287i $$-0.546635\pi$$
0.929740 0.368216i $$-0.120031\pi$$
$$62$$ −0.485281 −0.0616308
$$63$$ 0 0
$$64$$ −4.17157 −0.521447
$$65$$ 4.41421 7.64564i 0.547516 0.948325i
$$66$$ 0 0
$$67$$ 2.82843 + 4.89898i 0.345547 + 0.598506i 0.985453 0.169948i $$-0.0543599\pi$$
−0.639906 + 0.768453i $$0.721027\pi$$
$$68$$ −2.05025 + 3.55114i −0.248630 + 0.430639i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −9.31371 −1.10533 −0.552667 0.833402i $$-0.686390\pi$$
−0.552667 + 0.833402i $$0.686390\pi$$
$$72$$ 0 0
$$73$$ 6.94975 + 12.0373i 0.813406 + 1.40886i 0.910467 + 0.413583i $$0.135723\pi$$
−0.0970601 + 0.995279i $$0.530944\pi$$
$$74$$ −0.828427 1.43488i −0.0963027 0.166801i
$$75$$ 0 0
$$76$$ −5.17157 −0.593220
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i $$0.445543\pi$$
−0.938507 + 0.345261i $$0.887790\pi$$
$$80$$ −5.12132 8.87039i −0.572581 0.991739i
$$81$$ 0 0
$$82$$ 1.29289 2.23936i 0.142776 0.247296i
$$83$$ 7.31371 0.802784 0.401392 0.915906i $$-0.368527\pi$$
0.401392 + 0.915906i $$0.368527\pi$$
$$84$$ 0 0
$$85$$ −7.65685 −0.830502
$$86$$ 1.17157 2.02922i 0.126334 0.218817i
$$87$$ 0 0
$$88$$ −1.58579 2.74666i −0.169045 0.292795i
$$89$$ 7.12132 12.3345i 0.754858 1.30745i −0.190586 0.981670i $$-0.561039\pi$$
0.945445 0.325783i $$-0.105628\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −14.0000 −1.45960
$$93$$ 0 0
$$94$$ −0.585786 1.01461i −0.0604193 0.104649i
$$95$$ −4.82843 8.36308i −0.495386 0.858034i
$$96$$ 0 0
$$97$$ −2.58579 −0.262547 −0.131273 0.991346i $$-0.541907\pi$$
−0.131273 + 0.991346i $$0.541907\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 6.08579 10.5409i 0.608579 1.05409i
$$101$$ −1.46447 2.53653i −0.145720 0.252394i 0.783921 0.620860i $$-0.213216\pi$$
−0.929641 + 0.368466i $$0.879883\pi$$
$$102$$ 0 0
$$103$$ 2.24264 3.88437i 0.220974 0.382738i −0.734130 0.679009i $$-0.762410\pi$$
0.955104 + 0.296271i $$0.0957431\pi$$
$$104$$ −4.10051 −0.402088
$$105$$ 0 0
$$106$$ −0.828427 −0.0804640
$$107$$ −0.171573 + 0.297173i −0.0165866 + 0.0287288i −0.874200 0.485567i $$-0.838613\pi$$
0.857613 + 0.514296i $$0.171947\pi$$
$$108$$ 0 0
$$109$$ 2.82843 + 4.89898i 0.270914 + 0.469237i 0.969096 0.246683i $$-0.0793407\pi$$
−0.698182 + 0.715920i $$0.746007\pi$$
$$110$$ 1.41421 2.44949i 0.134840 0.233550i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 5.31371 0.499872 0.249936 0.968262i $$-0.419590\pi$$
0.249936 + 0.968262i $$0.419590\pi$$
$$114$$ 0 0
$$115$$ −13.0711 22.6398i −1.21888 2.11117i
$$116$$ 6.24264 + 10.8126i 0.579615 + 1.00392i
$$117$$ 0 0
$$118$$ 0.485281 0.0446738
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ −2.53553 4.39167i −0.229556 0.397603i
$$123$$ 0 0
$$124$$ 1.07107 1.85514i 0.0961847 0.166597i
$$125$$ 5.65685 0.505964
$$126$$ 0 0
$$127$$ −1.65685 −0.147022 −0.0735110 0.997294i $$-0.523420\pi$$
−0.0735110 + 0.997294i $$0.523420\pi$$
$$128$$ −5.27817 + 9.14207i −0.466529 + 0.808052i
$$129$$ 0 0
$$130$$ −1.82843 3.16693i −0.160364 0.277758i
$$131$$ 7.65685 13.2621i 0.668982 1.15871i −0.309207 0.950995i $$-0.600063\pi$$
0.978189 0.207717i $$-0.0666032\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.34315 0.202417
$$135$$ 0 0
$$136$$ 1.77817 + 3.07989i 0.152477 + 0.264098i
$$137$$ 7.07107 + 12.2474i 0.604122 + 1.04637i 0.992190 + 0.124739i $$0.0398094\pi$$
−0.388067 + 0.921631i $$0.626857\pi$$
$$138$$ 0 0
$$139$$ 17.6569 1.49763 0.748817 0.662776i $$-0.230622\pi$$
0.748817 + 0.662776i $$0.230622\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1.92893 + 3.34101i −0.161872 + 0.280371i
$$143$$ 2.58579 + 4.47871i 0.216234 + 0.374529i
$$144$$ 0 0
$$145$$ −11.6569 + 20.1903i −0.968049 + 1.67671i
$$146$$ 5.75736 0.476482
$$147$$ 0 0
$$148$$ 7.31371 0.601183
$$149$$ 8.65685 14.9941i 0.709197 1.22837i −0.255958 0.966688i $$-0.582391\pi$$
0.965155 0.261678i $$-0.0842757\pi$$
$$150$$ 0 0
$$151$$ −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i $$-0.329040\pi$$
−0.999909 + 0.0134886i $$0.995706\pi$$
$$152$$ −2.24264 + 3.88437i −0.181902 + 0.315064i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ 5.87868 + 10.1822i 0.469170 + 0.812626i 0.999379 0.0352411i $$-0.0112199\pi$$
−0.530209 + 0.847867i $$0.677887\pi$$
$$158$$ 2.82843 + 4.89898i 0.225018 + 0.389742i
$$159$$ 0 0
$$160$$ −15.0711 −1.19147
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.65685 9.79796i 0.443079 0.767435i −0.554837 0.831959i $$-0.687219\pi$$
0.997916 + 0.0645236i $$0.0205528\pi$$
$$164$$ 5.70711 + 9.88500i 0.445650 + 0.771889i
$$165$$ 0 0
$$166$$ 1.51472 2.62357i 0.117565 0.203628i
$$167$$ −19.7990 −1.53209 −0.766046 0.642786i $$-0.777779\pi$$
−0.766046 + 0.642786i $$0.777779\pi$$
$$168$$ 0 0
$$169$$ −6.31371 −0.485670
$$170$$ −1.58579 + 2.74666i −0.121624 + 0.210659i
$$171$$ 0 0
$$172$$ 5.17157 + 8.95743i 0.394329 + 0.682997i
$$173$$ −10.5355 + 18.2481i −0.801002 + 1.38738i 0.117956 + 0.993019i $$0.462366\pi$$
−0.918957 + 0.394357i $$0.870967\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 6.00000 0.452267
$$177$$ 0 0
$$178$$ −2.94975 5.10911i −0.221093 0.382944i
$$179$$ −9.82843 17.0233i −0.734611 1.27238i −0.954894 0.296948i $$-0.904031\pi$$
0.220283 0.975436i $$-0.429302\pi$$
$$180$$ 0 0
$$181$$ 2.58579 0.192200 0.0961000 0.995372i $$-0.469363\pi$$
0.0961000 + 0.995372i $$0.469363\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −6.07107 + 10.5154i −0.447565 + 0.775205i
$$185$$ 6.82843 + 11.8272i 0.502036 + 0.869552i
$$186$$ 0 0
$$187$$ 2.24264 3.88437i 0.163998 0.284053i
$$188$$ 5.17157 0.377176
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i $$0.392408\pi$$
−0.982828 + 0.184525i $$0.940925\pi$$
$$192$$ 0 0
$$193$$ −2.65685 4.60181i −0.191245 0.331245i 0.754418 0.656394i $$-0.227919\pi$$
−0.945663 + 0.325149i $$0.894586\pi$$
$$194$$ −0.535534 + 0.927572i −0.0384491 + 0.0665958i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 10.8284 + 18.7554i 0.767607 + 1.32953i 0.938857 + 0.344307i $$0.111886\pi$$
−0.171250 + 0.985228i $$0.554781\pi$$
$$200$$ −5.27817 9.14207i −0.373223 0.646442i
$$201$$ 0 0
$$202$$ −1.21320 −0.0853607
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −10.6569 + 18.4582i −0.744307 + 1.28918i
$$206$$ −0.928932 1.60896i −0.0647218 0.112101i
$$207$$ 0 0
$$208$$ 3.87868 6.71807i 0.268938 0.465814i
$$209$$ 5.65685 0.391293
$$210$$ 0 0
$$211$$ 12.9706 0.892930 0.446465 0.894801i $$-0.352683\pi$$
0.446465 + 0.894801i $$0.352683\pi$$
$$212$$ 1.82843 3.16693i 0.125577 0.217506i
$$213$$ 0 0
$$214$$ 0.0710678 + 0.123093i 0.00485810 + 0.00841447i
$$215$$ −9.65685 + 16.7262i −0.658592 + 1.14071i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 2.34315 0.158698
$$219$$ 0 0
$$220$$ 6.24264 + 10.8126i 0.420879 + 0.728983i
$$221$$ −2.89949 5.02207i −0.195041 0.337821i
$$222$$ 0 0
$$223$$ −24.9706 −1.67215 −0.836076 0.548613i $$-0.815156\pi$$
−0.836076 + 0.548613i $$0.815156\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.10051 1.90613i 0.0732045 0.126794i
$$227$$ −11.8995 20.6105i −0.789797 1.36797i −0.926091 0.377300i $$-0.876852\pi$$
0.136294 0.990668i $$-0.456481\pi$$
$$228$$ 0 0
$$229$$ −0.121320 + 0.210133i −0.00801707 + 0.0138860i −0.870006 0.493041i $$-0.835885\pi$$
0.861989 + 0.506927i $$0.169219\pi$$
$$230$$ −10.8284 −0.714005
$$231$$ 0 0
$$232$$ 10.8284 0.710921
$$233$$ −3.07107 + 5.31925i −0.201192 + 0.348475i −0.948913 0.315538i $$-0.897815\pi$$
0.747721 + 0.664014i $$0.231148\pi$$
$$234$$ 0 0
$$235$$ 4.82843 + 8.36308i 0.314972 + 0.545547i
$$236$$ −1.07107 + 1.85514i −0.0697206 + 0.120760i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 15.6569 1.01276 0.506379 0.862311i $$-0.330984\pi$$
0.506379 + 0.862311i $$0.330984\pi$$
$$240$$ 0 0
$$241$$ −8.12132 14.0665i −0.523140 0.906105i −0.999637 0.0269294i $$-0.991427\pi$$
0.476497 0.879176i $$-0.341906\pi$$
$$242$$ −1.44975 2.51104i −0.0931933 0.161416i
$$243$$ 0 0
$$244$$ 22.3848 1.43304
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3.65685 6.33386i 0.232680 0.403014i
$$248$$ −0.928932 1.60896i −0.0589873 0.102169i
$$249$$ 0 0
$$250$$ 1.17157 2.02922i 0.0740968 0.128339i
$$251$$ −12.4853 −0.788064 −0.394032 0.919097i $$-0.628920\pi$$
−0.394032 + 0.919097i $$0.628920\pi$$
$$252$$ 0 0
$$253$$ 15.3137 0.962765
$$254$$ −0.343146 + 0.594346i −0.0215309 + 0.0372926i
$$255$$ 0 0
$$256$$ −1.98528 3.43861i −0.124080 0.214913i
$$257$$ −11.6066 + 20.1032i −0.724000 + 1.25400i 0.235384 + 0.971902i $$0.424365\pi$$
−0.959384 + 0.282102i $$0.908968\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 16.1421 1.00109
$$261$$ 0 0
$$262$$ −3.17157 5.49333i −0.195940 0.339379i
$$263$$ 2.65685 + 4.60181i 0.163829 + 0.283760i 0.936239 0.351365i $$-0.114282\pi$$
−0.772410 + 0.635124i $$0.780949\pi$$
$$264$$ 0 0
$$265$$ 6.82843 0.419467
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −5.17157 + 8.95743i −0.315904 + 0.547162i
$$269$$ 7.36396 + 12.7548i 0.448989 + 0.777671i 0.998320 0.0579332i $$-0.0184510\pi$$
−0.549332 + 0.835604i $$0.685118\pi$$
$$270$$ 0 0
$$271$$ −5.07107 + 8.78335i −0.308045 + 0.533550i −0.977935 0.208911i $$-0.933008\pi$$
0.669889 + 0.742461i $$0.266342\pi$$
$$272$$ −6.72792 −0.407940
$$273$$ 0 0
$$274$$ 5.85786 0.353887
$$275$$ −6.65685 + 11.5300i −0.401423 + 0.695286i
$$276$$ 0 0
$$277$$ 4.65685 + 8.06591i 0.279803 + 0.484633i 0.971336 0.237712i $$-0.0763974\pi$$
−0.691532 + 0.722345i $$0.743064\pi$$
$$278$$ 3.65685 6.33386i 0.219324 0.379880i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −0.485281 −0.0289495 −0.0144747 0.999895i $$-0.504608\pi$$
−0.0144747 + 0.999895i $$0.504608\pi$$
$$282$$ 0 0
$$283$$ −4.24264 7.34847i −0.252199 0.436821i 0.711932 0.702248i $$-0.247820\pi$$
−0.964131 + 0.265427i $$0.914487\pi$$
$$284$$ −8.51472 14.7479i −0.505256 0.875128i
$$285$$ 0 0
$$286$$ 2.14214 0.126667
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 5.98528 10.3668i 0.352075 0.609812i
$$290$$ 4.82843 + 8.36308i 0.283535 + 0.491097i
$$291$$ 0 0
$$292$$ −12.7071 + 22.0094i −0.743627 + 1.28800i
$$293$$ 16.5858 0.968952 0.484476 0.874805i $$-0.339010\pi$$
0.484476 + 0.874805i $$0.339010\pi$$
$$294$$ 0 0
$$295$$ −4.00000 −0.232889
$$296$$ 3.17157 5.49333i 0.184344 0.319293i
$$297$$ 0 0
$$298$$ −3.58579 6.21076i −0.207719 0.359780i
$$299$$ 9.89949 17.1464i 0.572503 0.991604i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −4.97056 −0.286024
$$303$$ 0 0
$$304$$ −4.24264 7.34847i −0.243332 0.421464i
$$305$$ 20.8995 + 36.1990i 1.19670 + 2.07275i
$$306$$ 0 0
$$307$$ −30.1421 −1.72030 −0.860151 0.510039i $$-0.829631\pi$$
−0.860151 + 0.510039i $$0.829631\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0.828427 1.43488i 0.0470515 0.0814956i
$$311$$ −3.07107 5.31925i −0.174144 0.301627i 0.765721 0.643173i $$-0.222383\pi$$
−0.939865 + 0.341547i $$0.889049\pi$$
$$312$$ 0 0
$$313$$ 0.949747 1.64501i 0.0536829 0.0929815i −0.837935 0.545770i $$-0.816237\pi$$
0.891618 + 0.452788i $$0.149571\pi$$
$$314$$ 4.87006 0.274833
$$315$$ 0 0
$$316$$ −24.9706 −1.40470
$$317$$ 5.00000 8.66025i 0.280828 0.486408i −0.690761 0.723083i $$-0.742724\pi$$
0.971589 + 0.236675i $$0.0760576\pi$$
$$318$$ 0 0
$$319$$ −6.82843 11.8272i −0.382319 0.662195i
$$320$$ 7.12132 12.3345i 0.398094 0.689519i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −6.34315 −0.352942
$$324$$ 0 0
$$325$$ 8.60660 + 14.9071i 0.477408 + 0.826896i
$$326$$ −2.34315 4.05845i −0.129775 0.224777i
$$327$$ 0 0
$$328$$ 9.89949 0.546608
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i $$-0.798271\pi$$
0.915742 + 0.401768i $$0.131604\pi$$
$$332$$ 6.68629 + 11.5810i 0.366958 + 0.635590i
$$333$$ 0 0
$$334$$ −4.10051 + 7.10228i −0.224370 + 0.388620i
$$335$$ −19.3137 −1.05522
$$336$$ 0 0
$$337$$ −29.6569 −1.61551 −0.807756 0.589517i $$-0.799318\pi$$
−0.807756 + 0.589517i $$0.799318\pi$$
$$338$$ −1.30761 + 2.26485i −0.0711247 + 0.123192i
$$339$$ 0 0
$$340$$ −7.00000 12.1244i −0.379628 0.657536i
$$341$$ −1.17157 + 2.02922i −0.0634442 + 0.109889i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 8.97056 0.483660
$$345$$ 0 0
$$346$$ 4.36396 + 7.55860i 0.234608 + 0.406353i
$$347$$ 16.6569 + 28.8505i 0.894187 + 1.54878i 0.834808 + 0.550541i $$0.185579\pi$$
0.0593789 + 0.998236i $$0.481088\pi$$
$$348$$ 0 0
$$349$$ 9.89949 0.529908 0.264954 0.964261i $$-0.414643\pi$$
0.264954 + 0.964261i $$0.414643\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 4.41421 7.64564i 0.235278 0.407514i
$$353$$ 7.36396 + 12.7548i 0.391944 + 0.678867i 0.992706 0.120561i $$-0.0384693\pi$$
−0.600762 + 0.799428i $$0.705136\pi$$
$$354$$ 0 0
$$355$$ 15.8995 27.5387i 0.843858 1.46160i
$$356$$ 26.0416 1.38020
$$357$$ 0 0
$$358$$ −8.14214 −0.430325
$$359$$ −0.171573 + 0.297173i −0.00905527 + 0.0156842i −0.870518 0.492137i $$-0.836216\pi$$
0.861462 + 0.507822i $$0.169549\pi$$
$$360$$ 0 0
$$361$$ 5.50000 + 9.52628i 0.289474 + 0.501383i
$$362$$ 0.535534 0.927572i 0.0281470 0.0487521i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −47.4558 −2.48395
$$366$$ 0 0
$$367$$ −1.65685 2.86976i −0.0864871 0.149800i 0.819537 0.573027i $$-0.194231\pi$$
−0.906024 + 0.423226i $$0.860897\pi$$
$$368$$ −11.4853 19.8931i −0.598712 1.03700i
$$369$$ 0 0
$$370$$ 5.65685 0.294086
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 5.34315 9.25460i 0.276658 0.479185i −0.693894 0.720077i $$-0.744107\pi$$
0.970552 + 0.240892i $$0.0774399\pi$$
$$374$$ −0.928932 1.60896i −0.0480339 0.0831972i
$$375$$ 0 0
$$376$$ 2.24264 3.88437i 0.115655 0.200321i
$$377$$ −17.6569 −0.909374
$$378$$ 0 0
$$379$$ 8.68629 0.446185 0.223092 0.974797i $$-0.428385\pi$$
0.223092 + 0.974797i $$0.428385\pi$$
$$380$$ 8.82843 15.2913i 0.452889 0.784426i
$$381$$ 0 0
$$382$$ 3.72792 + 6.45695i 0.190737 + 0.330366i
$$383$$ 9.17157 15.8856i 0.468645 0.811718i −0.530712 0.847552i $$-0.678076\pi$$
0.999358 + 0.0358343i $$0.0114088\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −2.20101 −0.112028
$$387$$ 0 0
$$388$$ −2.36396 4.09450i −0.120012 0.207867i
$$389$$ −9.07107 15.7116i −0.459921 0.796607i 0.539035 0.842283i $$-0.318789\pi$$
−0.998956 + 0.0456762i $$0.985456\pi$$
$$390$$ 0 0
$$391$$ −17.1716 −0.868404
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −0.414214 + 0.717439i −0.0208678 + 0.0361441i
$$395$$ −23.3137 40.3805i −1.17304 2.03176i
$$396$$ 0 0
$$397$$ −1.19239 + 2.06528i −0.0598442 + 0.103653i −0.894395 0.447277i $$-0.852394\pi$$
0.834551 + 0.550931i $$0.185727\pi$$
$$398$$ 8.97056 0.449654
$$399$$ 0 0
$$400$$ 19.9706 0.998528
$$401$$ −3.07107 + 5.31925i −0.153362 + 0.265630i −0.932461 0.361270i $$-0.882343\pi$$
0.779100 + 0.626900i $$0.215677\pi$$
$$402$$ 0 0
$$403$$ 1.51472 + 2.62357i 0.0754535 + 0.130689i
$$404$$ 2.67767 4.63786i 0.133219 0.230742i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −8.00000 −0.396545
$$408$$ 0 0
$$409$$ −10.7071 18.5453i −0.529432 0.917004i −0.999411 0.0343258i $$-0.989072\pi$$
0.469978 0.882678i $$-0.344262\pi$$
$$410$$ 4.41421 + 7.64564i 0.218002 + 0.377591i
$$411$$ 0 0
$$412$$ 8.20101 0.404035
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.4853 + 21.6251i −0.612878 + 1.06154i
$$416$$ −5.70711 9.88500i −0.279814 0.484652i
$$417$$ 0 0
$$418$$ 1.17157 2.02922i 0.0573035 0.0992526i
$$419$$ 33.1716 1.62054 0.810269 0.586059i $$-0.199321\pi$$
0.810269 + 0.586059i $$0.199321\pi$$
$$420$$ 0 0
$$421$$ 16.6274 0.810371 0.405185 0.914235i $$-0.367207\pi$$
0.405185 + 0.914235i $$0.367207\pi$$
$$422$$ 2.68629 4.65279i 0.130767 0.226494i
$$423$$ 0 0
$$424$$ −1.58579 2.74666i −0.0770126 0.133390i
$$425$$ 7.46447 12.9288i 0.362080 0.627141i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −0.627417 −0.0303273
$$429$$ 0 0
$$430$$ 4.00000 + 6.92820i 0.192897 + 0.334108i
$$431$$ −13.4853 23.3572i −0.649563 1.12508i −0.983227 0.182384i $$-0.941618\pi$$
0.333664 0.942692i $$-0.391715\pi$$
$$432$$ 0 0
$$433$$ 20.2426 0.972799 0.486400 0.873736i $$-0.338310\pi$$
0.486400 + 0.873736i $$0.338310\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −5.17157 + 8.95743i −0.247673 + 0.428983i
$$437$$ −10.8284 18.7554i −0.517994 0.897192i
$$438$$ 0 0
$$439$$ 6.34315 10.9867i 0.302742 0.524364i −0.674014 0.738718i $$-0.735431\pi$$
0.976756 + 0.214354i $$0.0687647\pi$$
$$440$$ 10.8284 0.516225
$$441$$ 0 0
$$442$$ −2.40202 −0.114252
$$443$$ 17.4853 30.2854i 0.830751 1.43890i −0.0666929 0.997774i $$-0.521245\pi$$
0.897444 0.441129i $$-0.145422\pi$$
$$444$$ 0 0
$$445$$ 24.3137 + 42.1126i 1.15258 + 1.99633i
$$446$$ −5.17157 + 8.95743i −0.244881 + 0.424146i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 5.31371 0.250769 0.125385 0.992108i $$-0.459983\pi$$
0.125385 + 0.992108i $$0.459983\pi$$
$$450$$ 0 0
$$451$$ −6.24264 10.8126i −0.293954 0.509144i
$$452$$ 4.85786 + 8.41407i 0.228495 + 0.395764i
$$453$$ 0 0
$$454$$ −9.85786 −0.462652
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i $$-0.695012\pi$$
0.996038 + 0.0889312i $$0.0283451\pi$$
$$458$$ 0.0502525 + 0.0870399i 0.00234815 + 0.00406711i
$$459$$ 0 0
$$460$$ 23.8995 41.3951i 1.11432 1.93006i
$$461$$ −16.5858 −0.772477 −0.386239 0.922399i $$-0.626226\pi$$
−0.386239 + 0.922399i $$0.626226\pi$$
$$462$$ 0 0
$$463$$ −26.6274 −1.23748 −0.618741 0.785595i $$-0.712357\pi$$
−0.618741 + 0.785595i $$0.712357\pi$$
$$464$$ −10.2426 + 17.7408i −0.475503 + 0.823595i
$$465$$ 0 0
$$466$$ 1.27208 + 2.20330i 0.0589279 + 0.102066i
$$467$$ −0.100505 + 0.174080i −0.00465082 + 0.00805546i −0.868341 0.495967i $$-0.834814\pi$$
0.863691 + 0.504022i $$0.168147\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 4.00000 0.184506
$$471$$ 0 0
$$472$$ 0.928932 + 1.60896i 0.0427576 + 0.0740583i
$$473$$ −5.65685 9.79796i −0.260102 0.450511i
$$474$$ 0 0
$$475$$ 18.8284 0.863907
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 3.24264 5.61642i 0.148315 0.256889i
$$479$$ −0.928932 1.60896i −0.0424440 0.0735152i 0.844023 0.536307i $$-0.180181\pi$$
−0.886467 + 0.462792i $$0.846848\pi$$
$$480$$ 0 0
$$481$$ −5.17157 + 8.95743i −0.235803 + 0.408424i
$$482$$ −6.72792 −0.306448
$$483$$ 0 0
$$484$$ 12.7990 0.581772
$$485$$ 4.41421 7.64564i 0.200439 0.347171i
$$486$$ 0 0
$$487$$ −13.3137 23.0600i −0.603302 1.04495i −0.992317 0.123718i $$-0.960518\pi$$
0.389016 0.921231i $$-0.372815\pi$$
$$488$$ 9.70711 16.8132i 0.439420 0.761098i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −5.02944 −0.226975 −0.113488 0.993539i $$-0.536202\pi$$
−0.113488 + 0.993539i $$0.536202\pi$$
$$492$$ 0 0
$$493$$ 7.65685 + 13.2621i 0.344847 + 0.597293i
$$494$$ −1.51472 2.62357i −0.0681504 0.118040i
$$495$$ 0 0
$$496$$ 3.51472 0.157816
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −1.65685 + 2.86976i −0.0741710 + 0.128468i −0.900725 0.434389i $$-0.856964\pi$$
0.826554 + 0.562857i $$0.190298\pi$$
$$500$$ 5.17157 + 8.95743i 0.231280 + 0.400588i
$$501$$ 0 0
$$502$$ −2.58579 + 4.47871i −0.115409 + 0.199895i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 10.0000 0.444994
$$506$$ 3.17157 5.49333i 0.140994 0.244208i
$$507$$ 0 0
$$508$$ −1.51472 2.62357i −0.0672048 0.116402i
$$509$$ −2.77817 + 4.81194i −0.123140 + 0.213285i −0.921005 0.389552i $$-0.872630\pi$$
0.797864 + 0.602837i $$0.205963\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −22.7574 −1.00574
$$513$$ 0 0
$$514$$ 4.80761 + 8.32703i 0.212055 + 0.367289i
$$515$$ 7.65685 + 13.2621i 0.337401 + 0.584396i
$$516$$ 0 0
$$517$$ −5.65685 −0.248788
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 7.00000 12.1244i 0.306970 0.531688i
$$521$$ 17.7071 + 30.6696i 0.775762 + 1.34366i 0.934365 + 0.356317i $$0.115968\pi$$
−0.158603 + 0.987343i $$0.550699\pi$$
$$522$$ 0 0
$$523$$ −12.8284 + 22.2195i −0.560948 + 0.971590i 0.436466 + 0.899721i $$0.356230\pi$$
−0.997414 + 0.0718696i $$0.977103\pi$$
$$524$$ 28.0000 1.22319
$$525$$ 0 0
$$526$$ 2.20101 0.0959686
$$527$$ 1.31371 2.27541i 0.0572260 0.0991184i
$$528$$ 0 0
$$529$$ −17.8137 30.8542i −0.774509 1.34149i
$$530$$ 1.41421 2.44949i 0.0614295 0.106399i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −16.1421 −0.699194
$$534$$ 0 0
$$535$$ −0.585786 1.01461i −0.0253258 0.0438655i
$$536$$ 4.48528 + 7.76874i 0.193735 + 0.335558i
$$537$$ 0 0
$$538$$ 6.10051 0.263011
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −8.65685 + 14.9941i −0.372187 + 0.644647i −0.989902 0.141755i $$-0.954725\pi$$
0.617715 + 0.786402i $$0.288059\pi$$
$$542$$ 2.10051 + 3.63818i 0.0902244 + 0.156273i
$$543$$ 0 0
$$544$$ −4.94975 + 8.57321i −0.212219 + 0.367574i
$$545$$ −19.3137 −0.827308
$$546$$ 0 0
$$547$$ −36.9706 −1.58075 −0.790374 0.612625i $$-0.790114\pi$$
−0.790374 + 0.612625i $$0.790114\pi$$
$$548$$ −12.9289 + 22.3936i −0.552297 + 0.956606i
$$549$$ 0 0
$$550$$ 2.75736 + 4.77589i 0.117574 + 0.203644i
$$551$$ −9.65685 + 16.7262i −0.411396 + 0.712558i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 3.85786 0.163905
$$555$$ 0 0
$$556$$ 16.1421 + 27.9590i 0.684579 + 1.18573i
$$557$$ 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i $$0.0190212\pi$$
−0.447387 + 0.894340i $$0.647645\pi$$
$$558$$ 0 0
$$559$$ −14.6274 −0.618674
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.100505 + 0.174080i −0.00423955 + 0.00734312i
$$563$$ 0.585786 + 1.01461i 0.0246880 + 0.0427608i 0.878105 0.478467i $$-0.158807\pi$$
−0.853417 + 0.521228i $$0.825474\pi$$
$$564$$ 0 0
$$565$$ −9.07107 + 15.7116i −0.381623 + 0.660990i
$$566$$ −3.51472 −0.147735
$$567$$ 0 0
$$568$$ −14.7696 −0.619717
$$569$$ −8.24264 + 14.2767i −0.345549 + 0.598509i −0.985453 0.169946i $$-0.945641\pi$$
0.639904 + 0.768455i $$0.278974\pi$$
$$570$$ 0 0
$$571$$ −11.1716 19.3497i −0.467516 0.809761i 0.531795 0.846873i $$-0.321518\pi$$
−0.999311 + 0.0371118i $$0.988184\pi$$
$$572$$ −4.72792 + 8.18900i −0.197684 + 0.342399i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 50.9706 2.12562
$$576$$ 0 0
$$577$$ −16.9497 29.3578i −0.705627 1.22218i −0.966465 0.256799i $$-0.917332\pi$$
0.260837 0.965383i $$-0.416001\pi$$
$$578$$ −2.47918 4.29407i −0.103120 0.178610i
$$579$$ 0 0
$$580$$ −42.6274 −1.77001
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −2.00000 + 3.46410i −0.0828315 + 0.143468i
$$584$$ 11.0208 + 19.0886i 0.456045 + 0.789892i
$$585$$ 0 0
$$586$$ 3.43503 5.94964i 0.141900 0.245778i
$$587$$ −22.8284 −0.942230 −0.471115 0.882072i $$-0.656148\pi$$
−0.471115 + 0.882072i $$0.656148\pi$$
$$588$$ 0 0
$$589$$ 3.31371 0.136539
$$590$$ −0.828427 + 1.43488i −0.0341058 + 0.0590730i
$$591$$ 0 0
$$592$$ 6.00000 + 10.3923i 0.246598 + 0.427121i
$$593$$ 3.46447 6.00063i 0.142269 0.246416i −0.786082 0.618122i $$-0.787894\pi$$
0.928351 + 0.371706i $$0.121227\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 31.6569 1.29672
$$597$$ 0 0
$$598$$ −4.10051 7.10228i −0.167682 0.290434i
$$599$$ −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i $$-0.179676\pi$$
−0.885732 + 0.464198i $$0.846343\pi$$
$$600$$ 0 0
$$601$$ 15.0711 0.614762 0.307381 0.951587i $$-0.400547\pi$$
0.307381 + 0.951587i $$0.400547\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 10.9706 19.0016i 0.446386 0.773163i
$$605$$ 11.9497 + 20.6976i 0.485826 + 0.841476i
$$606$$ 0 0
$$607$$ −9.17157 + 15.8856i −0.372263 + 0.644778i −0.989913 0.141675i $$-0.954751\pi$$
0.617651 + 0.786453i $$0.288085\pi$$
$$608$$ −12.4853 −0.506345
$$609$$ 0 0
$$610$$ 17.3137 0.701012
$$611$$ −3.65685 + 6.33386i −0.147940 + 0.256240i
$$612$$ 0 0
$$613$$ −2.34315 4.05845i −0.0946388 0.163919i 0.814819 0.579715i $$-0.196836\pi$$
−0.909458 + 0.415796i $$0.863503\pi$$
$$614$$ −6.24264 + 10.8126i −0.251932 + 0.436360i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 24.4853 0.985740 0.492870 0.870103i $$-0.335948\pi$$
0.492870 + 0.870103i $$0.335948\pi$$
$$618$$ 0 0
$$619$$ 14.4853 + 25.0892i 0.582213 + 1.00842i 0.995217 + 0.0976926i $$0.0311462\pi$$
−0.413004 + 0.910729i $$0.635520\pi$$
$$620$$ 3.65685 + 6.33386i 0.146863 + 0.254374i
$$621$$ 0 0
$$622$$ −2.54416 −0.102011
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 6.98528 12.0989i 0.279411 0.483954i
$$626$$ −0.393398 0.681386i −0.0157234 0.0272337i
$$627$$ 0 0
$$628$$ −10.7487 + 18.6174i −0.428921 + 0.742914i
$$629$$ 8.97056 0.357680
$$630$$ 0 0
$$631$$ 23.3137 0.928104 0.464052 0.885808i $$-0.346395\pi$$
0.464052 + 0.885808i $$0.346395\pi$$
$$632$$ −10.8284 + 18.7554i −0.430732 + 0.746049i
$$633$$ 0 0
$$634$$ −2.07107 3.58719i −0.0822526 0.142466i
$$635$$ 2.82843 4.89898i 0.112243 0.194410i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −5.65685 −0.223957
$$639$$ 0 0
$$640$$ −18.0208 31.2130i −0.712335 1.23380i
$$641$$ −5.41421 9.37769i −0.213849 0.370397i 0.739067 0.673632i $$-0.235267\pi$$
−0.952916 + 0.303235i $$0.901933\pi$$
$$642$$ 0 0
$$643$$ 34.4264 1.35764 0.678822 0.734302i $$-0.262491\pi$$
0.678822 + 0.734302i $$0.262491\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −1.31371 + 2.27541i −0.0516872 + 0.0895248i
$$647$$ −13.4142 23.2341i −0.527367 0.913427i −0.999491 0.0318946i $$-0.989846\pi$$
0.472124 0.881532i $$-0.343487\pi$$
$$648$$ 0 0
$$649$$ 1.17157 2.02922i 0.0459883 0.0796540i
$$650$$ 7.12994 0.279659
$$651$$ 0 0
$$652$$ 20.6863 0.810138
$$653$$ 18.2426 31.5972i 0.713890 1.23649i −0.249497 0.968376i $$-0.580265\pi$$
0.963386 0.268118i $$-0.0864016\pi$$
$$654$$ 0 0
$$655$$ 26.1421 + 45.2795i 1.02146 + 1.76922i
$$656$$ −9.36396 + 16.2189i −0.365601 + 0.633240i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −9.31371 −0.362811 −0.181405 0.983408i $$-0.558065\pi$$
−0.181405 + 0.983408i $$0.558065\pi$$
$$660$$ 0 0
$$661$$ −11.7782 20.4004i −0.458118 0.793483i 0.540744 0.841187i $$-0.318143\pi$$
−0.998862 + 0.0477040i $$0.984810\pi$$
$$662$$ −0.828427 1.43488i −0.0321977 0.0557681i
$$663$$ 0 0
$$664$$ 11.5980 0.450089
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −26.1421 + 45.2795i −1.01223 + 1.75323i
$$668$$ −18.1005 31.3510i −0.700330 1.21301i
$$669$$ 0 0
$$670$$ −4.00000 + 6.92820i −0.154533 + 0.267660i
$$671$$ −24.4853 −0.945244
$$672$$ 0 0
$$673$$ 23.3137 0.898677 0.449339 0.893361i $$-0.351660\pi$$
0.449339 + 0.893361i $$0.351660\pi$$
$$674$$ −6.14214 + 10.6385i −0.236586 + 0.409779i
$$675$$ 0 0
$$676$$ −5.77208 9.99753i −0.222003 0.384520i
$$677$$ −15.7071 + 27.2055i −0.603673 + 1.04559i 0.388587 + 0.921412i $$0.372963\pi$$
−0.992260 + 0.124180i $$0.960370\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −12.1421 −0.465630
$$681$$ 0 0
$$682$$ 0.485281 + 0.840532i 0.0185824 + 0.0321856i
$$683$$ −9.82843 17.0233i −0.376074 0.651380i 0.614413 0.788985i $$-0.289393\pi$$
−0.990487 + 0.137605i $$0.956060\pi$$
$$684$$ 0 0
$$685$$ −48.2843 −1.84485
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −8.48528 + 14.6969i −0.323498 + 0.560316i
$$689$$ 2.58579 + 4.47871i 0.0985106 + 0.170625i
$$690$$ 0 0
$$691$$ −0.343146 + 0.594346i −0.0130539 + 0.0226100i −0.872479 0.488652i $$-0.837489\pi$$
0.859425 + 0.511262i $$0.170822\pi$$
$$692$$ −38.5269 −1.46457
$$693$$ 0 0
$$694$$ 13.7990 0.523802
$$695$$ −30.1421 + 52.2077i −1.14336 + 1.98035i
$$696$$ 0 0
$$697$$ 7.00000 + 12.1244i 0.265144 + 0.459243i
$$698$$ 2.05025 3.55114i 0.0776032 0.134413i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 17.1716 0.648561 0.324281 0.945961i $$-0.394878\pi$$
0.324281 + 0.945961i $$0.394878\pi$$
$$702$$ 0 0
$$703$$ 5.65685 + 9.79796i 0.213352 + 0.369537i
$$704$$ 4.17157 + 7.22538i 0.157222 + 0.272317i
$$705$$ 0 0
$$706$$ 6.10051 0.229596
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 18.1421 31.4231i 0.681342 1.18012i −0.293229 0.956042i $$-0.594730\pi$$
0.974571 0.224077i $$-0.0719368\pi$$
$$710$$ −6.58579 11.4069i −0.247160 0.428094i
$$711$$ 0 0
$$712$$ 11.2929 19.5599i 0.423219 0.733037i
$$713$$ 8.97056 0.335950
$$714$$ 0 0
$$715$$ −17.6569 −0.660329
$$716$$ 17.9706 31.1259i 0.671591 1.16323i
$$717$$ 0 0
$$718$$ 0.0710678 + 0.123093i 0.00265223 + 0.00459379i
$$719$$ −20.9706 + 36.3221i −0.782070 + 1.35459i 0.148664 + 0.988888i $$0.452503\pi$$
−0.930734 + 0.365697i $$0.880831\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 4.55635 0.169570
$$723$$ 0 0
$$724$$ 2.36396 + 4.09450i 0.0878559 + 0.152171i
$$725$$ −22.7279 39.3659i −0.844094 1.46201i
$$726$$ 0 0
$$727$$ −12.4853 −0.463053 −0.231527 0.972829i $$-0.574372\pi$$
−0.231527 + 0.972829i $$0.574372\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −9.82843 + 17.0233i −0.363766 + 0.630062i
$$731$$ 6.34315 + 10.9867i 0.234610 + 0.406356i
$$732$$ 0 0
$$733$$ 24.8492 43.0402i 0.917828 1.58972i 0.115120 0.993352i $$-0.463275\pi$$
0.802708 0.596373i $$-0.203392\pi$$
$$734$$ −1.37258 −0.0506630
$$735$$ 0 0
$$736$$ −33.7990 −1.24585
$$737$$ 5.65685 9.79796i 0.208373 0.360912i
$$738$$ 0 0
$$739$$ −2.34315 4.05845i −0.0861940 0.149292i 0.819705 0.572785i $$-0.194137\pi$$
−0.905899 + 0.423493i $$0.860804\pi$$
$$740$$ −12.4853 + 21.6251i −0.458968 + 0.794956i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 50.9706 1.86993 0.934964 0.354742i $$-0.115431\pi$$
0.934964 + 0.354742i $$0.115431\pi$$
$$744$$ 0 0
$$745$$ 29.5563 + 51.1931i 1.08286 + 1.87557i
$$746$$ −2.21320 3.83338i −0.0810311 0.140350i
$$747$$ 0 0
$$748$$ 8.20101 0.299859
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −6.82843 + 11.8272i −0.249173 + 0.431580i −0.963297 0.268440i $$-0.913492\pi$$
0.714124 + 0.700020i $$0.246825\pi$$
$$752$$ 4.24264 + 7.34847i 0.154713 + 0.267971i
$$753$$ 0 0
$$754$$ −3.65685 + 6.33386i −0.133175 + 0.230665i
$$755$$ 40.9706 1.49107
$$756$$ 0 0
$$757$$ 26.3431 0.957458 0.478729 0.877963i $$-0.341098\pi$$
0.478729 + 0.877963i $$0.341098\pi$$
$$758$$ 1.79899 3.11594i 0.0653423 0.113176i
$$759$$ 0 0
$$760$$ −7.65685 13.2621i −0.277743 0.481065i
$$761$$ 9.26346 16.0448i 0.335800 0.581623i −0.647838 0.761778i $$-0.724327\pi$$
0.983638 + 0.180155i $$0.0576600\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −32.9117 −1.19070
$$765$$ 0 0
$$766$$ −3.79899 6.58004i −0.137263 0.237747i
$$767$$ −1.51472 2.62357i −0.0546933 0.0947316i
$$768$$ 0 0
$$769$$ −29.6985 −1.07095 −0.535477 0.844550i $$-0.679868\pi$$
−0.535477 + 0.844550i $$0.679868\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 4.85786 8.41407i 0.174838 0.302829i
$$773$$ 4.77817 + 8.27604i 0.171859 + 0.297669i 0.939070 0.343727i $$-0.111689\pi$$
−0.767211 + 0.641395i $$0.778356\pi$$
$$774$$ 0 0
$$775$$ −3.89949 + 6.75412i −0.140074 + 0.242615i
$$776$$ −4.10051 −0.147200
$$777$$ 0 0
$$778$$ −7.51472 −0.269416
$$779$$ −8.82843 + 15.2913i −0.316311 + 0.547867i
$$780$$ 0 0
$$781$$ 9.31371 + 16.1318i 0.333271 + 0.577242i
$$782$$ −3.55635 + 6.15978i −0.127175 + 0.220273i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −40.1421 −1.43273
$$786$$ 0 0
$$787$$ 12.3431 + 21.3790i