# Properties

 Label 567.2.i.d.269.2 Level $567$ Weight $2$ Character 567.269 Analytic conductor $4.528$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(215,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("567.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.i (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: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ 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: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 269.2 Root $$-1.22474 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.269 Dual form 567.2.i.d.215.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.41421i q^{2} +(-1.22474 + 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +O(q^{10})$$ $$q+1.41421i q^{2} +(-1.22474 + 2.12132i) q^{5} +(-2.00000 - 1.73205i) q^{7} +2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +(1.22474 - 0.707107i) q^{11} +(-4.50000 + 2.59808i) q^{13} +(2.44949 - 2.82843i) q^{14} -4.00000 q^{16} +(-2.44949 + 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 + 1.73205i) q^{22} +(-4.89898 - 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.67423 - 6.36396i) q^{26} +(2.44949 + 1.41421i) q^{29} -1.73205i q^{31} +(-6.00000 - 3.46410i) q^{34} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} +(1.22474 + 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} +(3.67423 + 6.36396i) q^{41} +(0.500000 - 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} -12.2474 q^{47} +(1.00000 + 6.92820i) q^{49} +(1.22474 - 0.707107i) q^{50} +(2.44949 + 1.41421i) q^{53} +3.46410i q^{55} +(4.89898 - 5.65685i) q^{56} +(-2.00000 + 3.46410i) q^{58} +4.89898 q^{59} -3.46410i q^{61} +2.44949 q^{62} -8.00000 q^{64} -12.7279i q^{65} +11.0000 q^{67} +(3.00000 + 8.66025i) q^{70} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} +(-1.22474 + 0.707107i) q^{74} +(-3.67423 - 0.707107i) q^{77} +5.00000 q^{79} +(4.89898 - 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(-3.67423 + 6.36396i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(1.22474 + 0.707107i) q^{86} +(2.00000 + 3.46410i) q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} -17.3205i q^{94} +4.24264i q^{95} +(9.00000 + 5.19615i) q^{97} +(-9.79796 + 1.41421i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{7}+O(q^{10})$$ 4 * q - 8 * q^7 $$4 q - 8 q^{7} - 12 q^{10} - 18 q^{13} - 16 q^{16} + 6 q^{19} + 4 q^{22} - 2 q^{25} - 24 q^{34} + 2 q^{37} - 24 q^{40} + 2 q^{43} + 16 q^{46} + 4 q^{49} - 8 q^{58} - 32 q^{64} + 44 q^{67} + 12 q^{70} + 6 q^{73} + 20 q^{79} - 36 q^{82} - 24 q^{85} + 8 q^{88} + 54 q^{91} + 36 q^{97}+O(q^{100})$$ 4 * q - 8 * q^7 - 12 * q^10 - 18 * q^13 - 16 * q^16 + 6 * q^19 + 4 * q^22 - 2 * q^25 - 24 * q^34 + 2 * q^37 - 24 * q^40 + 2 * q^43 + 16 * q^46 + 4 * q^49 - 8 * q^58 - 32 * q^64 + 44 * q^67 + 12 * q^70 + 6 * q^73 + 20 * q^79 - 36 * q^82 - 24 * q^85 + 8 * q^88 + 54 * q^91 + 36 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.22474 + 2.12132i −0.547723 + 0.948683i 0.450708 + 0.892672i $$0.351172\pi$$
−0.998430 + 0.0560116i $$0.982162\pi$$
$$6$$ 0 0
$$7$$ −2.00000 1.73205i −0.755929 0.654654i
$$8$$ 2.82843i 1.00000i
$$9$$ 0 0
$$10$$ −3.00000 1.73205i −0.948683 0.547723i
$$11$$ 1.22474 0.707107i 0.369274 0.213201i −0.303867 0.952714i $$-0.598278\pi$$
0.673141 + 0.739514i $$0.264945\pi$$
$$12$$ 0 0
$$13$$ −4.50000 + 2.59808i −1.24808 + 0.720577i −0.970725 0.240192i $$-0.922790\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 2.44949 2.82843i 0.654654 0.755929i
$$15$$ 0 0
$$16$$ −4.00000 −1.00000
$$17$$ −2.44949 + 4.24264i −0.594089 + 1.02899i 0.399586 + 0.916696i $$0.369154\pi$$
−0.993675 + 0.112296i $$0.964180\pi$$
$$18$$ 0 0
$$19$$ 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i $$-0.603001\pi$$
0.662094 + 0.749421i $$0.269668\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 + 1.73205i 0.213201 + 0.369274i
$$23$$ −4.89898 2.82843i −1.02151 0.589768i −0.106967 0.994263i $$-0.534114\pi$$
−0.914540 + 0.404495i $$0.867447\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −3.67423 6.36396i −0.720577 1.24808i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 2.44949 + 1.41421i 0.454859 + 0.262613i 0.709880 0.704323i $$-0.248749\pi$$
−0.255021 + 0.966935i $$0.582082\pi$$
$$30$$ 0 0
$$31$$ 1.73205i 0.311086i −0.987829 0.155543i $$-0.950287\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ −6.00000 3.46410i −1.02899 0.594089i
$$35$$ 6.12372 2.12132i 1.03510 0.358569i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 1.22474 + 2.12132i 0.198680 + 0.344124i
$$39$$ 0 0
$$40$$ −6.00000 3.46410i −0.948683 0.547723i
$$41$$ 3.67423 + 6.36396i 0.573819 + 0.993884i 0.996169 + 0.0874508i $$0.0278721\pi$$
−0.422350 + 0.906433i $$0.638795\pi$$
$$42$$ 0 0
$$43$$ 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i $$-0.809039\pi$$
0.901629 + 0.432511i $$0.142372\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 4.00000 6.92820i 0.589768 1.02151i
$$47$$ −12.2474 −1.78647 −0.893237 0.449586i $$-0.851571\pi$$
−0.893237 + 0.449586i $$0.851571\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 1.22474 0.707107i 0.173205 0.100000i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.44949 + 1.41421i 0.336463 + 0.194257i 0.658707 0.752400i $$-0.271104\pi$$
−0.322244 + 0.946657i $$0.604437\pi$$
$$54$$ 0 0
$$55$$ 3.46410i 0.467099i
$$56$$ 4.89898 5.65685i 0.654654 0.755929i
$$57$$ 0 0
$$58$$ −2.00000 + 3.46410i −0.262613 + 0.454859i
$$59$$ 4.89898 0.637793 0.318896 0.947790i $$-0.396688\pi$$
0.318896 + 0.947790i $$0.396688\pi$$
$$60$$ 0 0
$$61$$ 3.46410i 0.443533i −0.975100 0.221766i $$-0.928818\pi$$
0.975100 0.221766i $$-0.0711822\pi$$
$$62$$ 2.44949 0.311086
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ 12.7279i 1.57870i
$$66$$ 0 0
$$67$$ 11.0000 1.34386 0.671932 0.740613i $$-0.265465\pi$$
0.671932 + 0.740613i $$0.265465\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 3.00000 + 8.66025i 0.358569 + 1.03510i
$$71$$ 7.07107i 0.839181i −0.907713 0.419591i $$-0.862174\pi$$
0.907713 0.419591i $$-0.137826\pi$$
$$72$$ 0 0
$$73$$ 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i $$-0.301014\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ −1.22474 + 0.707107i −0.142374 + 0.0821995i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −3.67423 0.707107i −0.418718 0.0805823i
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 4.89898 8.48528i 0.547723 0.948683i
$$81$$ 0 0
$$82$$ −9.00000 + 5.19615i −0.993884 + 0.573819i
$$83$$ −3.67423 + 6.36396i −0.403300 + 0.698535i −0.994122 0.108266i $$-0.965470\pi$$
0.590822 + 0.806802i $$0.298803\pi$$
$$84$$ 0 0
$$85$$ −6.00000 10.3923i −0.650791 1.12720i
$$86$$ 1.22474 + 0.707107i 0.132068 + 0.0762493i
$$87$$ 0 0
$$88$$ 2.00000 + 3.46410i 0.213201 + 0.369274i
$$89$$ 2.44949 + 4.24264i 0.259645 + 0.449719i 0.966147 0.257993i $$-0.0830610\pi$$
−0.706502 + 0.707712i $$0.749728\pi$$
$$90$$ 0 0
$$91$$ 13.5000 + 2.59808i 1.41518 + 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 17.3205i 1.78647i
$$95$$ 4.24264i 0.435286i
$$96$$ 0 0
$$97$$ 9.00000 + 5.19615i 0.913812 + 0.527589i 0.881656 0.471894i $$-0.156429\pi$$
0.0321560 + 0.999483i $$0.489763\pi$$
$$98$$ −9.79796 + 1.41421i −0.989743 + 0.142857i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.57321 + 14.8492i 0.853067 + 1.47755i 0.878427 + 0.477876i $$0.158593\pi$$
−0.0253604 + 0.999678i $$0.508073\pi$$
$$102$$ 0 0
$$103$$ 7.50000 + 4.33013i 0.738997 + 0.426660i 0.821705 0.569914i $$-0.193023\pi$$
−0.0827075 + 0.996574i $$0.526357\pi$$
$$104$$ −7.34847 12.7279i −0.720577 1.24808i
$$105$$ 0 0
$$106$$ −2.00000 + 3.46410i −0.194257 + 0.336463i
$$107$$ −2.44949 + 1.41421i −0.236801 + 0.136717i −0.613706 0.789535i $$-0.710322\pi$$
0.376905 + 0.926252i $$0.376988\pi$$
$$108$$ 0 0
$$109$$ 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i $$-0.818083\pi$$
0.888977 + 0.457951i $$0.151417\pi$$
$$110$$ −4.89898 −0.467099
$$111$$ 0 0
$$112$$ 8.00000 + 6.92820i 0.755929 + 0.654654i
$$113$$ 1.22474 0.707107i 0.115214 0.0665190i −0.441285 0.897367i $$-0.645477\pi$$
0.556500 + 0.830848i $$0.312144\pi$$
$$114$$ 0 0
$$115$$ 12.0000 6.92820i 1.11901 0.646058i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 6.92820i 0.637793i
$$119$$ 12.2474 4.24264i 1.12272 0.388922i
$$120$$ 0 0
$$121$$ −4.50000 + 7.79423i −0.409091 + 0.708566i
$$122$$ 4.89898 0.443533
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.79796 −0.876356
$$126$$ 0 0
$$127$$ 11.0000 0.976092 0.488046 0.872818i $$-0.337710\pi$$
0.488046 + 0.872818i $$0.337710\pi$$
$$128$$ 11.3137i 1.00000i
$$129$$ 0 0
$$130$$ 18.0000 1.57870
$$131$$ −1.22474 + 2.12132i −0.107006 + 0.185341i −0.914556 0.404459i $$-0.867460\pi$$
0.807550 + 0.589799i $$0.200793\pi$$
$$132$$ 0 0
$$133$$ −4.50000 0.866025i −0.390199 0.0750939i
$$134$$ 15.5563i 1.34386i
$$135$$ 0 0
$$136$$ −12.0000 6.92820i −1.02899 0.594089i
$$137$$ −9.79796 + 5.65685i −0.837096 + 0.483298i −0.856276 0.516518i $$-0.827228\pi$$
0.0191800 + 0.999816i $$0.493894\pi$$
$$138$$ 0 0
$$139$$ −4.50000 + 2.59808i −0.381685 + 0.220366i −0.678551 0.734553i $$-0.737392\pi$$
0.296866 + 0.954919i $$0.404058\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 10.0000 0.839181
$$143$$ −3.67423 + 6.36396i −0.307255 + 0.532181i
$$144$$ 0 0
$$145$$ −6.00000 + 3.46410i −0.498273 + 0.287678i
$$146$$ −1.22474 + 2.12132i −0.101361 + 0.175562i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.89898 2.82843i −0.401340 0.231714i 0.285722 0.958313i $$-0.407767\pi$$
−0.687062 + 0.726599i $$0.741100\pi$$
$$150$$ 0 0
$$151$$ 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i $$0.186277\pi$$
0.0615699 + 0.998103i $$0.480389\pi$$
$$152$$ 2.44949 + 4.24264i 0.198680 + 0.344124i
$$153$$ 0 0
$$154$$ 1.00000 5.19615i 0.0805823 0.418718i
$$155$$ 3.67423 + 2.12132i 0.295122 + 0.170389i
$$156$$ 0 0
$$157$$ 17.3205i 1.38233i −0.722698 0.691164i $$-0.757098\pi$$
0.722698 0.691164i $$-0.242902\pi$$
$$158$$ 7.07107i 0.562544i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.89898 + 14.1421i 0.386094 + 1.11456i
$$162$$ 0 0
$$163$$ 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i $$-0.0385779\pi$$
−0.601035 + 0.799223i $$0.705245\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −9.00000 5.19615i −0.698535 0.403300i
$$167$$ 3.67423 + 6.36396i 0.284321 + 0.492458i 0.972444 0.233136i $$-0.0748986\pi$$
−0.688123 + 0.725594i $$0.741565\pi$$
$$168$$ 0 0
$$169$$ 7.00000 12.1244i 0.538462 0.932643i
$$170$$ 14.6969 8.48528i 1.12720 0.650791i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 9.79796 0.744925 0.372463 0.928047i $$-0.378514\pi$$
0.372463 + 0.928047i $$0.378514\pi$$
$$174$$ 0 0
$$175$$ −0.500000 + 2.59808i −0.0377964 + 0.196396i
$$176$$ −4.89898 + 2.82843i −0.369274 + 0.213201i
$$177$$ 0 0
$$178$$ −6.00000 + 3.46410i −0.449719 + 0.259645i
$$179$$ −8.57321 4.94975i −0.640792 0.369961i 0.144127 0.989559i $$-0.453962\pi$$
−0.784920 + 0.619598i $$0.787296\pi$$
$$180$$ 0 0
$$181$$ 15.5885i 1.15868i 0.815086 + 0.579340i $$0.196690\pi$$
−0.815086 + 0.579340i $$0.803310\pi$$
$$182$$ −3.67423 + 19.0919i −0.272352 + 1.41518i
$$183$$ 0 0
$$184$$ 8.00000 13.8564i 0.589768 1.02151i
$$185$$ −2.44949 −0.180090
$$186$$ 0 0
$$187$$ 6.92820i 0.506640i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −6.00000 −0.435286
$$191$$ 1.41421i 0.102329i 0.998690 + 0.0511645i $$0.0162933\pi$$
−0.998690 + 0.0511645i $$0.983707\pi$$
$$192$$ 0 0
$$193$$ 11.0000 0.791797 0.395899 0.918294i $$-0.370433\pi$$
0.395899 + 0.918294i $$0.370433\pi$$
$$194$$ −7.34847 + 12.7279i −0.527589 + 0.913812i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.7990i 1.41062i −0.708899 0.705310i $$-0.750808\pi$$
0.708899 0.705310i $$-0.249192\pi$$
$$198$$ 0 0
$$199$$ −12.0000 6.92820i −0.850657 0.491127i 0.0102152 0.999948i $$-0.496748\pi$$
−0.860873 + 0.508821i $$0.830082\pi$$
$$200$$ 2.44949 1.41421i 0.173205 0.100000i
$$201$$ 0 0
$$202$$ −21.0000 + 12.1244i −1.47755 + 0.853067i
$$203$$ −2.44949 7.07107i −0.171920 0.496292i
$$204$$ 0 0
$$205$$ −18.0000 −1.25717
$$206$$ −6.12372 + 10.6066i −0.426660 + 0.738997i
$$207$$ 0 0
$$208$$ 18.0000 10.3923i 1.24808 0.720577i
$$209$$ 1.22474 2.12132i 0.0847174 0.146735i
$$210$$ 0 0
$$211$$ 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i $$0.106801\pi$$
−0.186966 + 0.982366i $$0.559865\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −2.00000 3.46410i −0.136717 0.236801i
$$215$$ 1.22474 + 2.12132i 0.0835269 + 0.144673i
$$216$$ 0 0
$$217$$ −3.00000 + 3.46410i −0.203653 + 0.235159i
$$218$$ 1.22474 + 0.707107i 0.0829502 + 0.0478913i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 25.4558i 1.71235i
$$222$$ 0 0
$$223$$ −18.0000 10.3923i −1.20537 0.695920i −0.243625 0.969870i $$-0.578337\pi$$
−0.961744 + 0.273949i $$0.911670\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.00000 + 1.73205i 0.0665190 + 0.115214i
$$227$$ −13.4722 23.3345i −0.894181 1.54877i −0.834815 0.550530i $$-0.814425\pi$$
−0.0593658 0.998236i $$-0.518908\pi$$
$$228$$ 0 0
$$229$$ −19.5000 11.2583i −1.28860 0.743971i −0.310192 0.950674i $$-0.600393\pi$$
−0.978404 + 0.206702i $$0.933727\pi$$
$$230$$ 9.79796 + 16.9706i 0.646058 + 1.11901i
$$231$$ 0 0
$$232$$ −4.00000 + 6.92820i −0.262613 + 0.454859i
$$233$$ 8.57321 4.94975i 0.561650 0.324269i −0.192158 0.981364i $$-0.561548\pi$$
0.753807 + 0.657095i $$0.228215\pi$$
$$234$$ 0 0
$$235$$ 15.0000 25.9808i 0.978492 1.69480i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 6.00000 + 17.3205i 0.388922 + 1.12272i
$$239$$ 23.2702 13.4350i 1.50522 0.869040i 0.505239 0.862979i $$-0.331404\pi$$
0.999982 0.00606055i $$-0.00192914\pi$$
$$240$$ 0 0
$$241$$ 12.0000 6.92820i 0.772988 0.446285i −0.0609515 0.998141i $$-0.519414\pi$$
0.833939 + 0.551856i $$0.186080\pi$$
$$242$$ −11.0227 6.36396i −0.708566 0.409091i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −15.9217 6.36396i −1.01720 0.406579i
$$246$$ 0 0
$$247$$ −4.50000 + 7.79423i −0.286328 + 0.495935i
$$248$$ 4.89898 0.311086
$$249$$ 0 0
$$250$$ 13.8564i 0.876356i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −8.00000 −0.502956
$$254$$ 15.5563i 0.976092i
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.22474 + 2.12132i −0.0763975 + 0.132324i −0.901693 0.432377i $$-0.857675\pi$$
0.825296 + 0.564701i $$0.191008\pi$$
$$258$$ 0 0
$$259$$ 0.500000 2.59808i 0.0310685 0.161437i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.00000 1.73205i −0.185341 0.107006i
$$263$$ 12.2474 7.07107i 0.755210 0.436021i −0.0723633 0.997378i $$-0.523054\pi$$
0.827573 + 0.561358i $$0.189721\pi$$
$$264$$ 0 0
$$265$$ −6.00000 + 3.46410i −0.368577 + 0.212798i
$$266$$ 1.22474 6.36396i 0.0750939 0.390199i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 8.57321 14.8492i 0.522718 0.905374i −0.476932 0.878940i $$-0.658251\pi$$
0.999651 0.0264343i $$-0.00841529\pi$$
$$270$$ 0 0
$$271$$ −12.0000 + 6.92820i −0.728948 + 0.420858i −0.818037 0.575165i $$-0.804938\pi$$
0.0890891 + 0.996024i $$0.471604\pi$$
$$272$$ 9.79796 16.9706i 0.594089 1.02899i
$$273$$ 0 0
$$274$$ −8.00000 13.8564i −0.483298 0.837096i
$$275$$ −1.22474 0.707107i −0.0738549 0.0426401i
$$276$$ 0 0
$$277$$ −11.5000 19.9186i −0.690968 1.19679i −0.971521 0.236953i $$-0.923851\pi$$
0.280553 0.959839i $$-0.409482\pi$$
$$278$$ −3.67423 6.36396i −0.220366 0.381685i
$$279$$ 0 0
$$280$$ 6.00000 + 17.3205i 0.358569 + 1.03510i
$$281$$ −19.5959 11.3137i −1.16899 0.674919i −0.215551 0.976492i $$-0.569155\pi$$
−0.953443 + 0.301573i $$0.902488\pi$$
$$282$$ 0 0
$$283$$ 1.73205i 0.102960i −0.998674 0.0514799i $$-0.983606\pi$$
0.998674 0.0514799i $$-0.0163938\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −9.00000 5.19615i −0.532181 0.307255i
$$287$$ 3.67423 19.0919i 0.216883 1.12696i
$$288$$ 0 0
$$289$$ −3.50000 6.06218i −0.205882 0.356599i
$$290$$ −4.89898 8.48528i −0.287678 0.498273i
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −7.34847 12.7279i −0.429302 0.743573i 0.567509 0.823367i $$-0.307907\pi$$
−0.996811 + 0.0797939i $$0.974574\pi$$
$$294$$ 0 0
$$295$$ −6.00000 + 10.3923i −0.349334 + 0.605063i
$$296$$ −2.44949 + 1.41421i −0.142374 + 0.0821995i
$$297$$ 0 0
$$298$$ 4.00000 6.92820i 0.231714 0.401340i
$$299$$ 29.3939 1.69989
$$300$$ 0 0
$$301$$ −2.50000 + 0.866025i −0.144098 + 0.0499169i
$$302$$ −26.9444 + 15.5563i −1.55048 + 0.895167i
$$303$$ 0 0
$$304$$ −6.00000 + 3.46410i −0.344124 + 0.198680i
$$305$$ 7.34847 + 4.24264i 0.420772 + 0.242933i
$$306$$ 0 0
$$307$$ 15.5885i 0.889680i −0.895610 0.444840i $$-0.853260\pi$$
0.895610 0.444840i $$-0.146740\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −3.00000 + 5.19615i −0.170389 + 0.295122i
$$311$$ −17.1464 −0.972285 −0.486142 0.873880i $$-0.661596\pi$$
−0.486142 + 0.873880i $$0.661596\pi$$
$$312$$ 0 0
$$313$$ 12.1244i 0.685309i 0.939461 + 0.342655i $$0.111326\pi$$
−0.939461 + 0.342655i $$0.888674\pi$$
$$314$$ 24.4949 1.38233
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 14.1421i 0.794301i 0.917753 + 0.397151i $$0.130001\pi$$
−0.917753 + 0.397151i $$0.869999\pi$$
$$318$$ 0 0
$$319$$ 4.00000 0.223957
$$320$$ 9.79796 16.9706i 0.547723 0.948683i
$$321$$ 0 0
$$322$$ −20.0000 + 6.92820i −1.11456 + 0.386094i
$$323$$ 8.48528i 0.472134i
$$324$$ 0 0
$$325$$ 4.50000 + 2.59808i 0.249615 + 0.144115i
$$326$$ −12.2474 + 7.07107i −0.678323 + 0.391630i
$$327$$ 0 0
$$328$$ −18.0000 + 10.3923i −0.993884 + 0.573819i
$$329$$ 24.4949 + 21.2132i 1.35045 + 1.16952i
$$330$$ 0 0
$$331$$ −31.0000 −1.70391 −0.851957 0.523612i $$-0.824584\pi$$
−0.851957 + 0.523612i $$0.824584\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −9.00000 + 5.19615i −0.492458 + 0.284321i
$$335$$ −13.4722 + 23.3345i −0.736065 + 1.27490i
$$336$$ 0 0
$$337$$ −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i $$-0.951176\pi$$
0.361815 0.932250i $$-0.382157\pi$$
$$338$$ 17.1464 + 9.89949i 0.932643 + 0.538462i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.22474 2.12132i −0.0663237 0.114876i
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 2.44949 + 1.41421i 0.132068 + 0.0762493i
$$345$$ 0 0
$$346$$ 13.8564i 0.744925i
$$347$$ 31.1127i 1.67022i 0.550085 + 0.835109i $$0.314595\pi$$
−0.550085 + 0.835109i $$0.685405\pi$$
$$348$$ 0 0
$$349$$ 9.00000 + 5.19615i 0.481759 + 0.278144i 0.721149 0.692780i $$-0.243614\pi$$
−0.239390 + 0.970923i $$0.576948\pi$$
$$350$$ −3.67423 0.707107i −0.196396 0.0377964i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.57321 + 14.8492i 0.456306 + 0.790345i 0.998762 0.0497387i $$-0.0158389\pi$$
−0.542456 + 0.840084i $$0.682506\pi$$
$$354$$ 0 0
$$355$$ 15.0000 + 8.66025i 0.796117 + 0.459639i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 7.00000 12.1244i 0.369961 0.640792i
$$359$$ −24.4949 + 14.1421i −1.29279 + 0.746393i −0.979148 0.203148i $$-0.934883\pi$$
−0.313643 + 0.949541i $$0.601550\pi$$
$$360$$ 0 0
$$361$$ −8.00000 + 13.8564i −0.421053 + 0.729285i
$$362$$ −22.0454 −1.15868
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −3.67423 + 2.12132i −0.192318 + 0.111035i
$$366$$ 0 0
$$367$$ −1.50000 + 0.866025i −0.0782994 + 0.0452062i −0.538639 0.842537i $$-0.681061\pi$$
0.460339 + 0.887743i $$0.347728\pi$$
$$368$$ 19.5959 + 11.3137i 1.02151 + 0.589768i
$$369$$ 0 0
$$370$$ 3.46410i 0.180090i
$$371$$ −2.44949 7.07107i −0.127171 0.367112i
$$372$$ 0 0
$$373$$ −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i $$0.436990\pi$$
−0.947444 + 0.319921i $$0.896344\pi$$
$$374$$ −9.79796 −0.506640
$$375$$ 0 0
$$376$$ 34.6410i 1.78647i
$$377$$ −14.6969 −0.756931
$$378$$ 0 0
$$379$$ −7.00000 −0.359566 −0.179783 0.983706i $$-0.557540\pi$$
−0.179783 + 0.983706i $$0.557540\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −2.00000 −0.102329
$$383$$ 9.79796 16.9706i 0.500652 0.867155i −0.499347 0.866402i $$-0.666427\pi$$
1.00000 0.000753393i $$-0.000239813\pi$$
$$384$$ 0 0
$$385$$ 6.00000 6.92820i 0.305788 0.353094i
$$386$$ 15.5563i 0.791797i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 23.2702 13.4350i 1.17984 0.681183i 0.223865 0.974620i $$-0.428132\pi$$
0.955978 + 0.293437i $$0.0947991\pi$$
$$390$$ 0 0
$$391$$ 24.0000 13.8564i 1.21373 0.700749i
$$392$$ −19.5959 + 2.82843i −0.989743 + 0.142857i
$$393$$ 0 0
$$394$$ 28.0000 1.41062
$$395$$ −6.12372 + 10.6066i −0.308118 + 0.533676i
$$396$$ 0 0
$$397$$ 1.50000 0.866025i 0.0752828 0.0434646i −0.461886 0.886939i $$-0.652827\pi$$
0.537169 + 0.843475i $$0.319494\pi$$
$$398$$ 9.79796 16.9706i 0.491127 0.850657i
$$399$$ 0 0
$$400$$ 2.00000 + 3.46410i 0.100000 + 0.173205i
$$401$$ 17.1464 + 9.89949i 0.856252 + 0.494357i 0.862755 0.505622i $$-0.168737\pi$$
−0.00650355 + 0.999979i $$0.502070\pi$$
$$402$$ 0 0
$$403$$ 4.50000 + 7.79423i 0.224161 + 0.388258i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 10.0000 3.46410i 0.496292 0.171920i
$$407$$ 1.22474 + 0.707107i 0.0607083 + 0.0350500i
$$408$$ 0 0
$$409$$ 32.9090i 1.62724i −0.581394 0.813622i $$-0.697493\pi$$
0.581394 0.813622i $$-0.302507\pi$$
$$410$$ 25.4558i 1.25717i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −9.79796 8.48528i −0.482126 0.417533i
$$414$$ 0 0
$$415$$ −9.00000 15.5885i −0.441793 0.765207i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 3.00000 + 1.73205i 0.146735 + 0.0847174i
$$419$$ −18.3712 31.8198i −0.897491 1.55450i −0.830692 0.556733i $$-0.812055\pi$$
−0.0667989 0.997766i $$-0.521279\pi$$
$$420$$ 0 0
$$421$$ 0.500000 0.866025i 0.0243685 0.0422075i −0.853584 0.520955i $$-0.825576\pi$$
0.877952 + 0.478748i $$0.158909\pi$$
$$422$$ −26.9444 + 15.5563i −1.31163 + 0.757271i
$$423$$ 0 0
$$424$$ −4.00000 + 6.92820i −0.194257 + 0.336463i
$$425$$ 4.89898 0.237635
$$426$$ 0 0
$$427$$ −6.00000 + 6.92820i −0.290360 + 0.335279i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ −3.00000 + 1.73205i −0.144673 + 0.0835269i
$$431$$ 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i $$-0.211092\pi$$
−0.139114 + 0.990276i $$0.544426\pi$$
$$432$$ 0 0
$$433$$ 15.5885i 0.749133i 0.927200 + 0.374567i $$0.122209\pi$$
−0.927200 + 0.374567i $$0.877791\pi$$
$$434$$ −4.89898 4.24264i −0.235159 0.203653i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −9.79796 −0.468700
$$438$$ 0 0
$$439$$ 27.7128i 1.32266i 0.750095 + 0.661330i $$0.230008\pi$$
−0.750095 + 0.661330i $$0.769992\pi$$
$$440$$ −9.79796 −0.467099
$$441$$ 0 0
$$442$$ 36.0000 1.71235
$$443$$ 39.5980i 1.88136i 0.339300 + 0.940678i $$0.389810\pi$$
−0.339300 + 0.940678i $$0.610190\pi$$
$$444$$ 0 0
$$445$$ −12.0000 −0.568855
$$446$$ 14.6969 25.4558i 0.695920 1.20537i
$$447$$ 0 0
$$448$$ 16.0000 + 13.8564i 0.755929 + 0.654654i
$$449$$ 7.07107i 0.333704i −0.985982 0.166852i $$-0.946640\pi$$
0.985982 0.166852i $$-0.0533603\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 5.19615i 0.423793 + 0.244677i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 33.0000 19.0526i 1.54877 0.894181i
$$455$$ −22.0454 + 25.4558i −1.03350 + 1.19339i
$$456$$ 0 0
$$457$$ 5.00000 0.233890 0.116945 0.993138i $$-0.462690\pi$$
0.116945 + 0.993138i $$0.462690\pi$$
$$458$$ 15.9217 27.5772i 0.743971 1.28860i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 7.34847 12.7279i 0.342252 0.592798i −0.642598 0.766203i $$-0.722144\pi$$
0.984851 + 0.173405i $$0.0554769\pi$$
$$462$$ 0 0
$$463$$ 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i $$-0.0689855\pi$$
−0.674526 + 0.738251i $$0.735652\pi$$
$$464$$ −9.79796 5.65685i −0.454859 0.262613i
$$465$$ 0 0
$$466$$ 7.00000 + 12.1244i 0.324269 + 0.561650i
$$467$$ 13.4722 + 23.3345i 0.623419 + 1.07979i 0.988844 + 0.148952i $$0.0475901\pi$$
−0.365426 + 0.930841i $$0.619077\pi$$
$$468$$ 0 0
$$469$$ −22.0000 19.0526i −1.01587 0.879765i
$$470$$ 36.7423 + 21.2132i 1.69480 + 0.978492i
$$471$$ 0 0
$$472$$ 13.8564i 0.637793i
$$473$$ 1.41421i 0.0650256i
$$474$$ 0 0
$$475$$ −1.50000 0.866025i −0.0688247 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 19.0000 + 32.9090i 0.869040 + 1.50522i
$$479$$ −2.44949 4.24264i −0.111920 0.193851i 0.804624 0.593784i $$-0.202367\pi$$
−0.916544 + 0.399933i $$0.869033\pi$$
$$480$$ 0 0
$$481$$ −4.50000 2.59808i −0.205182 0.118462i
$$482$$ 9.79796 + 16.9706i 0.446285 + 0.772988i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −22.0454 + 12.7279i −1.00103 + 0.577945i
$$486$$ 0 0
$$487$$ −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i $$-0.959191\pi$$
0.606621 + 0.794991i $$0.292524\pi$$
$$488$$ 9.79796 0.443533
$$489$$ 0 0
$$490$$ 9.00000 22.5167i 0.406579 1.01720i
$$491$$ −9.79796 + 5.65685i −0.442176 + 0.255290i −0.704520 0.709684i $$-0.748838\pi$$
0.262344 + 0.964974i $$0.415504\pi$$
$$492$$ 0 0
$$493$$ −12.0000 + 6.92820i −0.540453 + 0.312031i
$$494$$ −11.0227 6.36396i −0.495935 0.286328i
$$495$$ 0 0
$$496$$ 6.92820i 0.311086i
$$497$$ −12.2474 + 14.1421i −0.549373 + 0.634361i
$$498$$ 0 0
$$499$$ 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i $$-0.644297\pi$$
0.997532 0.0702185i $$-0.0223697\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 22.0454 0.982956 0.491478 0.870890i $$-0.336457\pi$$
0.491478 + 0.870890i $$0.336457\pi$$
$$504$$ 0 0
$$505$$ −42.0000 −1.86898
$$506$$ 11.3137i 0.502956i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −1.22474 + 2.12132i −0.0542859 + 0.0940259i −0.891891 0.452250i $$-0.850622\pi$$
0.837605 + 0.546276i $$0.183955\pi$$
$$510$$ 0 0
$$511$$ −1.50000 4.33013i −0.0663561 0.191554i
$$512$$ 22.6274i 1.00000i
$$513$$ 0 0
$$514$$ −3.00000 1.73205i −0.132324 0.0763975i
$$515$$ −18.3712 + 10.6066i −0.809531 + 0.467383i
$$516$$ 0 0
$$517$$ −15.0000 + 8.66025i −0.659699 + 0.380878i
$$518$$ 3.67423 + 0.707107i 0.161437 + 0.0310685i
$$519$$ 0 0
$$520$$ 36.0000 1.57870
$$521$$ −2.44949 + 4.24264i −0.107314 + 0.185873i −0.914681 0.404176i $$-0.867558\pi$$
0.807367 + 0.590049i $$0.200892\pi$$
$$522$$ 0 0
$$523$$ 1.50000 0.866025i 0.0655904 0.0378686i −0.466846 0.884339i $$-0.654610\pi$$
0.532437 + 0.846470i $$0.321276\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 10.0000 + 17.3205i 0.436021 + 0.755210i
$$527$$ 7.34847 + 4.24264i 0.320104 + 0.184812i
$$528$$ 0 0
$$529$$ 4.50000 + 7.79423i 0.195652 + 0.338880i
$$530$$ −4.89898 8.48528i −0.212798 0.368577i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −33.0681 19.0919i −1.43234 0.826961i
$$534$$ 0 0
$$535$$ 6.92820i 0.299532i
$$536$$ 31.1127i 1.34386i
$$537$$ 0 0
$$538$$ 21.0000 + 12.1244i 0.905374 + 0.522718i
$$539$$ 6.12372 + 7.77817i 0.263767 + 0.335030i
$$540$$ 0 0
$$541$$ −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i $$-0.285749\pi$$
−0.988847 + 0.148933i $$0.952416\pi$$
$$542$$ −9.79796 16.9706i −0.420858 0.728948i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 1.22474 + 2.12132i 0.0524623 + 0.0908674i
$$546$$ 0 0
$$547$$ 5.00000 8.66025i 0.213785 0.370286i −0.739111 0.673583i $$-0.764754\pi$$
0.952896 + 0.303298i $$0.0980876\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 1.00000 1.73205i 0.0426401 0.0738549i
$$551$$ 4.89898 0.208704
$$552$$ 0 0
$$553$$ −10.0000 8.66025i −0.425243 0.368271i
$$554$$ 28.1691 16.2635i 1.19679 0.690968i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 13.4722 + 7.77817i 0.570835 + 0.329572i 0.757483 0.652855i $$-0.226429\pi$$
−0.186648 + 0.982427i $$0.559762\pi$$
$$558$$ 0 0
$$559$$ 5.19615i 0.219774i
$$560$$ −24.4949 + 8.48528i −1.03510 + 0.358569i
$$561$$ 0 0
$$562$$ 16.0000 27.7128i 0.674919 1.16899i
$$563$$ 26.9444 1.13557 0.567785 0.823177i $$-0.307800\pi$$
0.567785 + 0.823177i $$0.307800\pi$$
$$564$$ 0 0
$$565$$ 3.46410i 0.145736i
$$566$$ 2.44949 0.102960
$$567$$ 0 0
$$568$$ 20.0000 0.839181
$$569$$ 1.41421i 0.0592869i 0.999561 + 0.0296435i $$0.00943719\pi$$
−0.999561 + 0.0296435i $$0.990563\pi$$
$$570$$ 0 0
$$571$$ 11.0000 0.460336 0.230168 0.973151i $$-0.426072\pi$$
0.230168 + 0.973151i $$0.426072\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 27.0000 + 5.19615i 1.12696 + 0.216883i
$$575$$ 5.65685i 0.235907i
$$576$$ 0 0
$$577$$ 1.50000 + 0.866025i 0.0624458 + 0.0360531i 0.530898 0.847436i $$-0.321855\pi$$
−0.468452 + 0.883489i $$0.655188\pi$$
$$578$$ 8.57321 4.94975i 0.356599 0.205882i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 18.3712 6.36396i 0.762165 0.264022i
$$582$$ 0 0
$$583$$ 4.00000 0.165663
$$584$$ −2.44949 + 4.24264i −0.101361 + 0.175562i
$$585$$ 0 0
$$586$$ 18.0000 10.3923i 0.743573 0.429302i
$$587$$ 7.34847 12.7279i 0.303304 0.525338i −0.673578 0.739116i $$-0.735244\pi$$
0.976882 + 0.213778i $$0.0685770\pi$$
$$588$$ 0 0
$$589$$ −1.50000 2.59808i −0.0618064 0.107052i
$$590$$ −14.6969 8.48528i −0.605063 0.349334i
$$591$$ 0 0
$$592$$ −2.00000 3.46410i −0.0821995 0.142374i
$$593$$ −8.57321 14.8492i −0.352060 0.609785i 0.634550 0.772881i $$-0.281185\pi$$
−0.986610 + 0.163096i $$0.947852\pi$$
$$594$$ 0 0
$$595$$ −6.00000 + 31.1769i −0.245976 + 1.27813i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 41.5692i 1.69989i
$$599$$ 5.65685i 0.231133i 0.993300 + 0.115566i $$0.0368683\pi$$
−0.993300 + 0.115566i $$0.963132\pi$$
$$600$$ 0 0
$$601$$ 22.5000 + 12.9904i 0.917794 + 0.529889i 0.882931 0.469503i $$-0.155567\pi$$
0.0348635 + 0.999392i $$0.488900\pi$$
$$602$$ −1.22474 3.53553i −0.0499169 0.144098i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −11.0227 19.0919i −0.448137 0.776195i
$$606$$ 0 0
$$607$$ 34.5000 + 19.9186i 1.40031 + 0.808470i 0.994424 0.105453i $$-0.0336291\pi$$
0.405887 + 0.913923i $$0.366962\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −6.00000 + 10.3923i −0.242933 + 0.420772i
$$611$$ 55.1135 31.8198i 2.22965 1.28729i
$$612$$ 0 0
$$613$$ −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i $$-0.884985\pi$$
0.773869 + 0.633345i $$0.218319\pi$$
$$614$$ 22.0454 0.889680
$$615$$ 0 0
$$616$$ 2.00000 10.3923i 0.0805823 0.418718i
$$617$$ −20.8207 + 12.0208i −0.838208 + 0.483940i −0.856655 0.515890i $$-0.827461\pi$$
0.0184465 + 0.999830i $$0.494128\pi$$
$$618$$ 0 0
$$619$$ 25.5000 14.7224i 1.02493 0.591744i 0.109403 0.993997i $$-0.465106\pi$$
0.915529 + 0.402253i $$0.131773\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 24.2487i 0.972285i
$$623$$ 2.44949 12.7279i 0.0981367 0.509933i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ −17.1464 −0.685309
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −4.89898 −0.195335
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ 14.1421i 0.562544i
$$633$$ 0 0
$$634$$ −20.0000 −0.794301
$$635$$ −13.4722 + 23.3345i −0.534628 + 0.926002i
$$636$$ 0 0
$$637$$ −22.5000 28.5788i −0.891482 1.13233i
$$638$$ 5.65685i 0.223957i
$$639$$ 0 0
$$640$$ 24.0000 + 13.8564i 0.948683 + 0.547723i
$$641$$ 12.2474 7.07107i 0.483745 0.279290i −0.238231 0.971209i $$-0.576567\pi$$
0.721976 + 0.691918i $$0.243234\pi$$
$$642$$ 0 0
$$643$$ 22.5000 12.9904i 0.887313 0.512291i 0.0142506 0.999898i $$-0.495464\pi$$
0.873063 + 0.487608i $$0.162130\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −12.0000 −0.472134
$$647$$ 8.57321 14.8492i 0.337048 0.583784i −0.646828 0.762636i $$-0.723905\pi$$
0.983876 + 0.178852i $$0.0572383\pi$$
$$648$$ 0 0
$$649$$ 6.00000 3.46410i 0.235521 0.135978i
$$650$$ −3.67423 + 6.36396i −0.144115 + 0.249615i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 6.12372 + 3.53553i 0.239640 + 0.138356i 0.615011 0.788518i $$-0.289151\pi$$
−0.375371 + 0.926875i $$0.622485\pi$$
$$654$$ 0 0
$$655$$ −3.00000 5.19615i −0.117220 0.203030i
$$656$$ −14.6969 25.4558i −0.573819 0.993884i
$$657$$ 0 0
$$658$$ −30.0000 + 34.6410i −1.16952 + 1.35045i
$$659$$ −19.5959 11.3137i −0.763349 0.440720i 0.0671481 0.997743i $$-0.478610\pi$$
−0.830497 + 0.557024i $$0.811943\pi$$
$$660$$ 0 0
$$661$$ 29.4449i 1.14527i 0.819810 + 0.572636i $$0.194079\pi$$
−0.819810 + 0.572636i $$0.805921\pi$$
$$662$$ 43.8406i 1.70391i
$$663$$ 0 0
$$664$$ −18.0000 10.3923i −0.698535 0.403300i
$$665$$ 7.34847 8.48528i 0.284961 0.329045i
$$666$$ 0 0
$$667$$ −8.00000 13.8564i −0.309761 0.536522i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −33.0000 19.0526i −1.27490 0.736065i
$$671$$ −2.44949 4.24264i −0.0945615 0.163785i
$$672$$ 0 0
$$673$$ −17.5000 + 30.3109i −0.674575 + 1.16840i 0.302017 + 0.953302i $$0.402340\pi$$
−0.976593 + 0.215096i $$0.930993\pi$$
$$674$$ 28.1691 16.2635i 1.08503 0.626445i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 9.79796 0.376566 0.188283 0.982115i $$-0.439708\pi$$
0.188283 + 0.982115i $$0.439708\pi$$
$$678$$ 0 0
$$679$$ −9.00000 25.9808i −0.345388 0.997050i
$$680$$ 29.3939 16.9706i 1.12720 0.650791i
$$681$$ 0 0
$$682$$ 3.00000 1.73205i 0.114876 0.0663237i
$$683$$ −41.6413 24.0416i −1.59336 0.919927i −0.992725 0.120405i $$-0.961581\pi$$
−0.600636 0.799522i $$-0.705086\pi$$
$$684$$ 0 0
$$685$$ 27.7128i 1.05885i
$$686$$ 22.0454 + 14.1421i 0.841698 + 0.539949i
$$687$$ 0 0
$$688$$ −2.00000 + 3.46410i −0.0762493 + 0.132068i
$$689$$ −14.6969 −0.559909
$$690$$ 0 0
$$691$$ 43.3013i 1.64726i 0.567129 + 0.823629i $$0.308054\pi$$
−0.567129 + 0.823629i $$0.691946\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −44.0000 −1.67022
$$695$$ 12.7279i 0.482798i
$$696$$ 0 0
$$697$$ −36.0000 −1.36360
$$698$$ −7.34847 + 12.7279i −0.278144 + 0.481759i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.65685i 0.213656i 0.994277 + 0.106828i $$0.0340695\pi$$
−0.994277 + 0.106828i $$0.965931\pi$$
$$702$$ 0 0
$$703$$ 1.50000 + 0.866025i 0.0565736 + 0.0326628i
$$704$$ −9.79796 + 5.65685i −0.369274 + 0.213201i
$$705$$ 0 0
$$706$$ −21.0000 + 12.1244i −0.790345 + 0.456306i
$$707$$ 8.57321 44.5477i 0.322429 1.67539i
$$708$$ 0 0
$$709$$ −40.0000 −1.50223 −0.751116 0.660171i $$-0.770484\pi$$
−0.751116 + 0.660171i $$0.770484\pi$$
$$710$$ −12.2474 + 21.2132i −0.459639 + 0.796117i
$$711$$ 0 0
$$712$$ −12.0000 + 6.92820i −0.449719 + 0.259645i
$$713$$ −4.89898 + 8.48528i −0.183468 + 0.317776i
$$714$$ 0 0
$$715$$ −9.00000 15.5885i −0.336581 0.582975i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ −20.0000 34.6410i −0.746393 1.29279i
$$719$$ 13.4722 + 23.3345i 0.502428 + 0.870231i 0.999996 + 0.00280593i $$0.000893157\pi$$
−0.497568 + 0.867425i $$0.665774\pi$$
$$720$$ 0 0
$$721$$ −7.50000 21.6506i −0.279315 0.806312i
$$722$$ −19.5959 11.3137i −0.729285 0.421053i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.82843i 0.105045i
$$726$$ 0 0
$$727$$ 22.5000 + 12.9904i 0.834479 + 0.481787i 0.855384 0.517995i $$-0.173321\pi$$
−0.0209049 + 0.999781i $$0.506655\pi$$
$$728$$ −7.34847 + 38.1838i −0.272352 + 1.41518i
$$729$$ 0 0
$$730$$ −3.00000 5.19615i −0.111035 0.192318i
$$731$$ 2.44949 + 4.24264i 0.0905977 + 0.156920i
$$732$$ 0 0
$$733$$ 34.5000 + 19.9186i 1.27429 + 0.735710i 0.975792 0.218702i $$-0.0701821\pi$$
0.298495 + 0.954411i $$0.403515\pi$$
$$734$$ −1.22474 2.12132i −0.0452062 0.0782994i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.4722 7.77817i 0.496255 0.286513i
$$738$$ 0 0
$$739$$ 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i $$-0.827478\pi$$
0.875075 + 0.483987i $$0.160812\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 10.0000 3.46410i 0.367112 0.127171i
$$743$$ −20.8207 + 12.0208i −0.763836 + 0.441001i −0.830671 0.556763i $$-0.812043\pi$$
0.0668353 + 0.997764i $$0.478710\pi$$
$$744$$ 0 0
$$745$$ 12.0000 6.92820i 0.439646 0.253830i
$$746$$ −35.5176 20.5061i −1.30039 0.750782i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 7.34847 + 1.41421i 0.268507 + 0.0516742i
$$750$$ 0 0
$$751$$ −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i $$0.344142\pi$$
−0.999424 + 0.0339490i $$0.989192\pi$$
$$752$$ 48.9898 1.78647
$$753$$ 0 0
$$754$$ 20.7846i 0.756931i
$$755$$ −53.8888 −1.96121
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 9.89949i 0.359566i
$$759$$ 0 0
$$760$$ −12.0000 −0.435286
$$761$$ −12.2474 + 21.2132i −0.443970 + 0.768978i −0.997980 0.0635319i $$-0.979764\pi$$
0.554010 + 0.832510i $$0.313097\pi$$
$$762$$ 0 0
$$763$$ −2.50000 + 0.866025i −0.0905061 + 0.0313522i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 24.0000 + 13.8564i 0.867155 + 0.500652i
$$767$$ −22.0454 + 12.7279i −0.796014 + 0.459579i
$$768$$ 0 0
$$769$$ 22.5000 12.9904i 0.811371 0.468445i −0.0360609 0.999350i $$-0.511481\pi$$
0.847432 + 0.530904i $$0.178148\pi$$
$$770$$ 9.79796 + 8.48528i 0.353094 + 0.305788i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −13.4722 + 23.3345i −0.484561 + 0.839284i −0.999843 0.0177365i $$-0.994354\pi$$
0.515282 + 0.857021i $$0.327687\pi$$
$$774$$ 0 0
$$775$$ −1.50000 + 0.866025i −0.0538816 + 0.0311086i
$$776$$ −14.6969 + 25.4558i −0.527589 + 0.913812i
$$777$$ 0 0
$$778$$ 19.0000 + 32.9090i 0.681183 + 1.17984i
$$779$$ 11.0227 + 6.36396i 0.394929 + 0.228013i
$$780$$ 0 0
$$781$$ −5.00000 8.66025i −0.178914 0.309888i
$$782$$ 19.5959 + 33.9411i 0.700749 + 1.21373i
$$783$$ 0 0
$$784$$ −4.00000 27.7128i −0.142857 0.989743i
$$785$$ 36.7423 + 21.2132i 1.31139 + 0.757132i
$$786$$ 0