# Properties

 Label 225.2.k.a.124.2 Level $225$ Weight $2$ Character 225.124 Analytic conductor $1.797$ 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] = [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: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 45) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 124.2 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 225.124 Dual form 225.2.k.a.49.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205i q^{6} +(-2.59808 - 1.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205i q^{6} +(-2.59808 - 1.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(-1.73205 + 1.00000i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} -4.00000i q^{17} +(-2.59808 + 1.50000i) q^{18} +8.00000 q^{19} +5.19615i q^{21} +(1.73205 - 1.00000i) q^{22} +(2.59808 - 1.50000i) q^{23} +(-4.50000 + 2.59808i) q^{24} -2.00000 q^{26} +5.19615 q^{27} +3.00000i q^{28} +(-0.500000 + 0.866025i) q^{29} +(-4.33013 + 2.50000i) q^{32} -3.46410 q^{33} +(2.00000 - 3.46410i) q^{34} +3.00000 q^{36} +4.00000i q^{37} +(6.92820 + 4.00000i) q^{38} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-2.59808 + 4.50000i) q^{42} +(6.92820 + 4.00000i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(6.06218 + 3.50000i) q^{47} -1.73205 q^{48} +(1.00000 + 1.73205i) q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.73205 + 1.00000i) q^{52} -2.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(-4.50000 + 7.79423i) q^{56} +(-6.92820 - 12.0000i) q^{57} +(-0.866025 + 0.500000i) q^{58} +(-7.00000 - 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(7.79423 - 4.50000i) q^{63} -7.00000 q^{64} +(-3.00000 - 1.73205i) q^{66} +(2.59808 - 1.50000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(-4.50000 - 2.59808i) q^{69} +2.00000 q^{71} +(7.79423 + 4.50000i) q^{72} +4.00000i q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 - 6.92820i) q^{76} +(-5.19615 + 3.00000i) q^{77} +(1.73205 + 3.00000i) q^{78} +(-3.00000 + 5.19615i) q^{79} +(-4.50000 - 7.79423i) q^{81} -5.00000i q^{82} +(-7.79423 - 4.50000i) q^{83} +(4.50000 - 2.59808i) q^{84} +(4.00000 + 6.92820i) q^{86} +1.73205 q^{87} +(-5.19615 - 3.00000i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(-2.59808 - 1.50000i) q^{92} +(3.50000 + 6.06218i) q^{94} +(7.50000 + 4.33013i) q^{96} +(1.73205 + 1.00000i) q^{97} +2.00000i q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{4} - 6 q^{9}+O(q^{10})$$ 4 * q - 2 * q^4 - 6 * q^9 $$4 q - 2 q^{4} - 6 q^{9} + 4 q^{11} - 6 q^{14} + 2 q^{16} + 32 q^{19} - 18 q^{24} - 8 q^{26} - 2 q^{29} + 8 q^{34} + 12 q^{36} + 12 q^{39} - 10 q^{41} - 8 q^{44} + 12 q^{46} + 4 q^{49} - 24 q^{51} + 18 q^{54} - 18 q^{56} - 28 q^{59} - 14 q^{61} - 28 q^{64} - 12 q^{66} - 18 q^{69} + 8 q^{71} - 8 q^{74} - 16 q^{76} - 12 q^{79} - 18 q^{81} + 18 q^{84} + 16 q^{86} + 60 q^{89} + 24 q^{91} + 14 q^{94} + 30 q^{96} + 12 q^{99}+O(q^{100})$$ 4 * q - 2 * q^4 - 6 * q^9 + 4 * q^11 - 6 * q^14 + 2 * q^16 + 32 * q^19 - 18 * q^24 - 8 * q^26 - 2 * q^29 + 8 * q^34 + 12 * q^36 + 12 * q^39 - 10 * q^41 - 8 * q^44 + 12 * q^46 + 4 * q^49 - 24 * q^51 + 18 * q^54 - 18 * q^56 - 28 * q^59 - 14 * q^61 - 28 * q^64 - 12 * q^66 - 18 * q^69 + 8 * q^71 - 8 * q^74 - 16 * q^76 - 12 * q^79 - 18 * q^81 + 18 * q^84 + 16 * q^86 + 60 * q^89 + 24 * q^91 + 14 * q^94 + 30 * q^96 + 12 * q^99

## Character values

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

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 + 0.500000i 0.612372 + 0.353553i 0.773893 0.633316i $$-0.218307\pi$$
−0.161521 + 0.986869i $$0.551640\pi$$
$$3$$ −0.866025 1.50000i −0.500000 0.866025i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ 1.73205i 0.707107i
$$7$$ −2.59808 1.50000i −0.981981 0.566947i −0.0791130 0.996866i $$-0.525209\pi$$
−0.902867 + 0.429919i $$0.858542\pi$$
$$8$$ 3.00000i 1.06066i
$$9$$ −1.50000 + 2.59808i −0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ −0.866025 + 1.50000i −0.250000 + 0.433013i
$$13$$ −1.73205 + 1.00000i −0.480384 + 0.277350i −0.720577 0.693375i $$-0.756123\pi$$
0.240192 + 0.970725i $$0.422790\pi$$
$$14$$ −1.50000 2.59808i −0.400892 0.694365i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 4.00000i 0.970143i −0.874475 0.485071i $$-0.838794\pi$$
0.874475 0.485071i $$-0.161206\pi$$
$$18$$ −2.59808 + 1.50000i −0.612372 + 0.353553i
$$19$$ 8.00000 1.83533 0.917663 0.397360i $$-0.130073\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 5.19615i 1.13389i
$$22$$ 1.73205 1.00000i 0.369274 0.213201i
$$23$$ 2.59808 1.50000i 0.541736 0.312772i −0.204046 0.978961i $$-0.565409\pi$$
0.745782 + 0.666190i $$0.232076\pi$$
$$24$$ −4.50000 + 2.59808i −0.918559 + 0.530330i
$$25$$ 0 0
$$26$$ −2.00000 −0.392232
$$27$$ 5.19615 1.00000
$$28$$ 3.00000i 0.566947i
$$29$$ −0.500000 + 0.866025i −0.0928477 + 0.160817i −0.908708 0.417432i $$-0.862930\pi$$
0.815861 + 0.578249i $$0.196264\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$32$$ −4.33013 + 2.50000i −0.765466 + 0.441942i
$$33$$ −3.46410 −0.603023
$$34$$ 2.00000 3.46410i 0.342997 0.594089i
$$35$$ 0 0
$$36$$ 3.00000 0.500000
$$37$$ 4.00000i 0.657596i 0.944400 + 0.328798i $$0.106644\pi$$
−0.944400 + 0.328798i $$0.893356\pi$$
$$38$$ 6.92820 + 4.00000i 1.12390 + 0.648886i
$$39$$ 3.00000 + 1.73205i 0.480384 + 0.277350i
$$40$$ 0 0
$$41$$ −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i $$-0.294342\pi$$
−0.992507 + 0.122189i $$0.961009\pi$$
$$42$$ −2.59808 + 4.50000i −0.400892 + 0.694365i
$$43$$ 6.92820 + 4.00000i 1.05654 + 0.609994i 0.924473 0.381246i $$-0.124505\pi$$
0.132068 + 0.991241i $$0.457838\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 0 0
$$46$$ 3.00000 0.442326
$$47$$ 6.06218 + 3.50000i 0.884260 + 0.510527i 0.872060 0.489398i $$-0.162783\pi$$
0.0121990 + 0.999926i $$0.496117\pi$$
$$48$$ −1.73205 −0.250000
$$49$$ 1.00000 + 1.73205i 0.142857 + 0.247436i
$$50$$ 0 0
$$51$$ −6.00000 + 3.46410i −0.840168 + 0.485071i
$$52$$ 1.73205 + 1.00000i 0.240192 + 0.138675i
$$53$$ 2.00000i 0.274721i −0.990521 0.137361i $$-0.956138\pi$$
0.990521 0.137361i $$-0.0438619\pi$$
$$54$$ 4.50000 + 2.59808i 0.612372 + 0.353553i
$$55$$ 0 0
$$56$$ −4.50000 + 7.79423i −0.601338 + 1.04155i
$$57$$ −6.92820 12.0000i −0.917663 1.58944i
$$58$$ −0.866025 + 0.500000i −0.113715 + 0.0656532i
$$59$$ −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i $$-0.801729\pi$$
−0.0991242 0.995075i $$-0.531604\pi$$
$$60$$ 0 0
$$61$$ −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i $$-0.981243\pi$$
0.550135 + 0.835076i $$0.314576\pi$$
$$62$$ 0 0
$$63$$ 7.79423 4.50000i 0.981981 0.566947i
$$64$$ −7.00000 −0.875000
$$65$$ 0 0
$$66$$ −3.00000 1.73205i −0.369274 0.213201i
$$67$$ 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i $$-0.608004\pi$$
0.650236 + 0.759733i $$0.274670\pi$$
$$68$$ −3.46410 + 2.00000i −0.420084 + 0.242536i
$$69$$ −4.50000 2.59808i −0.541736 0.312772i
$$70$$ 0 0
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ 7.79423 + 4.50000i 0.918559 + 0.530330i
$$73$$ 4.00000i 0.468165i 0.972217 + 0.234082i $$0.0752085\pi$$
−0.972217 + 0.234082i $$0.924791\pi$$
$$74$$ −2.00000 + 3.46410i −0.232495 + 0.402694i
$$75$$ 0 0
$$76$$ −4.00000 6.92820i −0.458831 0.794719i
$$77$$ −5.19615 + 3.00000i −0.592157 + 0.341882i
$$78$$ 1.73205 + 3.00000i 0.196116 + 0.339683i
$$79$$ −3.00000 + 5.19615i −0.337526 + 0.584613i −0.983967 0.178352i $$-0.942924\pi$$
0.646440 + 0.762964i $$0.276257\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 5.00000i 0.552158i
$$83$$ −7.79423 4.50000i −0.855528 0.493939i 0.00698436 0.999976i $$-0.497777\pi$$
−0.862512 + 0.506036i $$0.831110\pi$$
$$84$$ 4.50000 2.59808i 0.490990 0.283473i
$$85$$ 0 0
$$86$$ 4.00000 + 6.92820i 0.431331 + 0.747087i
$$87$$ 1.73205 0.185695
$$88$$ −5.19615 3.00000i −0.553912 0.319801i
$$89$$ 15.0000 1.59000 0.794998 0.606612i $$-0.207472\pi$$
0.794998 + 0.606612i $$0.207472\pi$$
$$90$$ 0 0
$$91$$ 6.00000 0.628971
$$92$$ −2.59808 1.50000i −0.270868 0.156386i
$$93$$ 0 0
$$94$$ 3.50000 + 6.06218i 0.360997 + 0.625266i
$$95$$ 0 0
$$96$$ 7.50000 + 4.33013i 0.765466 + 0.441942i
$$97$$ 1.73205 + 1.00000i 0.175863 + 0.101535i 0.585348 0.810782i $$-0.300958\pi$$
−0.409484 + 0.912317i $$0.634291\pi$$
$$98$$ 2.00000i 0.202031i
$$99$$ 3.00000 + 5.19615i 0.301511 + 0.522233i
$$100$$ 0 0
$$101$$ 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i $$-0.480128\pi$$
0.833143 0.553058i $$-0.186539\pi$$
$$102$$ −6.92820 −0.685994
$$103$$ 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i $$-0.537712\pi$$
0.800855 + 0.598858i $$0.204379\pi$$
$$104$$ 3.00000 + 5.19615i 0.294174 + 0.509525i
$$105$$ 0 0
$$106$$ 1.00000 1.73205i 0.0971286 0.168232i
$$107$$ 3.00000i 0.290021i −0.989430 0.145010i $$-0.953678\pi$$
0.989430 0.145010i $$-0.0463216\pi$$
$$108$$ −2.59808 4.50000i −0.250000 0.433013i
$$109$$ −5.00000 −0.478913 −0.239457 0.970907i $$-0.576969\pi$$
−0.239457 + 0.970907i $$0.576969\pi$$
$$110$$ 0 0
$$111$$ 6.00000 3.46410i 0.569495 0.328798i
$$112$$ −2.59808 + 1.50000i −0.245495 + 0.141737i
$$113$$ −6.92820 + 4.00000i −0.651751 + 0.376288i −0.789127 0.614231i $$-0.789466\pi$$
0.137376 + 0.990519i $$0.456133\pi$$
$$114$$ 13.8564i 1.29777i
$$115$$ 0 0
$$116$$ 1.00000 0.0928477
$$117$$ 6.00000i 0.554700i
$$118$$ 14.0000i 1.28880i
$$119$$ −6.00000 + 10.3923i −0.550019 + 0.952661i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ −6.06218 + 3.50000i −0.548844 + 0.316875i
$$123$$ −4.33013 + 7.50000i −0.390434 + 0.676252i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 9.00000 0.801784
$$127$$ 5.00000i 0.443678i 0.975083 + 0.221839i $$0.0712060\pi$$
−0.975083 + 0.221839i $$0.928794\pi$$
$$128$$ 2.59808 + 1.50000i 0.229640 + 0.132583i
$$129$$ 13.8564i 1.21999i
$$130$$ 0 0
$$131$$ 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i $$-0.0822479\pi$$
−0.704692 + 0.709514i $$0.748915\pi$$
$$132$$ 1.73205 + 3.00000i 0.150756 + 0.261116i
$$133$$ −20.7846 12.0000i −1.80225 1.04053i
$$134$$ 3.00000 0.259161
$$135$$ 0 0
$$136$$ −12.0000 −1.02899
$$137$$ 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i $$-0.162010\pi$$
0.0146279 + 0.999893i $$0.495344\pi$$
$$138$$ −2.59808 4.50000i −0.221163 0.383065i
$$139$$ −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i $$-0.929275\pi$$
0.296866 0.954919i $$-0.404058\pi$$
$$140$$ 0 0
$$141$$ 12.1244i 1.02105i
$$142$$ 1.73205 + 1.00000i 0.145350 + 0.0839181i
$$143$$ 4.00000i 0.334497i
$$144$$ 1.50000 + 2.59808i 0.125000 + 0.216506i
$$145$$ 0 0
$$146$$ −2.00000 + 3.46410i −0.165521 + 0.286691i
$$147$$ 1.73205 3.00000i 0.142857 0.247436i
$$148$$ 3.46410 2.00000i 0.284747 0.164399i
$$149$$ 8.50000 + 14.7224i 0.696347 + 1.20611i 0.969724 + 0.244202i $$0.0785259\pi$$
−0.273377 + 0.961907i $$0.588141\pi$$
$$150$$ 0 0
$$151$$ 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i $$-0.807401\pi$$
0.903842 + 0.427865i $$0.140734\pi$$
$$152$$ 24.0000i 1.94666i
$$153$$ 10.3923 + 6.00000i 0.840168 + 0.485071i
$$154$$ −6.00000 −0.483494
$$155$$ 0 0
$$156$$ 3.46410i 0.277350i
$$157$$ −12.1244 + 7.00000i −0.967629 + 0.558661i −0.898513 0.438948i $$-0.855351\pi$$
−0.0691164 + 0.997609i $$0.522018\pi$$
$$158$$ −5.19615 + 3.00000i −0.413384 + 0.238667i
$$159$$ −3.00000 + 1.73205i −0.237915 + 0.137361i
$$160$$ 0 0
$$161$$ −9.00000 −0.709299
$$162$$ 9.00000i 0.707107i
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ −2.50000 + 4.33013i −0.195217 + 0.338126i
$$165$$ 0 0
$$166$$ −4.50000 7.79423i −0.349268 0.604949i
$$167$$ 7.79423 4.50000i 0.603136 0.348220i −0.167139 0.985933i $$-0.553453\pi$$
0.770274 + 0.637713i $$0.220119\pi$$
$$168$$ 15.5885 1.20268
$$169$$ −4.50000 + 7.79423i −0.346154 + 0.599556i
$$170$$ 0 0
$$171$$ −12.0000 + 20.7846i −0.917663 + 1.58944i
$$172$$ 8.00000i 0.609994i
$$173$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 1.50000 + 0.866025i 0.113715 + 0.0656532i
$$175$$ 0 0
$$176$$ −1.00000 1.73205i −0.0753778 0.130558i
$$177$$ −12.1244 + 21.0000i −0.911322 + 1.57846i
$$178$$ 12.9904 + 7.50000i 0.973670 + 0.562149i
$$179$$ 2.00000 0.149487 0.0747435 0.997203i $$-0.476186\pi$$
0.0747435 + 0.997203i $$0.476186\pi$$
$$180$$ 0 0
$$181$$ −7.00000 −0.520306 −0.260153 0.965567i $$-0.583773\pi$$
−0.260153 + 0.965567i $$0.583773\pi$$
$$182$$ 5.19615 + 3.00000i 0.385164 + 0.222375i
$$183$$ 12.1244 0.896258
$$184$$ −4.50000 7.79423i −0.331744 0.574598i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.92820 4.00000i −0.506640 0.292509i
$$188$$ 7.00000i 0.510527i
$$189$$ −13.5000 7.79423i −0.981981 0.566947i
$$190$$ 0 0
$$191$$ −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i $$-0.926799\pi$$
0.684244 + 0.729253i $$0.260132\pi$$
$$192$$ 6.06218 + 10.5000i 0.437500 + 0.757772i
$$193$$ −8.66025 + 5.00000i −0.623379 + 0.359908i −0.778183 0.628037i $$-0.783859\pi$$
0.154805 + 0.987945i $$0.450525\pi$$
$$194$$ 1.00000 + 1.73205i 0.0717958 + 0.124354i
$$195$$ 0 0
$$196$$ 1.00000 1.73205i 0.0714286 0.123718i
$$197$$ 12.0000i 0.854965i 0.904024 + 0.427482i $$0.140599\pi$$
−0.904024 + 0.427482i $$0.859401\pi$$
$$198$$ 6.00000i 0.426401i
$$199$$ −4.00000 −0.283552 −0.141776 0.989899i $$-0.545281\pi$$
−0.141776 + 0.989899i $$0.545281\pi$$
$$200$$ 0 0
$$201$$ −4.50000 2.59808i −0.317406 0.183254i
$$202$$ 15.5885 9.00000i 1.09680 0.633238i
$$203$$ 2.59808 1.50000i 0.182349 0.105279i
$$204$$ 6.00000 + 3.46410i 0.420084 + 0.242536i
$$205$$ 0 0
$$206$$ 8.00000 0.557386
$$207$$ 9.00000i 0.625543i
$$208$$ 2.00000i 0.138675i
$$209$$ 8.00000 13.8564i 0.553372 0.958468i
$$210$$ 0 0
$$211$$ 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i $$0.106801\pi$$
−0.186966 + 0.982366i $$0.559865\pi$$
$$212$$ −1.73205 + 1.00000i −0.118958 + 0.0686803i
$$213$$ −1.73205 3.00000i −0.118678 0.205557i
$$214$$ 1.50000 2.59808i 0.102538 0.177601i
$$215$$ 0 0
$$216$$ 15.5885i 1.06066i
$$217$$ 0 0
$$218$$ −4.33013 2.50000i −0.293273 0.169321i
$$219$$ 6.00000 3.46410i 0.405442 0.234082i
$$220$$ 0 0
$$221$$ 4.00000 + 6.92820i 0.269069 + 0.466041i
$$222$$ 6.92820 0.464991
$$223$$ 16.4545 + 9.50000i 1.10187 + 0.636167i 0.936713 0.350100i $$-0.113852\pi$$
0.165161 + 0.986267i $$0.447186\pi$$
$$224$$ 15.0000 1.00223
$$225$$ 0 0
$$226$$ −8.00000 −0.532152
$$227$$ −3.46410 2.00000i −0.229920 0.132745i 0.380615 0.924734i $$-0.375712\pi$$
−0.610535 + 0.791989i $$0.709046\pi$$
$$228$$ −6.92820 + 12.0000i −0.458831 + 0.794719i
$$229$$ 7.50000 + 12.9904i 0.495614 + 0.858429i 0.999987 0.00505719i $$-0.00160976\pi$$
−0.504373 + 0.863486i $$0.668276\pi$$
$$230$$ 0 0
$$231$$ 9.00000 + 5.19615i 0.592157 + 0.341882i
$$232$$ 2.59808 + 1.50000i 0.170572 + 0.0984798i
$$233$$ 24.0000i 1.57229i 0.618041 + 0.786146i $$0.287927\pi$$
−0.618041 + 0.786146i $$0.712073\pi$$
$$234$$ 3.00000 5.19615i 0.196116 0.339683i
$$235$$ 0 0
$$236$$ −7.00000 + 12.1244i −0.455661 + 0.789228i
$$237$$ 10.3923 0.675053
$$238$$ −10.3923 + 6.00000i −0.673633 + 0.388922i
$$239$$ −4.00000 6.92820i −0.258738 0.448148i 0.707166 0.707048i $$-0.249973\pi$$
−0.965904 + 0.258900i $$0.916640\pi$$
$$240$$ 0 0
$$241$$ 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i $$-0.718057\pi$$
0.986996 + 0.160748i $$0.0513906\pi$$
$$242$$ 7.00000i 0.449977i
$$243$$ −7.79423 + 13.5000i −0.500000 + 0.866025i
$$244$$ 7.00000 0.448129
$$245$$ 0 0
$$246$$ −7.50000 + 4.33013i −0.478183 + 0.276079i
$$247$$ −13.8564 + 8.00000i −0.881662 + 0.509028i
$$248$$ 0 0
$$249$$ 15.5885i 0.987878i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ −7.79423 4.50000i −0.490990 0.283473i
$$253$$ 6.00000i 0.377217i
$$254$$ −2.50000 + 4.33013i −0.156864 + 0.271696i
$$255$$ 0 0
$$256$$ 8.50000 + 14.7224i 0.531250 + 0.920152i
$$257$$ 5.19615 3.00000i 0.324127 0.187135i −0.329104 0.944294i $$-0.606747\pi$$
0.653231 + 0.757159i $$0.273413\pi$$
$$258$$ 6.92820 12.0000i 0.431331 0.747087i
$$259$$ 6.00000 10.3923i 0.372822 0.645746i
$$260$$ 0 0
$$261$$ −1.50000 2.59808i −0.0928477 0.160817i
$$262$$ 6.00000i 0.370681i
$$263$$ 13.8564 + 8.00000i 0.854423 + 0.493301i 0.862141 0.506669i $$-0.169123\pi$$
−0.00771799 + 0.999970i $$0.502457\pi$$
$$264$$ 10.3923i 0.639602i
$$265$$ 0 0
$$266$$ −12.0000 20.7846i −0.735767 1.27439i
$$267$$ −12.9904 22.5000i −0.794998 1.37698i
$$268$$ −2.59808 1.50000i −0.158703 0.0916271i
$$269$$ −25.0000 −1.52428 −0.762138 0.647414i $$-0.775850\pi$$
−0.762138 + 0.647414i $$0.775850\pi$$
$$270$$ 0 0
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ −3.46410 2.00000i −0.210042 0.121268i
$$273$$ −5.19615 9.00000i −0.314485 0.544705i
$$274$$ 6.00000 + 10.3923i 0.362473 + 0.627822i
$$275$$ 0 0
$$276$$ 5.19615i 0.312772i
$$277$$ 10.3923 + 6.00000i 0.624413 + 0.360505i 0.778585 0.627539i $$-0.215938\pi$$
−0.154172 + 0.988044i $$0.549271\pi$$
$$278$$ 16.0000i 0.959616i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i $$-0.685679\pi$$
0.998217 + 0.0596933i $$0.0190123\pi$$
$$282$$ 6.06218 10.5000i 0.360997 0.625266i
$$283$$ 18.1865 10.5000i 1.08108 0.624160i 0.149890 0.988703i $$-0.452108\pi$$
0.931187 + 0.364542i $$0.118775\pi$$
$$284$$ −1.00000 1.73205i −0.0593391 0.102778i
$$285$$ 0 0
$$286$$ −2.00000 + 3.46410i −0.118262 + 0.204837i
$$287$$ 15.0000i 0.885422i
$$288$$ 15.0000i 0.883883i
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ 3.46410i 0.203069i
$$292$$ 3.46410 2.00000i 0.202721 0.117041i
$$293$$ 10.3923 6.00000i 0.607125 0.350524i −0.164714 0.986341i $$-0.552670\pi$$
0.771839 + 0.635818i $$0.219337\pi$$
$$294$$ 3.00000 1.73205i 0.174964 0.101015i
$$295$$ 0 0
$$296$$ 12.0000 0.697486
$$297$$ 5.19615 9.00000i 0.301511 0.522233i
$$298$$ 17.0000i 0.984784i
$$299$$ −3.00000 + 5.19615i −0.173494 + 0.300501i
$$300$$ 0 0
$$301$$ −12.0000 20.7846i −0.691669 1.19800i
$$302$$ 1.73205 1.00000i 0.0996683 0.0575435i
$$303$$ −31.1769 −1.79107
$$304$$ 4.00000 6.92820i 0.229416 0.397360i
$$305$$ 0 0
$$306$$ 6.00000 + 10.3923i 0.342997 + 0.594089i
$$307$$ 7.00000i 0.399511i −0.979846 0.199756i $$-0.935985\pi$$
0.979846 0.199756i $$-0.0640148\pi$$
$$308$$ 5.19615 + 3.00000i 0.296078 + 0.170941i
$$309$$ −12.0000 6.92820i −0.682656 0.394132i
$$310$$ 0 0
$$311$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$312$$ 5.19615 9.00000i 0.294174 0.509525i
$$313$$ −12.1244 7.00000i −0.685309 0.395663i 0.116543 0.993186i $$-0.462819\pi$$
−0.801852 + 0.597522i $$0.796152\pi$$
$$314$$ −14.0000 −0.790066
$$315$$ 0 0
$$316$$ 6.00000 0.337526
$$317$$ −29.4449 17.0000i −1.65379 0.954815i −0.975494 0.220024i $$-0.929386\pi$$
−0.678294 0.734791i $$-0.737280\pi$$
$$318$$ −3.46410 −0.194257
$$319$$ 1.00000 + 1.73205i 0.0559893 + 0.0969762i
$$320$$ 0 0
$$321$$ −4.50000 + 2.59808i −0.251166 + 0.145010i
$$322$$ −7.79423 4.50000i −0.434355 0.250775i
$$323$$ 32.0000i 1.78053i
$$324$$ −4.50000 + 7.79423i −0.250000 + 0.433013i
$$325$$ 0 0
$$326$$ 2.00000 3.46410i 0.110770 0.191859i
$$327$$ 4.33013 + 7.50000i 0.239457 + 0.414751i
$$328$$ −12.9904 + 7.50000i −0.717274 + 0.414118i
$$329$$ −10.5000 18.1865i −0.578884 1.00266i
$$330$$ 0 0
$$331$$ 3.00000 5.19615i 0.164895 0.285606i −0.771723 0.635959i $$-0.780605\pi$$
0.936618 + 0.350352i $$0.113938\pi$$
$$332$$ 9.00000i 0.493939i
$$333$$ −10.3923 6.00000i −0.569495 0.328798i
$$334$$ 9.00000 0.492458
$$335$$ 0 0
$$336$$ 4.50000 + 2.59808i 0.245495 + 0.141737i
$$337$$ 6.92820 4.00000i 0.377403 0.217894i −0.299285 0.954164i $$-0.596748\pi$$
0.676688 + 0.736270i $$0.263415\pi$$
$$338$$ −7.79423 + 4.50000i −0.423950 + 0.244768i
$$339$$ 12.0000 + 6.92820i 0.651751 + 0.376288i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −20.7846 + 12.0000i −1.12390 + 0.648886i
$$343$$ 15.0000i 0.809924i
$$344$$ 12.0000 20.7846i 0.646997 1.12063i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −3.46410 + 2.00000i −0.185963 + 0.107366i −0.590091 0.807337i $$-0.700908\pi$$
0.404128 + 0.914702i $$0.367575\pi$$
$$348$$ −0.866025 1.50000i −0.0464238 0.0804084i
$$349$$ −2.50000 + 4.33013i −0.133822 + 0.231786i −0.925147 0.379610i $$-0.876058\pi$$
0.791325 + 0.611396i $$0.209392\pi$$
$$350$$ 0 0
$$351$$ −9.00000 + 5.19615i −0.480384 + 0.277350i
$$352$$ 10.0000i 0.533002i
$$353$$ −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i $$-0.553859\pi$$
−0.937856 + 0.347024i $$0.887192\pi$$
$$354$$ −21.0000 + 12.1244i −1.11614 + 0.644402i
$$355$$ 0 0
$$356$$ −7.50000 12.9904i −0.397499 0.688489i
$$357$$ 20.7846 1.10004
$$358$$ 1.73205 + 1.00000i 0.0915417 + 0.0528516i
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ 45.0000 2.36842
$$362$$ −6.06218 3.50000i −0.318621 0.183956i
$$363$$ 6.06218 10.5000i 0.318182 0.551107i
$$364$$ −3.00000 5.19615i −0.157243 0.272352i
$$365$$ 0 0
$$366$$ 10.5000 + 6.06218i 0.548844 + 0.316875i
$$367$$ 20.7846 + 12.0000i 1.08495 + 0.626395i 0.932227 0.361874i $$-0.117863\pi$$
0.152721 + 0.988269i $$0.451196\pi$$
$$368$$ 3.00000i 0.156386i
$$369$$ 15.0000 0.780869
$$370$$ 0 0
$$371$$ −3.00000 + 5.19615i −0.155752 + 0.269771i
$$372$$ 0 0
$$373$$ 8.66025 5.00000i 0.448411 0.258890i −0.258748 0.965945i $$-0.583310\pi$$
0.707159 + 0.707055i $$0.249977\pi$$
$$374$$ −4.00000 6.92820i −0.206835 0.358249i
$$375$$ 0 0
$$376$$ 10.5000 18.1865i 0.541496 0.937899i
$$377$$ 2.00000i 0.103005i
$$378$$ −7.79423 13.5000i −0.400892 0.694365i
$$379$$ 26.0000 1.33553 0.667765 0.744372i $$-0.267251\pi$$
0.667765 + 0.744372i $$0.267251\pi$$
$$380$$ 0 0
$$381$$ 7.50000 4.33013i 0.384237 0.221839i
$$382$$ −6.92820 + 4.00000i −0.354478 + 0.204658i
$$383$$ 31.1769 18.0000i 1.59307 0.919757i 0.600289 0.799783i $$-0.295052\pi$$
0.992777 0.119974i $$-0.0382810\pi$$
$$384$$ 5.19615i 0.265165i
$$385$$ 0 0
$$386$$ −10.0000 −0.508987
$$387$$ −20.7846 + 12.0000i −1.05654 + 0.609994i
$$388$$ 2.00000i 0.101535i
$$389$$ 16.5000 28.5788i 0.836583 1.44900i −0.0561516 0.998422i $$-0.517883\pi$$
0.892735 0.450582i $$-0.148784\pi$$
$$390$$ 0 0
$$391$$ −6.00000 10.3923i −0.303433 0.525561i
$$392$$ 5.19615 3.00000i 0.262445 0.151523i
$$393$$ 5.19615 9.00000i 0.262111 0.453990i
$$394$$ −6.00000 + 10.3923i −0.302276 + 0.523557i
$$395$$ 0 0
$$396$$ 3.00000 5.19615i 0.150756 0.261116i
$$397$$ 34.0000i 1.70641i −0.521575 0.853206i $$-0.674655\pi$$
0.521575 0.853206i $$-0.325345\pi$$
$$398$$ −3.46410 2.00000i −0.173640 0.100251i
$$399$$ 41.5692i 2.08106i
$$400$$ 0 0
$$401$$ 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i $$-0.0182907\pi$$
−0.548911 + 0.835881i $$0.684957\pi$$
$$402$$ −2.59808 4.50000i −0.129580 0.224440i
$$403$$ 0 0
$$404$$ −18.0000 −0.895533
$$405$$ 0 0
$$406$$ 3.00000 0.148888
$$407$$ 6.92820 + 4.00000i 0.343418 + 0.198273i
$$408$$ 10.3923 + 18.0000i 0.514496 + 0.891133i
$$409$$ 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i $$-0.0541630\pi$$
−0.639430 + 0.768849i $$0.720830\pi$$
$$410$$ 0 0
$$411$$ 20.7846i 1.02523i
$$412$$ −6.92820 4.00000i −0.341328 0.197066i
$$413$$ 42.0000i 2.06668i
$$414$$ −4.50000 + 7.79423i −0.221163 + 0.383065i
$$415$$ 0 0
$$416$$ 5.00000 8.66025i 0.245145 0.424604i
$$417$$ −13.8564 + 24.0000i −0.678551 + 1.17529i
$$418$$ 13.8564 8.00000i 0.677739 0.391293i
$$419$$ 13.0000 + 22.5167i 0.635092 + 1.10001i 0.986496 + 0.163787i $$0.0523710\pi$$
−0.351404 + 0.936224i $$0.614296\pi$$
$$420$$ 0 0
$$421$$ −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i $$0.477489\pi$$
−0.899192 + 0.437555i $$0.855845\pi$$
$$422$$ 22.0000i 1.07094i
$$423$$ −18.1865 + 10.5000i −0.884260 + 0.510527i
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ 3.46410i 0.167836i
$$427$$ 18.1865 10.5000i 0.880108 0.508131i
$$428$$ −2.59808 + 1.50000i −0.125583 + 0.0725052i
$$429$$ 6.00000 3.46410i 0.289683 0.167248i
$$430$$ 0 0
$$431$$ −30.0000 −1.44505 −0.722525 0.691345i $$-0.757018\pi$$
−0.722525 + 0.691345i $$0.757018\pi$$
$$432$$ 2.59808 4.50000i 0.125000 0.216506i
$$433$$ 28.0000i 1.34559i 0.739827 + 0.672797i $$0.234907\pi$$
−0.739827 + 0.672797i $$0.765093\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 2.50000 + 4.33013i 0.119728 + 0.207375i
$$437$$ 20.7846 12.0000i 0.994263 0.574038i
$$438$$ 6.92820 0.331042
$$439$$ 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i $$-0.600405\pi$$
0.978412 0.206666i $$-0.0662612\pi$$
$$440$$ 0 0
$$441$$ −6.00000 −0.285714
$$442$$ 8.00000i 0.380521i
$$443$$ −12.9904 7.50000i −0.617192 0.356336i 0.158583 0.987346i $$-0.449307\pi$$
−0.775775 + 0.631010i $$0.782641\pi$$
$$444$$ −6.00000 3.46410i −0.284747 0.164399i
$$445$$ 0 0
$$446$$ 9.50000 + 16.4545i 0.449838 + 0.779142i
$$447$$ 14.7224 25.5000i 0.696347 1.20611i
$$448$$ 18.1865 + 10.5000i 0.859233 + 0.496078i
$$449$$ 26.0000 1.22702 0.613508 0.789689i $$-0.289758\pi$$
0.613508 + 0.789689i $$0.289758\pi$$
$$450$$ 0 0
$$451$$ −10.0000 −0.470882
$$452$$ 6.92820 + 4.00000i 0.325875 + 0.188144i
$$453$$ −3.46410 −0.162758
$$454$$ −2.00000 3.46410i −0.0938647 0.162578i
$$455$$ 0 0
$$456$$ −36.0000 + 20.7846i −1.68585 + 0.973329i
$$457$$ −17.3205 10.0000i −0.810219 0.467780i 0.0368128 0.999322i $$-0.488279\pi$$
−0.847032 + 0.531542i $$0.821613\pi$$
$$458$$ 15.0000i 0.700904i
$$459$$ 20.7846i 0.970143i
$$460$$ 0 0
$$461$$ −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i $$-0.900545\pi$$
0.741998 + 0.670402i $$0.233878\pi$$
$$462$$ 5.19615 + 9.00000i 0.241747 + 0.418718i
$$463$$ −31.1769 + 18.0000i −1.44891 + 0.836531i −0.998417 0.0562469i $$-0.982087\pi$$
−0.450497 + 0.892778i $$0.648753\pi$$
$$464$$ 0.500000 + 0.866025i 0.0232119 + 0.0402042i
$$465$$ 0 0
$$466$$ −12.0000 + 20.7846i −0.555889 + 0.962828i
$$467$$ 20.0000i 0.925490i −0.886492 0.462745i $$-0.846865\pi$$
0.886492 0.462745i $$-0.153135\pi$$
$$468$$ −5.19615 + 3.00000i −0.240192 + 0.138675i
$$469$$ −9.00000 −0.415581
$$470$$ 0 0
$$471$$ 21.0000 + 12.1244i 0.967629 + 0.558661i
$$472$$ −36.3731 + 21.0000i −1.67421 + 0.966603i
$$473$$ 13.8564 8.00000i 0.637118 0.367840i
$$474$$ 9.00000 + 5.19615i 0.413384 + 0.238667i
$$475$$ 0 0
$$476$$ 12.0000 0.550019
$$477$$ 5.19615 + 3.00000i 0.237915 + 0.137361i
$$478$$ 8.00000i 0.365911i
$$479$$ −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i $$-0.968231\pi$$
0.583803 + 0.811895i $$0.301564\pi$$
$$480$$ 0 0
$$481$$ −4.00000 6.92820i −0.182384 0.315899i
$$482$$ 9.52628 5.50000i 0.433910 0.250518i
$$483$$ 7.79423 + 13.5000i 0.354650 + 0.614271i
$$484$$ 3.50000 6.06218i 0.159091 0.275554i
$$485$$ 0 0
$$486$$ −13.5000 + 7.79423i −0.612372 + 0.353553i
$$487$$ 16.0000i 0.725029i 0.931978 + 0.362515i $$0.118082\pi$$
−0.931978 + 0.362515i $$0.881918\pi$$
$$488$$ 18.1865 + 10.5000i 0.823266 + 0.475313i
$$489$$ −6.00000 + 3.46410i −0.271329 + 0.156652i
$$490$$ 0 0
$$491$$ −10.0000 17.3205i −0.451294 0.781664i 0.547173 0.837020i $$-0.315704\pi$$
−0.998467 + 0.0553560i $$0.982371\pi$$
$$492$$ 8.66025 0.390434
$$493$$ 3.46410 + 2.00000i 0.156015 + 0.0900755i
$$494$$ −16.0000 −0.719874
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5.19615 3.00000i −0.233079 0.134568i
$$498$$ −7.79423 + 13.5000i −0.349268 + 0.604949i
$$499$$ −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i $$-0.912520\pi$$
0.246214 0.969216i $$-0.420813\pi$$
$$500$$ 0 0
$$501$$ −13.5000 7.79423i −0.603136 0.348220i
$$502$$ 0 0
$$503$$ 7.00000i 0.312115i −0.987748 0.156057i $$-0.950122\pi$$
0.987748 0.156057i $$-0.0498784\pi$$
$$504$$ −13.5000 23.3827i −0.601338 1.04155i
$$505$$ 0 0
$$506$$ 3.00000 5.19615i 0.133366 0.230997i
$$507$$ 15.5885 0.692308
$$508$$ 4.33013 2.50000i 0.192118 0.110920i
$$509$$ 21.5000 + 37.2391i 0.952971 + 1.65059i 0.738945 + 0.673766i $$0.235324\pi$$
0.214026 + 0.976828i $$0.431342\pi$$
$$510$$ 0 0
$$511$$ 6.00000 10.3923i 0.265424 0.459728i
$$512$$ 11.0000i 0.486136i
$$513$$ 41.5692 1.83533
$$514$$ 6.00000 0.264649
$$515$$ 0 0
$$516$$ −12.0000 + 6.92820i −0.528271 + 0.304997i
$$517$$ 12.1244 7.00000i 0.533229 0.307860i
$$518$$ 10.3923 6.00000i 0.456612 0.263625i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 11.0000 0.481919 0.240959 0.970535i $$-0.422538\pi$$
0.240959 + 0.970535i $$0.422538\pi$$
$$522$$ 3.00000i 0.131306i
$$523$$ 29.0000i 1.26808i −0.773300 0.634041i $$-0.781395\pi$$
0.773300 0.634041i $$-0.218605\pi$$
$$524$$ 3.00000 5.19615i 0.131056 0.226995i
$$525$$ 0 0
$$526$$ 8.00000 + 13.8564i 0.348817 + 0.604168i
$$527$$ 0 0
$$528$$ −1.73205 + 3.00000i −0.0753778 + 0.130558i
$$529$$ −7.00000 + 12.1244i −0.304348 + 0.527146i
$$530$$ 0 0
$$531$$ 42.0000 1.82264
$$532$$ 24.0000i 1.04053i
$$533$$ 8.66025 + 5.00000i 0.375117 + 0.216574i
$$534$$ 25.9808i 1.12430i
$$535$$ 0 0
$$536$$ −4.50000 7.79423i −0.194370 0.336659i
$$537$$ −1.73205 3.00000i −0.0747435 0.129460i
$$538$$ −21.6506 12.5000i −0.933425 0.538913i
$$539$$ 4.00000 0.172292
$$540$$ 0 0
$$541$$ −39.0000 −1.67674 −0.838370 0.545101i $$-0.816491\pi$$
−0.838370 + 0.545101i $$0.816491\pi$$
$$542$$ −6.92820 4.00000i −0.297592 0.171815i
$$543$$ 6.06218 + 10.5000i 0.260153 + 0.450598i
$$544$$ 10.0000 + 17.3205i 0.428746 + 0.742611i
$$545$$ 0 0
$$546$$ 10.3923i 0.444750i
$$547$$ −25.1147 14.5000i −1.07383 0.619975i −0.144604 0.989490i $$-0.546191\pi$$
−0.929225 + 0.369514i $$0.879524\pi$$
$$548$$ 12.0000i 0.512615i
$$549$$ −10.5000 18.1865i −0.448129 0.776182i
$$550$$ 0 0
$$551$$ −4.00000 + 6.92820i −0.170406 + 0.295151i
$$552$$ −7.79423 + 13.5000i −0.331744 + 0.574598i
$$553$$ 15.5885 9.00000i 0.662889 0.382719i
$$554$$ 6.00000 + 10.3923i 0.254916 + 0.441527i
$$555$$ 0 0
$$556$$ −8.00000 + 13.8564i −0.339276 + 0.587643i
$$557$$ 30.0000i 1.27114i 0.772043 + 0.635570i $$0.219235\pi$$
−0.772043 + 0.635570i $$0.780765\pi$$
$$558$$ 0 0
$$559$$ −16.0000 −0.676728
$$560$$ 0 0
$$561$$ 13.8564i 0.585018i
$$562$$ 12.9904 7.50000i 0.547966 0.316368i
$$563$$ −18.1865 + 10.5000i −0.766471 + 0.442522i −0.831614 0.555354i $$-0.812583\pi$$
0.0651433 + 0.997876i $$0.479250\pi$$
$$564$$ −10.5000 + 6.06218i −0.442130 + 0.255264i
$$565$$ 0 0
$$566$$ 21.0000 0.882696
$$567$$ 27.0000i 1.13389i
$$568$$ 6.00000i 0.251754i
$$569$$ −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i $$-0.873472\pi$$
0.796266 + 0.604947i $$0.206806\pi$$
$$570$$ 0 0
$$571$$ −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i $$-0.933141\pi$$
0.308443 0.951243i $$-0.400192\pi$$
$$572$$ 3.46410 2.00000i 0.144841 0.0836242i
$$573$$ 13.8564 0.578860
$$574$$ −7.50000 + 12.9904i −0.313044 + 0.542208i
$$575$$ 0 0
$$576$$ 10.5000 18.1865i 0.437500 0.757772i
$$577$$ 10.0000i 0.416305i 0.978096 + 0.208153i $$0.0667451\pi$$
−0.978096 + 0.208153i $$0.933255\pi$$
$$578$$ 0.866025 + 0.500000i 0.0360219 + 0.0207973i
$$579$$ 15.0000 + 8.66025i 0.623379 + 0.359908i
$$580$$ 0 0
$$581$$ 13.5000 + 23.3827i 0.560074 + 0.970077i
$$582$$ 1.73205 3.00000i 0.0717958 0.124354i
$$583$$ −3.46410 2.00000i −0.143468 0.0828315i
$$584$$ 12.0000 0.496564
$$585$$ 0 0
$$586$$ 12.0000 0.495715
$$587$$ −28.5788 16.5000i −1.17957 0.681028i −0.223659 0.974668i $$-0.571800\pi$$
−0.955916 + 0.293640i $$0.905133\pi$$
$$588$$ −3.46410 −0.142857
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 18.0000 10.3923i 0.740421 0.427482i
$$592$$ 3.46410 + 2.00000i 0.142374 + 0.0821995i
$$593$$ 20.0000i 0.821302i 0.911793 + 0.410651i $$0.134698\pi$$
−0.911793 + 0.410651i $$0.865302\pi$$
$$594$$ 9.00000 5.19615i 0.369274 0.213201i
$$595$$ 0 0
$$596$$ 8.50000 14.7224i 0.348174 0.603054i
$$597$$ 3.46410 + 6.00000i 0.141776 + 0.245564i
$$598$$ −5.19615 + 3.00000i −0.212486 + 0.122679i
$$599$$ −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i $$-0.232157\pi$$
−0.949908 + 0.312531i $$0.898823\pi$$
$$600$$ 0 0
$$601$$ −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i $$-0.846321\pi$$
0.844909 + 0.534910i $$0.179654\pi$$
$$602$$ 24.0000i 0.978167i
$$603$$ 9.00000i 0.366508i
$$604$$ −2.00000 −0.0813788
$$605$$ 0 0
$$606$$ −27.0000 15.5885i −1.09680 0.633238i
$$607$$ 35.5070 20.5000i 1.44119 0.832069i 0.443257 0.896394i $$-0.353823\pi$$
0.997929 + 0.0643251i $$0.0204895\pi$$
$$608$$ −34.6410 + 20.0000i −1.40488 + 0.811107i
$$609$$ −4.50000 2.59808i −0.182349 0.105279i
$$610$$ 0 0
$$611$$ −14.0000 −0.566379
$$612$$ 12.0000i 0.485071i
$$613$$ 44.0000i 1.77714i −0.458738 0.888572i $$-0.651698\pi$$
0.458738 0.888572i $$-0.348302\pi$$
$$614$$ 3.50000 6.06218i 0.141249 0.244650i
$$615$$ 0 0
$$616$$ 9.00000 + 15.5885i 0.362620 + 0.628077i
$$617$$ 31.1769 18.0000i 1.25514 0.724653i 0.283011 0.959117i $$-0.408667\pi$$
0.972125 + 0.234464i $$0.0753335\pi$$
$$618$$ −6.92820 12.0000i −0.278693 0.482711i
$$619$$ −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i $$-0.858949\pi$$
0.823029 + 0.567999i $$0.192282\pi$$
$$620$$ 0 0
$$621$$ 13.5000 7.79423i 0.541736 0.312772i
$$622$$ 0 0
$$623$$ −38.9711 22.5000i −1.56135 0.901443i
$$624$$ 3.00000 1.73205i 0.120096 0.0693375i
$$625$$ 0 0
$$626$$ −7.00000 12.1244i −0.279776 0.484587i
$$627$$ −27.7128 −1.10674
$$628$$ 12.1244 + 7.00000i 0.483814 + 0.279330i
$$629$$ 16.0000 0.637962
$$630$$ 0 0
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ 15.5885 + 9.00000i 0.620076 + 0.358001i
$$633$$ 19.0526 33.0000i 0.757271 1.31163i
$$634$$ −17.0000 29.4449i −0.675156 1.16940i
$$635$$ 0 0
$$636$$ 3.00000 + 1.73205i 0.118958 + 0.0686803i
$$637$$ −3.46410 2.00000i −0.137253 0.0792429i
$$638$$ 2.00000i 0.0791808i
$$639$$ −3.00000 + 5.19615i −0.118678 + 0.205557i
$$640$$ 0 0
$$641$$ −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i $$0.392615\pi$$
−0.982708 + 0.185164i $$0.940718\pi$$
$$642$$ −5.19615 −0.205076
$$643$$ −7.79423 + 4.50000i −0.307374 + 0.177463i −0.645751 0.763548i $$-0.723456\pi$$
0.338377 + 0.941011i $$0.390122\pi$$
$$644$$ 4.50000 + 7.79423i 0.177325 + 0.307136i
$$645$$ 0 0
$$646$$ 16.0000 27.7128i 0.629512 1.09035i
$$647$$ 17.0000i 0.668339i 0.942513 + 0.334169i $$0.108456\pi$$
−0.942513 + 0.334169i $$0.891544\pi$$
$$648$$ −23.3827 + 13.5000i −0.918559 + 0.530330i
$$649$$ −28.0000 −1.09910
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −3.46410 + 2.00000i −0.135665 + 0.0783260i
$$653$$ −3.46410 + 2.00000i −0.135561 + 0.0782660i −0.566247 0.824236i $$-0.691605\pi$$
0.430686 + 0.902502i $$0.358272\pi$$
$$654$$ 8.66025i 0.338643i
$$655$$ 0 0
$$656$$ −5.00000 −0.195217
$$657$$ −10.3923 6.00000i −0.405442 0.234082i
$$658$$ 21.0000i 0.818665i
$$659$$ −4.00000 + 6.92820i −0.155818 + 0.269884i −0.933357 0.358951i $$-0.883135\pi$$
0.777539 + 0.628835i $$0.216468\pi$$
$$660$$ 0 0
$$661$$ 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i $$-0.0788928\pi$$
−0.697174 + 0.716902i $$0.745559\pi$$
$$662$$ 5.19615 3.00000i 0.201954 0.116598i
$$663$$ 6.92820 12.0000i 0.269069 0.466041i
$$664$$ −13.5000 + 23.3827i −0.523902 + 0.907424i
$$665$$ 0 0
$$666$$ −6.00000 10.3923i −0.232495 0.402694i
$$667$$ 3.00000i 0.116160i
$$668$$ −7.79423 4.50000i −0.301568 0.174110i
$$669$$ 32.9090i 1.27233i
$$670$$ 0 0
$$671$$ 7.00000 + 12.1244i 0.270232 + 0.468056i
$$672$$ −12.9904 22.5000i −0.501115 0.867956i
$$673$$ −5.19615 3.00000i −0.200297 0.115642i 0.396497 0.918036i $$-0.370226\pi$$
−0.596794 + 0.802395i $$0.703559\pi$$
$$674$$ 8.00000 0.308148
$$675$$ 0 0
$$676$$ 9.00000 0.346154
$$677$$ −36.3731 21.0000i −1.39793 0.807096i −0.403755 0.914867i $$-0.632295\pi$$
−0.994176 + 0.107772i $$0.965628\pi$$
$$678$$ 6.92820 + 12.0000i 0.266076 + 0.460857i
$$679$$ −3.00000 5.19615i −0.115129 0.199410i
$$680$$ 0 0
$$681$$ 6.92820i 0.265489i
$$682$$ 0 0
$$683$$ 12.0000i 0.459167i 0.973289 + 0.229584i $$0.0737364\pi$$
−0.973289 + 0.229584i $$0.926264\pi$$
$$684$$ 24.0000 0.917663
$$685$$ 0 0
$$686$$ −7.50000 + 12.9904i −0.286351 + 0.495975i
$$687$$ 12.9904 22.5000i 0.495614 0.858429i
$$688$$ 6.92820 4.00000i 0.264135 0.152499i
$$689$$ 2.00000 + 3.46410i 0.0761939 + 0.131972i
$$690$$ 0 0
$$691$$ 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i $$-0.747535\pi$$
0.967901 + 0.251330i $$0.0808679\pi$$
$$692$$ 0 0
$$693$$ 18.0000i 0.683763i
$$694$$ −4.00000 −0.151838
$$695$$ 0 0
$$696$$ 5.19615i 0.196960i
$$697$$ −17.3205 + 10.0000i −0.656061 + 0.378777i
$$698$$ −4.33013 + 2.50000i −0.163898 + 0.0946264i
$$699$$ 36.0000 20.7846i 1.36165 0.786146i
$$700$$ 0 0
$$701$$ 23.0000 0.868698 0.434349 0.900745i $$-0.356978\pi$$
0.434349 + 0.900745i $$0.356978\pi$$
$$702$$ −10.3923 −0.392232
$$703$$ 32.0000i 1.20690i
$$704$$ −7.00000 + 12.1244i −0.263822 + 0.456954i
$$705$$ 0 0
$$706$$ −12.0000 20.7846i −0.451626 0.782239i
$$707$$ −46.7654 + 27.0000i −1.75879 + 1.01544i
$$708$$ 24.2487 0.911322
$$709$$ −20.5000 + 35.5070i −0.769894 + 1.33349i 0.167727 + 0.985834i $$0.446357\pi$$
−0.937620 + 0.347661i $$0.886976\pi$$
$$710$$ 0 0
$$711$$ −9.00000 15.5885i −0.337526 0.584613i
$$712$$ 45.0000i 1.68645i
$$713$$ 0 0
$$714$$ 18.0000 + 10.3923i 0.673633 + 0.388922i
$$715$$ 0 0
$$716$$ −1.00000 1.73205i −0.0373718 0.0647298i
$$717$$ −6.92820 + 12.0000i −0.258738 + 0.448148i
$$718$$ −20.7846 12.0000i −0.775675 0.447836i
$$719$$ −6.00000 −0.223762 −0.111881 0.993722i $$-0.535688\pi$$
−0.111881 + 0.993722i $$0.535688\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 38.9711 + 22.5000i 1.45036 + 0.837363i
$$723$$ −19.0526 −0.708572
$$724$$ 3.50000 + 6.06218i 0.130076 + 0.225299i
$$725$$ 0 0
$$726$$ 10.5000 6.06218i 0.389692 0.224989i
$$727$$ 19.9186 + 11.5000i 0.738739 + 0.426511i 0.821611 0.570049i $$-0.193076\pi$$
−0.0828714 + 0.996560i $$0.526409\pi$$
$$728$$ 18.0000i 0.667124i
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 16.0000 27.7128i 0.591781 1.02500i
$$732$$ −6.06218 10.5000i −0.224065 0.388091i
$$733$$ −29.4449 + 17.0000i −1.08757 + 0.627909i −0.932929 0.360061i $$-0.882756\pi$$
−0.154642 + 0.987971i $$0.549422\pi$$
$$734$$ 12.0000 + 20.7846i 0.442928 + 0.767174i
$$735$$ 0 0
$$736$$ −7.50000 + 12.9904i −0.276454 + 0.478832i
$$737$$ 6.00000i 0.221013i
$$738$$ 12.9904 + 7.50000i 0.478183 + 0.276079i
$$739$$ 2.00000 0.0735712 0.0367856 0.999323i $$-0.488288\pi$$
0.0367856 + 0.999323i $$0.488288\pi$$
$$740$$ 0 0
$$741$$ 24.0000 + 13.8564i 0.881662 + 0.509028i
$$742$$ −5.19615 + 3.00000i −0.190757 + 0.110133i
$$743$$ −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i $$-0.845209\pi$$
−0.0372984 + 0.999304i $$0.511875\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 10.0000 0.366126
$$747$$ 23.3827 13.5000i 0.855528 0.493939i
$$748$$ 8.00000i 0.292509i
$$749$$ −4.50000 + 7.79423i −0.164426 + 0.284795i
$$750$$ 0 0
$$751$$ −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i $$-0.225070\pi$$
−0.942715 + 0.333599i $$0.891737\pi$$
$$752$$ 6.06218 3.50000i 0.221065 0.127632i
$$753$$ 0 0
$$754$$ 1.00000 1.73205i 0.0364179 0.0630776i
$$755$$ 0 0
$$756$$ 15.5885i 0.566947i
$$757$$ 26.0000i 0.944986i 0.881334 + 0.472493i $$0.156646\pi$$
−0.881334 + 0.472493i $$0.843354\pi$$
$$758$$ 22.5167 + 13.0000i 0.817842 + 0.472181i
$$759$$ −9.00000 + 5.19615i −0.326679 + 0.188608i
$$760$$ 0 0
$$761$$ −7.50000 12.9904i −0.271875 0.470901i 0.697467 0.716617i $$-0.254310\pi$$
−0.969342 + 0.245716i $$0.920977\pi$$
$$762$$ 8.66025 0.313728
$$763$$ 12.9904 + 7.50000i 0.470283 + 0.271518i
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ 36.0000 1.30073
$$767$$ 24.2487 + 14.0000i 0.875570 + 0.505511i
$$768$$ 14.7224 25.5000i 0.531250 0.920152i
$$769$$ 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i $$-0.137931\pi$$
−0.817423 + 0.576038i $$0.804598\pi$$
$$770$$ 0 0
$$771$$ −9.00000 5.19615i −0.324127 0.187135i
$$772$$ 8.66025 + 5.00000i 0.311689 + 0.179954i
$$773$$ 24.0000i 0.863220i −0.902060 0.431610i $$-0.857946\pi$$
0.902060 0.431610i $$-0.142054\pi$$
$$774$$ −24.0000 −0.862662
$$775$$ 0 0
$$776$$ 3.00000 5.19615i 0.107694 0.186531i
$$777$$ −20.7846 −0.745644
$$778$$ 28.5788 16.5000i 1.02460 0.591554i
$$779$$ −20.0000 34.6410i