Properties

 Label 324.3.f.b.271.1 Level $324$ Weight $3$ Character 324.271 Analytic conductor $8.828$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$324 = 2^{2} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 324.f (of order $$6$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$8.82836056527$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 108) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 271.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 324.271 Dual form 324.3.f.b.55.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +4.00000 q^{4} +(3.50000 - 6.06218i) q^{5} +(-7.50000 + 4.33013i) q^{7} -8.00000 q^{8} +O(q^{10})$$ $$q-2.00000 q^{2} +4.00000 q^{4} +(3.50000 - 6.06218i) q^{5} +(-7.50000 + 4.33013i) q^{7} -8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(-7.50000 + 4.33013i) q^{11} +(-10.0000 + 17.3205i) q^{13} +(15.0000 - 8.66025i) q^{14} +16.0000 q^{16} +8.00000 q^{17} +10.3923i q^{19} +(14.0000 - 24.2487i) q^{20} +(15.0000 - 8.66025i) q^{22} +(-3.00000 - 1.73205i) q^{23} +(-12.0000 - 20.7846i) q^{25} +(20.0000 - 34.6410i) q^{26} +(-30.0000 + 17.3205i) q^{28} +(5.00000 + 8.66025i) q^{29} +(46.5000 + 26.8468i) q^{31} -32.0000 q^{32} -16.0000 q^{34} +60.6218i q^{35} -10.0000 q^{37} -20.7846i q^{38} +(-28.0000 + 48.4974i) q^{40} +(-25.0000 + 43.3013i) q^{41} +(15.0000 - 8.66025i) q^{43} +(-30.0000 + 17.3205i) q^{44} +(6.00000 + 3.46410i) q^{46} +(-75.0000 + 43.3013i) q^{47} +(13.0000 - 22.5167i) q^{49} +(24.0000 + 41.5692i) q^{50} +(-40.0000 + 69.2820i) q^{52} +47.0000 q^{53} +60.6218i q^{55} +(60.0000 - 34.6410i) q^{56} +(-10.0000 - 17.3205i) q^{58} +(-30.0000 - 17.3205i) q^{59} +(32.0000 + 55.4256i) q^{61} +(-93.0000 - 53.6936i) q^{62} +64.0000 q^{64} +(70.0000 + 121.244i) q^{65} +(-75.0000 - 43.3013i) q^{67} +32.0000 q^{68} -121.244i q^{70} -55.0000 q^{73} +20.0000 q^{74} +41.5692i q^{76} +(37.5000 - 64.9519i) q^{77} +(6.00000 - 3.46410i) q^{79} +(56.0000 - 96.9948i) q^{80} +(50.0000 - 86.6025i) q^{82} +(-25.5000 + 14.7224i) q^{83} +(28.0000 - 48.4974i) q^{85} +(-30.0000 + 17.3205i) q^{86} +(60.0000 - 34.6410i) q^{88} -10.0000 q^{89} -173.205i q^{91} +(-12.0000 - 6.92820i) q^{92} +(150.000 - 86.6025i) q^{94} +(63.0000 + 36.3731i) q^{95} +(12.5000 + 21.6506i) q^{97} +(-26.0000 + 45.0333i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 4 q^{2} + 8 q^{4} + 7 q^{5} - 15 q^{7} - 16 q^{8}+O(q^{10})$$ 2 * q - 4 * q^2 + 8 * q^4 + 7 * q^5 - 15 * q^7 - 16 * q^8 $$2 q - 4 q^{2} + 8 q^{4} + 7 q^{5} - 15 q^{7} - 16 q^{8} - 14 q^{10} - 15 q^{11} - 20 q^{13} + 30 q^{14} + 32 q^{16} + 16 q^{17} + 28 q^{20} + 30 q^{22} - 6 q^{23} - 24 q^{25} + 40 q^{26} - 60 q^{28} + 10 q^{29} + 93 q^{31} - 64 q^{32} - 32 q^{34} - 20 q^{37} - 56 q^{40} - 50 q^{41} + 30 q^{43} - 60 q^{44} + 12 q^{46} - 150 q^{47} + 26 q^{49} + 48 q^{50} - 80 q^{52} + 94 q^{53} + 120 q^{56} - 20 q^{58} - 60 q^{59} + 64 q^{61} - 186 q^{62} + 128 q^{64} + 140 q^{65} - 150 q^{67} + 64 q^{68} - 110 q^{73} + 40 q^{74} + 75 q^{77} + 12 q^{79} + 112 q^{80} + 100 q^{82} - 51 q^{83} + 56 q^{85} - 60 q^{86} + 120 q^{88} - 20 q^{89} - 24 q^{92} + 300 q^{94} + 126 q^{95} + 25 q^{97} - 52 q^{98}+O(q^{100})$$ 2 * q - 4 * q^2 + 8 * q^4 + 7 * q^5 - 15 * q^7 - 16 * q^8 - 14 * q^10 - 15 * q^11 - 20 * q^13 + 30 * q^14 + 32 * q^16 + 16 * q^17 + 28 * q^20 + 30 * q^22 - 6 * q^23 - 24 * q^25 + 40 * q^26 - 60 * q^28 + 10 * q^29 + 93 * q^31 - 64 * q^32 - 32 * q^34 - 20 * q^37 - 56 * q^40 - 50 * q^41 + 30 * q^43 - 60 * q^44 + 12 * q^46 - 150 * q^47 + 26 * q^49 + 48 * q^50 - 80 * q^52 + 94 * q^53 + 120 * q^56 - 20 * q^58 - 60 * q^59 + 64 * q^61 - 186 * q^62 + 128 * q^64 + 140 * q^65 - 150 * q^67 + 64 * q^68 - 110 * q^73 + 40 * q^74 + 75 * q^77 + 12 * q^79 + 112 * q^80 + 100 * q^82 - 51 * q^83 + 56 * q^85 - 60 * q^86 + 120 * q^88 - 20 * q^89 - 24 * q^92 + 300 * q^94 + 126 * q^95 + 25 * q^97 - 52 * q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$$.

 $$n$$ $$163$$ $$245$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −1.00000
$$3$$ 0 0
$$4$$ 4.00000 1.00000
$$5$$ 3.50000 6.06218i 0.700000 1.21244i −0.268466 0.963289i $$-0.586517\pi$$
0.968466 0.249146i $$-0.0801500\pi$$
$$6$$ 0 0
$$7$$ −7.50000 + 4.33013i −1.07143 + 0.618590i −0.928571 0.371154i $$-0.878962\pi$$
−0.142857 + 0.989743i $$0.545629\pi$$
$$8$$ −8.00000 −1.00000
$$9$$ 0 0
$$10$$ −7.00000 + 12.1244i −0.700000 + 1.21244i
$$11$$ −7.50000 + 4.33013i −0.681818 + 0.393648i −0.800540 0.599280i $$-0.795454\pi$$
0.118722 + 0.992928i $$0.462120\pi$$
$$12$$ 0 0
$$13$$ −10.0000 + 17.3205i −0.769231 + 1.33235i 0.168750 + 0.985659i $$0.446027\pi$$
−0.937981 + 0.346688i $$0.887306\pi$$
$$14$$ 15.0000 8.66025i 1.07143 0.618590i
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ 8.00000 0.470588 0.235294 0.971924i $$-0.424395\pi$$
0.235294 + 0.971924i $$0.424395\pi$$
$$18$$ 0 0
$$19$$ 10.3923i 0.546963i 0.961877 + 0.273482i $$0.0881753\pi$$
−0.961877 + 0.273482i $$0.911825\pi$$
$$20$$ 14.0000 24.2487i 0.700000 1.21244i
$$21$$ 0 0
$$22$$ 15.0000 8.66025i 0.681818 0.393648i
$$23$$ −3.00000 1.73205i −0.130435 0.0753066i 0.433363 0.901220i $$-0.357327\pi$$
−0.563798 + 0.825913i $$0.690660\pi$$
$$24$$ 0 0
$$25$$ −12.0000 20.7846i −0.480000 0.831384i
$$26$$ 20.0000 34.6410i 0.769231 1.33235i
$$27$$ 0 0
$$28$$ −30.0000 + 17.3205i −1.07143 + 0.618590i
$$29$$ 5.00000 + 8.66025i 0.172414 + 0.298629i 0.939263 0.343198i $$-0.111510\pi$$
−0.766849 + 0.641827i $$0.778177\pi$$
$$30$$ 0 0
$$31$$ 46.5000 + 26.8468i 1.50000 + 0.866025i 1.00000 $$0$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ −32.0000 −1.00000
$$33$$ 0 0
$$34$$ −16.0000 −0.470588
$$35$$ 60.6218i 1.73205i
$$36$$ 0 0
$$37$$ −10.0000 −0.270270 −0.135135 0.990827i $$-0.543147\pi$$
−0.135135 + 0.990827i $$0.543147\pi$$
$$38$$ 20.7846i 0.546963i
$$39$$ 0 0
$$40$$ −28.0000 + 48.4974i −0.700000 + 1.21244i
$$41$$ −25.0000 + 43.3013i −0.609756 + 1.05613i 0.381524 + 0.924359i $$0.375399\pi$$
−0.991280 + 0.131770i $$0.957934\pi$$
$$42$$ 0 0
$$43$$ 15.0000 8.66025i 0.348837 0.201401i −0.315336 0.948980i $$-0.602117\pi$$
0.664173 + 0.747579i $$0.268784\pi$$
$$44$$ −30.0000 + 17.3205i −0.681818 + 0.393648i
$$45$$ 0 0
$$46$$ 6.00000 + 3.46410i 0.130435 + 0.0753066i
$$47$$ −75.0000 + 43.3013i −1.59574 + 0.921304i −0.603450 + 0.797401i $$0.706208\pi$$
−0.992294 + 0.123903i $$0.960459\pi$$
$$48$$ 0 0
$$49$$ 13.0000 22.5167i 0.265306 0.459524i
$$50$$ 24.0000 + 41.5692i 0.480000 + 0.831384i
$$51$$ 0 0
$$52$$ −40.0000 + 69.2820i −0.769231 + 1.33235i
$$53$$ 47.0000 0.886792 0.443396 0.896326i $$-0.353773\pi$$
0.443396 + 0.896326i $$0.353773\pi$$
$$54$$ 0 0
$$55$$ 60.6218i 1.10221i
$$56$$ 60.0000 34.6410i 1.07143 0.618590i
$$57$$ 0 0
$$58$$ −10.0000 17.3205i −0.172414 0.298629i
$$59$$ −30.0000 17.3205i −0.508475 0.293568i 0.223732 0.974651i $$-0.428176\pi$$
−0.732206 + 0.681083i $$0.761509\pi$$
$$60$$ 0 0
$$61$$ 32.0000 + 55.4256i 0.524590 + 0.908617i 0.999590 + 0.0286310i $$0.00911476\pi$$
−0.475000 + 0.879986i $$0.657552\pi$$
$$62$$ −93.0000 53.6936i −1.50000 0.866025i
$$63$$ 0 0
$$64$$ 64.0000 1.00000
$$65$$ 70.0000 + 121.244i 1.07692 + 1.86529i
$$66$$ 0 0
$$67$$ −75.0000 43.3013i −1.11940 0.646288i −0.178155 0.984003i $$-0.557013\pi$$
−0.941248 + 0.337715i $$0.890346\pi$$
$$68$$ 32.0000 0.470588
$$69$$ 0 0
$$70$$ 121.244i 1.73205i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −55.0000 −0.753425 −0.376712 0.926330i $$-0.622945\pi$$
−0.376712 + 0.926330i $$0.622945\pi$$
$$74$$ 20.0000 0.270270
$$75$$ 0 0
$$76$$ 41.5692i 0.546963i
$$77$$ 37.5000 64.9519i 0.487013 0.843531i
$$78$$ 0 0
$$79$$ 6.00000 3.46410i 0.0759494 0.0438494i −0.461544 0.887117i $$-0.652704\pi$$
0.537494 + 0.843268i $$0.319371\pi$$
$$80$$ 56.0000 96.9948i 0.700000 1.21244i
$$81$$ 0 0
$$82$$ 50.0000 86.6025i 0.609756 1.05613i
$$83$$ −25.5000 + 14.7224i −0.307229 + 0.177379i −0.645686 0.763603i $$-0.723428\pi$$
0.338457 + 0.940982i $$0.390095\pi$$
$$84$$ 0 0
$$85$$ 28.0000 48.4974i 0.329412 0.570558i
$$86$$ −30.0000 + 17.3205i −0.348837 + 0.201401i
$$87$$ 0 0
$$88$$ 60.0000 34.6410i 0.681818 0.393648i
$$89$$ −10.0000 −0.112360 −0.0561798 0.998421i $$-0.517892\pi$$
−0.0561798 + 0.998421i $$0.517892\pi$$
$$90$$ 0 0
$$91$$ 173.205i 1.90335i
$$92$$ −12.0000 6.92820i −0.130435 0.0753066i
$$93$$ 0 0
$$94$$ 150.000 86.6025i 1.59574 0.921304i
$$95$$ 63.0000 + 36.3731i 0.663158 + 0.382874i
$$96$$ 0 0
$$97$$ 12.5000 + 21.6506i 0.128866 + 0.223202i 0.923237 0.384230i $$-0.125533\pi$$
−0.794372 + 0.607432i $$0.792200\pi$$
$$98$$ −26.0000 + 45.0333i −0.265306 + 0.459524i
$$99$$ 0 0
$$100$$ −48.0000 83.1384i −0.480000 0.831384i
$$101$$ −77.5000 134.234i −0.767327 1.32905i −0.939008 0.343896i $$-0.888253\pi$$
0.171681 0.985153i $$-0.445080\pi$$
$$102$$ 0 0
$$103$$ −120.000 69.2820i −1.16505 0.672641i −0.212540 0.977152i $$-0.568174\pi$$
−0.952509 + 0.304511i $$0.901507\pi$$
$$104$$ 80.0000 138.564i 0.769231 1.33235i
$$105$$ 0 0
$$106$$ −94.0000 −0.886792
$$107$$ 129.904i 1.21405i 0.794681 + 0.607027i $$0.207638\pi$$
−0.794681 + 0.607027i $$0.792362\pi$$
$$108$$ 0 0
$$109$$ 134.000 1.22936 0.614679 0.788777i $$-0.289286\pi$$
0.614679 + 0.788777i $$0.289286\pi$$
$$110$$ 121.244i 1.10221i
$$111$$ 0 0
$$112$$ −120.000 + 69.2820i −1.07143 + 0.618590i
$$113$$ −37.0000 + 64.0859i −0.327434 + 0.567132i −0.982002 0.188871i $$-0.939517\pi$$
0.654568 + 0.756003i $$0.272850\pi$$
$$114$$ 0 0
$$115$$ −21.0000 + 12.1244i −0.182609 + 0.105429i
$$116$$ 20.0000 + 34.6410i 0.172414 + 0.298629i
$$117$$ 0 0
$$118$$ 60.0000 + 34.6410i 0.508475 + 0.293568i
$$119$$ −60.0000 + 34.6410i −0.504202 + 0.291101i
$$120$$ 0 0
$$121$$ −23.0000 + 39.8372i −0.190083 + 0.329233i
$$122$$ −64.0000 110.851i −0.524590 0.908617i
$$123$$ 0 0
$$124$$ 186.000 + 107.387i 1.50000 + 0.866025i
$$125$$ 7.00000 0.0560000
$$126$$ 0 0
$$127$$ 25.9808i 0.204573i −0.994755 0.102286i $$-0.967384\pi$$
0.994755 0.102286i $$-0.0326158\pi$$
$$128$$ −128.000 −1.00000
$$129$$ 0 0
$$130$$ −140.000 242.487i −1.07692 1.86529i
$$131$$ −142.500 82.2724i −1.08779 0.628034i −0.154800 0.987946i $$-0.549473\pi$$
−0.932986 + 0.359912i $$0.882807\pi$$
$$132$$ 0 0
$$133$$ −45.0000 77.9423i −0.338346 0.586032i
$$134$$ 150.000 + 86.6025i 1.11940 + 0.646288i
$$135$$ 0 0
$$136$$ −64.0000 −0.470588
$$137$$ −31.0000 53.6936i −0.226277 0.391924i 0.730425 0.682993i $$-0.239322\pi$$
−0.956702 + 0.291070i $$0.905989\pi$$
$$138$$ 0 0
$$139$$ 150.000 + 86.6025i 1.07914 + 0.623040i 0.930663 0.365877i $$-0.119231\pi$$
0.148473 + 0.988916i $$0.452564\pi$$
$$140$$ 242.487i 1.73205i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 173.205i 1.21122i
$$144$$ 0 0
$$145$$ 70.0000 0.482759
$$146$$ 110.000 0.753425
$$147$$ 0 0
$$148$$ −40.0000 −0.270270
$$149$$ 57.5000 99.5929i 0.385906 0.668409i −0.605988 0.795473i $$-0.707222\pi$$
0.991894 + 0.127065i $$0.0405556\pi$$
$$150$$ 0 0
$$151$$ 37.5000 21.6506i 0.248344 0.143382i −0.370662 0.928768i $$-0.620869\pi$$
0.619006 + 0.785386i $$0.287536\pi$$
$$152$$ 83.1384i 0.546963i
$$153$$ 0 0
$$154$$ −75.0000 + 129.904i −0.487013 + 0.843531i
$$155$$ 325.500 187.928i 2.10000 1.21244i
$$156$$ 0 0
$$157$$ −10.0000 + 17.3205i −0.0636943 + 0.110322i −0.896114 0.443824i $$-0.853622\pi$$
0.832420 + 0.554146i $$0.186955\pi$$
$$158$$ −12.0000 + 6.92820i −0.0759494 + 0.0438494i
$$159$$ 0 0
$$160$$ −112.000 + 193.990i −0.700000 + 1.21244i
$$161$$ 30.0000 0.186335
$$162$$ 0 0
$$163$$ 103.923i 0.637565i 0.947828 + 0.318782i $$0.103274\pi$$
−0.947828 + 0.318782i $$0.896726\pi$$
$$164$$ −100.000 + 173.205i −0.609756 + 1.05613i
$$165$$ 0 0
$$166$$ 51.0000 29.4449i 0.307229 0.177379i
$$167$$ 213.000 + 122.976i 1.27545 + 0.736381i 0.976008 0.217734i $$-0.0698665\pi$$
0.299441 + 0.954115i $$0.403200\pi$$
$$168$$ 0 0
$$169$$ −115.500 200.052i −0.683432 1.18374i
$$170$$ −56.0000 + 96.9948i −0.329412 + 0.570558i
$$171$$ 0 0
$$172$$ 60.0000 34.6410i 0.348837 0.201401i
$$173$$ 63.5000 + 109.985i 0.367052 + 0.635753i 0.989103 0.147224i $$-0.0470338\pi$$
−0.622051 + 0.782977i $$0.713700\pi$$
$$174$$ 0 0
$$175$$ 180.000 + 103.923i 1.02857 + 0.593846i
$$176$$ −120.000 + 69.2820i −0.681818 + 0.393648i
$$177$$ 0 0
$$178$$ 20.0000 0.112360
$$179$$ 233.827i 1.30630i −0.757231 0.653148i $$-0.773448\pi$$
0.757231 0.653148i $$-0.226552\pi$$
$$180$$ 0 0
$$181$$ 56.0000 0.309392 0.154696 0.987962i $$-0.450560\pi$$
0.154696 + 0.987962i $$0.450560\pi$$
$$182$$ 346.410i 1.90335i
$$183$$ 0 0
$$184$$ 24.0000 + 13.8564i 0.130435 + 0.0753066i
$$185$$ −35.0000 + 60.6218i −0.189189 + 0.327685i
$$186$$ 0 0
$$187$$ −60.0000 + 34.6410i −0.320856 + 0.185246i
$$188$$ −300.000 + 173.205i −1.59574 + 0.921304i
$$189$$ 0 0
$$190$$ −126.000 72.7461i −0.663158 0.382874i
$$191$$ −30.0000 + 17.3205i −0.157068 + 0.0906833i −0.576474 0.817116i $$-0.695572\pi$$
0.419406 + 0.907799i $$0.362238\pi$$
$$192$$ 0 0
$$193$$ −32.5000 + 56.2917i −0.168394 + 0.291667i −0.937855 0.347027i $$-0.887191\pi$$
0.769462 + 0.638693i $$0.220525\pi$$
$$194$$ −25.0000 43.3013i −0.128866 0.223202i
$$195$$ 0 0
$$196$$ 52.0000 90.0666i 0.265306 0.459524i
$$197$$ −253.000 −1.28426 −0.642132 0.766594i $$-0.721950\pi$$
−0.642132 + 0.766594i $$0.721950\pi$$
$$198$$ 0 0
$$199$$ 129.904i 0.652783i −0.945235 0.326391i $$-0.894167\pi$$
0.945235 0.326391i $$-0.105833\pi$$
$$200$$ 96.0000 + 166.277i 0.480000 + 0.831384i
$$201$$ 0 0
$$202$$ 155.000 + 268.468i 0.767327 + 1.32905i
$$203$$ −75.0000 43.3013i −0.369458 0.213307i
$$204$$ 0 0
$$205$$ 175.000 + 303.109i 0.853659 + 1.47858i
$$206$$ 240.000 + 138.564i 1.16505 + 0.672641i
$$207$$ 0 0
$$208$$ −160.000 + 277.128i −0.769231 + 1.33235i
$$209$$ −45.0000 77.9423i −0.215311 0.372930i
$$210$$ 0 0
$$211$$ −129.000 74.4782i −0.611374 0.352977i 0.162129 0.986770i $$-0.448164\pi$$
−0.773503 + 0.633792i $$0.781497\pi$$
$$212$$ 188.000 0.886792
$$213$$ 0 0
$$214$$ 259.808i 1.21405i
$$215$$ 121.244i 0.563924i
$$216$$ 0 0
$$217$$ −465.000 −2.14286
$$218$$ −268.000 −1.22936
$$219$$ 0 0
$$220$$ 242.487i 1.10221i
$$221$$ −80.0000 + 138.564i −0.361991 + 0.626987i
$$222$$ 0 0
$$223$$ −30.0000 + 17.3205i −0.134529 + 0.0776704i −0.565754 0.824574i $$-0.691415\pi$$
0.431225 + 0.902244i $$0.358082\pi$$
$$224$$ 240.000 138.564i 1.07143 0.618590i
$$225$$ 0 0
$$226$$ 74.0000 128.172i 0.327434 0.567132i
$$227$$ 78.0000 45.0333i 0.343612 0.198385i −0.318256 0.948005i $$-0.603097\pi$$
0.661868 + 0.749620i $$0.269764\pi$$
$$228$$ 0 0
$$229$$ −73.0000 + 126.440i −0.318777 + 0.552138i −0.980233 0.197846i $$-0.936606\pi$$
0.661456 + 0.749984i $$0.269939\pi$$
$$230$$ 42.0000 24.2487i 0.182609 0.105429i
$$231$$ 0 0
$$232$$ −40.0000 69.2820i −0.172414 0.298629i
$$233$$ −334.000 −1.43348 −0.716738 0.697342i $$-0.754366\pi$$
−0.716738 + 0.697342i $$0.754366\pi$$
$$234$$ 0 0
$$235$$ 606.218i 2.57965i
$$236$$ −120.000 69.2820i −0.508475 0.293568i
$$237$$ 0 0
$$238$$ 120.000 69.2820i 0.504202 0.291101i
$$239$$ 15.0000 + 8.66025i 0.0627615 + 0.0362354i 0.531052 0.847339i $$-0.321797\pi$$
−0.468291 + 0.883574i $$0.655130\pi$$
$$240$$ 0 0
$$241$$ −67.0000 116.047i −0.278008 0.481524i 0.692881 0.721052i $$-0.256341\pi$$
−0.970890 + 0.239527i $$0.923008\pi$$
$$242$$ 46.0000 79.6743i 0.190083 0.329233i
$$243$$ 0 0
$$244$$ 128.000 + 221.703i 0.524590 + 0.908617i
$$245$$ −91.0000 157.617i −0.371429 0.643333i
$$246$$ 0 0
$$247$$ −180.000 103.923i −0.728745 0.420741i
$$248$$ −372.000 214.774i −1.50000 0.866025i
$$249$$ 0 0
$$250$$ −14.0000 −0.0560000
$$251$$ 207.846i 0.828072i 0.910260 + 0.414036i $$0.135881\pi$$
−0.910260 + 0.414036i $$0.864119\pi$$
$$252$$ 0 0
$$253$$ 30.0000 0.118577
$$254$$ 51.9615i 0.204573i
$$255$$ 0 0
$$256$$ 256.000 1.00000
$$257$$ 134.000 232.095i 0.521401 0.903093i −0.478289 0.878202i $$-0.658743\pi$$
0.999690 0.0248904i $$-0.00792367\pi$$
$$258$$ 0 0
$$259$$ 75.0000 43.3013i 0.289575 0.167186i
$$260$$ 280.000 + 484.974i 1.07692 + 1.86529i
$$261$$ 0 0
$$262$$ 285.000 + 164.545i 1.08779 + 0.628034i
$$263$$ 375.000 216.506i 1.42586 0.823218i 0.429065 0.903274i $$-0.358843\pi$$
0.996790 + 0.0800555i $$0.0255098\pi$$
$$264$$ 0 0
$$265$$ 164.500 284.922i 0.620755 1.07518i
$$266$$ 90.0000 + 155.885i 0.338346 + 0.586032i
$$267$$ 0 0
$$268$$ −300.000 173.205i −1.11940 0.646288i
$$269$$ 350.000 1.30112 0.650558 0.759457i $$-0.274535\pi$$
0.650558 + 0.759457i $$0.274535\pi$$
$$270$$ 0 0
$$271$$ 36.3731i 0.134218i −0.997746 0.0671090i $$-0.978622\pi$$
0.997746 0.0671090i $$-0.0213775\pi$$
$$272$$ 128.000 0.470588
$$273$$ 0 0
$$274$$ 62.0000 + 107.387i 0.226277 + 0.391924i
$$275$$ 180.000 + 103.923i 0.654545 + 0.377902i
$$276$$ 0 0
$$277$$ 260.000 + 450.333i 0.938628 + 1.62575i 0.768033 + 0.640410i $$0.221236\pi$$
0.170595 + 0.985341i $$0.445431\pi$$
$$278$$ −300.000 173.205i −1.07914 0.623040i
$$279$$ 0 0
$$280$$ 484.974i 1.73205i
$$281$$ −220.000 381.051i −0.782918 1.35605i −0.930235 0.366965i $$-0.880397\pi$$
0.147317 0.989089i $$-0.452936\pi$$
$$282$$ 0 0
$$283$$ 285.000 + 164.545i 1.00707 + 0.581430i 0.910332 0.413880i $$-0.135827\pi$$
0.0967355 + 0.995310i $$0.469160\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 346.410i 1.21122i
$$287$$ 433.013i 1.50876i
$$288$$ 0 0
$$289$$ −225.000 −0.778547
$$290$$ −140.000 −0.482759
$$291$$ 0 0
$$292$$ −220.000 −0.753425
$$293$$ −109.000 + 188.794i −0.372014 + 0.644347i −0.989875 0.141940i $$-0.954666\pi$$
0.617862 + 0.786287i $$0.287999\pi$$
$$294$$ 0 0
$$295$$ −210.000 + 121.244i −0.711864 + 0.410995i
$$296$$ 80.0000 0.270270
$$297$$ 0 0
$$298$$ −115.000 + 199.186i −0.385906 + 0.668409i
$$299$$ 60.0000 34.6410i 0.200669 0.115856i
$$300$$ 0 0
$$301$$ −75.0000 + 129.904i −0.249169 + 0.431574i
$$302$$ −75.0000 + 43.3013i −0.248344 + 0.143382i
$$303$$ 0 0
$$304$$ 166.277i 0.546963i
$$305$$ 448.000 1.46885
$$306$$ 0 0
$$307$$ 207.846i 0.677023i −0.940962 0.338512i $$-0.890077\pi$$
0.940962 0.338512i $$-0.109923\pi$$
$$308$$ 150.000 259.808i 0.487013 0.843531i
$$309$$ 0 0
$$310$$ −651.000 + 375.855i −2.10000 + 1.21244i
$$311$$ −255.000 147.224i −0.819936 0.473390i 0.0304586 0.999536i $$-0.490303\pi$$
−0.850394 + 0.526146i $$0.823637\pi$$
$$312$$ 0 0
$$313$$ −242.500 420.022i −0.774760 1.34192i −0.934929 0.354835i $$-0.884537\pi$$
0.160169 0.987090i $$-0.448796\pi$$
$$314$$ 20.0000 34.6410i 0.0636943 0.110322i
$$315$$ 0 0
$$316$$ 24.0000 13.8564i 0.0759494 0.0438494i
$$317$$ 108.500 + 187.928i 0.342271 + 0.592831i 0.984854 0.173385i $$-0.0554705\pi$$
−0.642583 + 0.766216i $$0.722137\pi$$
$$318$$ 0 0
$$319$$ −75.0000 43.3013i −0.235110 0.135741i
$$320$$ 224.000 387.979i 0.700000 1.21244i
$$321$$ 0 0
$$322$$ −60.0000 −0.186335
$$323$$ 83.1384i 0.257395i
$$324$$ 0 0
$$325$$ 480.000 1.47692
$$326$$ 207.846i 0.637565i
$$327$$ 0 0
$$328$$ 200.000 346.410i 0.609756 1.05613i
$$329$$ 375.000 649.519i 1.13982 1.97422i
$$330$$ 0 0
$$331$$ 375.000 216.506i 1.13293 0.654098i 0.188260 0.982119i $$-0.439715\pi$$
0.944670 + 0.328021i $$0.106382\pi$$
$$332$$ −102.000 + 58.8897i −0.307229 + 0.177379i
$$333$$ 0 0
$$334$$ −426.000 245.951i −1.27545 0.736381i
$$335$$ −525.000 + 303.109i −1.56716 + 0.904803i
$$336$$ 0 0
$$337$$ 155.000 268.468i 0.459941 0.796641i −0.539017 0.842295i $$-0.681204\pi$$
0.998957 + 0.0456545i $$0.0145373\pi$$
$$338$$ 231.000 + 400.104i 0.683432 + 1.18374i
$$339$$ 0 0
$$340$$ 112.000 193.990i 0.329412 0.570558i
$$341$$ −465.000 −1.36364
$$342$$ 0 0
$$343$$ 199.186i 0.580717i
$$344$$ −120.000 + 69.2820i −0.348837 + 0.201401i
$$345$$ 0 0
$$346$$ −127.000 219.970i −0.367052 0.635753i
$$347$$ −187.500 108.253i −0.540346 0.311969i 0.204873 0.978789i $$-0.434322\pi$$
−0.745219 + 0.666820i $$0.767655\pi$$
$$348$$ 0 0
$$349$$ −37.0000 64.0859i −0.106017 0.183627i 0.808136 0.588996i $$-0.200477\pi$$
−0.914153 + 0.405369i $$0.867143\pi$$
$$350$$ −360.000 207.846i −1.02857 0.593846i
$$351$$ 0 0
$$352$$ 240.000 138.564i 0.681818 0.393648i
$$353$$ 197.000 + 341.214i 0.558074 + 0.966612i 0.997657 + 0.0684103i $$0.0217927\pi$$
−0.439584 + 0.898202i $$0.644874\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −40.0000 −0.112360
$$357$$ 0 0
$$358$$ 467.654i 1.30630i
$$359$$ 571.577i 1.59214i 0.605207 + 0.796068i $$0.293090\pi$$
−0.605207 + 0.796068i $$0.706910\pi$$
$$360$$ 0 0
$$361$$ 253.000 0.700831
$$362$$ −112.000 −0.309392
$$363$$ 0 0
$$364$$ 692.820i 1.90335i
$$365$$ −192.500 + 333.420i −0.527397 + 0.913479i
$$366$$ 0 0
$$367$$ 487.500 281.458i 1.32834 0.766916i 0.343295 0.939228i $$-0.388457\pi$$
0.985043 + 0.172311i $$0.0551235\pi$$
$$368$$ −48.0000 27.7128i −0.130435 0.0753066i
$$369$$ 0 0
$$370$$ 70.0000 121.244i 0.189189 0.327685i
$$371$$ −352.500 + 203.516i −0.950135 + 0.548561i
$$372$$ 0 0
$$373$$ 20.0000 34.6410i 0.0536193 0.0928714i −0.837970 0.545716i $$-0.816258\pi$$
0.891589 + 0.452845i $$0.149591\pi$$
$$374$$ 120.000 69.2820i 0.320856 0.185246i
$$375$$ 0 0
$$376$$ 600.000 346.410i 1.59574 0.921304i
$$377$$ −200.000 −0.530504
$$378$$ 0 0
$$379$$ 685.892i 1.80974i −0.425686 0.904871i $$-0.639967\pi$$
0.425686 0.904871i $$-0.360033\pi$$
$$380$$ 252.000 + 145.492i 0.663158 + 0.382874i
$$381$$ 0 0
$$382$$ 60.0000 34.6410i 0.157068 0.0906833i
$$383$$ 312.000 + 180.133i 0.814621 + 0.470322i 0.848558 0.529102i $$-0.177471\pi$$
−0.0339368 + 0.999424i $$0.510804\pi$$
$$384$$ 0 0
$$385$$ −262.500 454.663i −0.681818 1.18094i
$$386$$ 65.0000 112.583i 0.168394 0.291667i
$$387$$ 0 0
$$388$$ 50.0000 + 86.6025i 0.128866 + 0.223202i
$$389$$ 237.500 + 411.362i 0.610540 + 1.05749i 0.991150 + 0.132750i $$0.0423808\pi$$
−0.380610 + 0.924736i $$0.624286\pi$$
$$390$$ 0 0
$$391$$ −24.0000 13.8564i −0.0613811 0.0354384i
$$392$$ −104.000 + 180.133i −0.265306 + 0.459524i
$$393$$ 0 0
$$394$$ 506.000 1.28426
$$395$$ 48.4974i 0.122778i
$$396$$ 0 0
$$397$$ 260.000 0.654912 0.327456 0.944866i $$-0.393809\pi$$
0.327456 + 0.944866i $$0.393809\pi$$
$$398$$ 259.808i 0.652783i
$$399$$ 0 0
$$400$$ −192.000 332.554i −0.480000 0.831384i
$$401$$ −370.000 + 640.859i −0.922693 + 1.59815i −0.127464 + 0.991843i $$0.540684\pi$$
−0.795230 + 0.606308i $$0.792650\pi$$
$$402$$ 0 0
$$403$$ −930.000 + 536.936i −2.30769 + 1.33235i
$$404$$ −310.000 536.936i −0.767327 1.32905i
$$405$$ 0 0
$$406$$ 150.000 + 86.6025i 0.369458 + 0.213307i
$$407$$ 75.0000 43.3013i 0.184275 0.106391i
$$408$$ 0 0
$$409$$ −329.500 + 570.711i −0.805623 + 1.39538i 0.110246 + 0.993904i $$0.464836\pi$$
−0.915869 + 0.401476i $$0.868497\pi$$
$$410$$ −350.000 606.218i −0.853659 1.47858i
$$411$$ 0 0
$$412$$ −480.000 277.128i −1.16505 0.672641i
$$413$$ 300.000 0.726392
$$414$$ 0 0
$$415$$ 206.114i 0.496660i
$$416$$ 320.000 554.256i 0.769231 1.33235i
$$417$$ 0 0
$$418$$ 90.0000 + 155.885i 0.215311 + 0.372930i
$$419$$ 510.000 + 294.449i 1.21718 + 0.702741i 0.964315 0.264759i $$-0.0852924\pi$$
0.252869 + 0.967500i $$0.418626\pi$$
$$420$$ 0 0
$$421$$ 248.000 + 429.549i 0.589074 + 1.02031i 0.994354 + 0.106113i $$0.0338405\pi$$
−0.405280 + 0.914192i $$0.632826\pi$$
$$422$$ 258.000 + 148.956i 0.611374 + 0.352977i
$$423$$ 0 0
$$424$$ −376.000 −0.886792
$$425$$ −96.0000 166.277i −0.225882 0.391240i
$$426$$ 0 0
$$427$$ −480.000 277.128i −1.12412 0.649012i
$$428$$ 519.615i 1.21405i
$$429$$ 0 0
$$430$$ 242.487i 0.563924i
$$431$$ 571.577i 1.32616i 0.748547 + 0.663082i $$0.230752\pi$$
−0.748547 + 0.663082i $$0.769248\pi$$
$$432$$ 0 0
$$433$$ −235.000 −0.542725 −0.271363 0.962477i $$-0.587474\pi$$
−0.271363 + 0.962477i $$0.587474\pi$$
$$434$$ 930.000 2.14286
$$435$$ 0 0
$$436$$ 536.000 1.22936
$$437$$ 18.0000 31.1769i 0.0411899 0.0713431i
$$438$$ 0 0
$$439$$ −358.500 + 206.980i −0.816629 + 0.471481i −0.849253 0.527987i $$-0.822947\pi$$
0.0326238 + 0.999468i $$0.489614\pi$$
$$440$$ 484.974i 1.10221i
$$441$$ 0 0
$$442$$ 160.000 277.128i 0.361991 0.626987i
$$443$$ −498.000 + 287.520i −1.12415 + 0.649030i −0.942458 0.334325i $$-0.891492\pi$$
−0.181695 + 0.983355i $$0.558159\pi$$
$$444$$ 0 0
$$445$$ −35.0000 + 60.6218i −0.0786517 + 0.136229i
$$446$$ 60.0000 34.6410i 0.134529 0.0776704i
$$447$$ 0 0
$$448$$ −480.000 + 277.128i −1.07143 + 0.618590i
$$449$$ 470.000 1.04677 0.523385 0.852096i $$-0.324669\pi$$
0.523385 + 0.852096i $$0.324669\pi$$
$$450$$ 0 0
$$451$$ 433.013i 0.960117i
$$452$$ −148.000 + 256.344i −0.327434 + 0.567132i
$$453$$ 0 0
$$454$$ −156.000 + 90.0666i −0.343612 + 0.198385i
$$455$$ −1050.00 606.218i −2.30769 1.33235i
$$456$$ 0 0
$$457$$ 162.500 + 281.458i 0.355580 + 0.615882i 0.987217 0.159382i $$-0.0509501\pi$$
−0.631637 + 0.775264i $$0.717617\pi$$
$$458$$ 146.000 252.879i 0.318777 0.552138i
$$459$$ 0 0
$$460$$ −84.0000 + 48.4974i −0.182609 + 0.105429i
$$461$$ 327.500 + 567.247i 0.710412 + 1.23047i 0.964703 + 0.263342i $$0.0848248\pi$$
−0.254290 + 0.967128i $$0.581842\pi$$
$$462$$ 0 0
$$463$$ −142.500 82.2724i −0.307775 0.177694i 0.338155 0.941090i $$-0.390197\pi$$
−0.645931 + 0.763396i $$0.723530\pi$$
$$464$$ 80.0000 + 138.564i 0.172414 + 0.298629i
$$465$$ 0 0
$$466$$ 668.000 1.43348
$$467$$ 57.1577i 0.122393i −0.998126 0.0611967i $$-0.980508\pi$$
0.998126 0.0611967i $$-0.0194917\pi$$
$$468$$ 0 0
$$469$$ 750.000 1.59915
$$470$$ 1212.44i 2.57965i
$$471$$ 0 0
$$472$$ 240.000 + 138.564i 0.508475 + 0.293568i
$$473$$ −75.0000 + 129.904i −0.158562 + 0.274638i
$$474$$ 0 0
$$475$$ 216.000 124.708i 0.454737 0.262542i
$$476$$ −240.000 + 138.564i −0.504202 + 0.291101i
$$477$$ 0 0
$$478$$ −30.0000 17.3205i −0.0627615 0.0362354i
$$479$$ 285.000 164.545i 0.594990 0.343517i −0.172078 0.985083i $$-0.555048\pi$$
0.767068 + 0.641566i $$0.221715\pi$$
$$480$$ 0 0
$$481$$ 100.000 173.205i 0.207900 0.360094i
$$482$$ 134.000 + 232.095i 0.278008 + 0.481524i
$$483$$ 0 0
$$484$$ −92.0000 + 159.349i −0.190083 + 0.329233i
$$485$$ 175.000 0.360825
$$486$$ 0 0
$$487$$ 519.615i 1.06697i 0.845809 + 0.533486i $$0.179118\pi$$
−0.845809 + 0.533486i $$0.820882\pi$$
$$488$$ −256.000 443.405i −0.524590 0.908617i
$$489$$ 0 0
$$490$$ 182.000 + 315.233i 0.371429 + 0.643333i
$$491$$ −187.500 108.253i −0.381874 0.220475i 0.296759 0.954952i $$-0.404094\pi$$
−0.678633 + 0.734477i $$0.737427\pi$$
$$492$$ 0 0
$$493$$ 40.0000 + 69.2820i 0.0811359 + 0.140532i
$$494$$ 360.000 + 207.846i 0.728745 + 0.420741i
$$495$$ 0 0
$$496$$ 744.000 + 429.549i 1.50000 + 0.866025i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −39.0000 22.5167i −0.0781563 0.0451236i 0.460413 0.887705i $$-0.347701\pi$$
−0.538569 + 0.842581i $$0.681035\pi$$
$$500$$ 28.0000 0.0560000
$$501$$ 0 0
$$502$$ 415.692i 0.828072i
$$503$$ 384.515i 0.764444i 0.924071 + 0.382222i $$0.124841\pi$$
−0.924071 + 0.382222i $$0.875159\pi$$
$$504$$ 0 0
$$505$$ −1085.00 −2.14851
$$506$$ −60.0000 −0.118577
$$507$$ 0 0
$$508$$ 103.923i 0.204573i
$$509$$ 132.500 229.497i 0.260314 0.450878i −0.706011 0.708201i $$-0.749507\pi$$
0.966325 + 0.257323i $$0.0828405\pi$$
$$510$$ 0 0
$$511$$ 412.500 238.157i 0.807241 0.466061i
$$512$$ −512.000 −1.00000
$$513$$ 0 0
$$514$$ −268.000 + 464.190i −0.521401 + 0.903093i
$$515$$ −840.000 + 484.974i −1.63107 + 0.941698i
$$516$$ 0 0
$$517$$ 375.000 649.519i 0.725338 1.25632i
$$518$$ −150.000 + 86.6025i −0.289575 + 0.167186i
$$519$$ 0 0
$$520$$ −560.000 969.948i −1.07692 1.86529i
$$521$$ 380.000 0.729367 0.364683 0.931132i $$-0.381177\pi$$
0.364683 + 0.931132i $$0.381177\pi$$
$$522$$ 0 0
$$523$$ 623.538i 1.19223i 0.802898 + 0.596117i $$0.203291\pi$$
−0.802898 + 0.596117i $$0.796709\pi$$
$$524$$ −570.000 329.090i −1.08779 0.628034i
$$525$$ 0 0
$$526$$ −750.000 + 433.013i −1.42586 + 0.823218i
$$527$$ 372.000 + 214.774i 0.705882 + 0.407541i
$$528$$ 0 0
$$529$$ −258.500 447.735i −0.488658 0.846380i
$$530$$ −329.000 + 569.845i −0.620755 + 1.07518i
$$531$$ 0 0
$$532$$ −180.000 311.769i −0.338346 0.586032i
$$533$$ −500.000 866.025i −0.938086 1.62481i
$$534$$ 0 0
$$535$$ 787.500 + 454.663i 1.47196 + 0.849838i
$$536$$ 600.000 + 346.410i 1.11940 + 0.646288i
$$537$$ 0 0
$$538$$ −700.000 −1.30112
$$539$$ 225.167i 0.417749i
$$540$$ 0 0
$$541$$ −532.000 −0.983364 −0.491682 0.870775i $$-0.663618\pi$$
−0.491682 + 0.870775i $$0.663618\pi$$
$$542$$ 72.7461i 0.134218i
$$543$$ 0 0
$$544$$ −256.000 −0.470588
$$545$$ 469.000 812.332i 0.860550 1.49052i
$$546$$ 0 0
$$547$$ 780.000 450.333i 1.42596 0.823278i 0.429161 0.903228i $$-0.358809\pi$$
0.996799 + 0.0799498i $$0.0254760\pi$$
$$548$$ −124.000 214.774i −0.226277 0.391924i
$$549$$ 0 0
$$550$$ −360.000 207.846i −0.654545 0.377902i
$$551$$ −90.0000 + 51.9615i −0.163339 + 0.0943040i
$$552$$ 0 0
$$553$$ −30.0000 + 51.9615i −0.0542495 + 0.0939630i
$$554$$ −520.000 900.666i −0.938628 1.62575i
$$555$$ 0 0
$$556$$ 600.000 + 346.410i 1.07914 + 0.623040i
$$557$$ 89.0000 0.159785 0.0798923 0.996804i $$-0.474542\pi$$
0.0798923 + 0.996804i $$0.474542\pi$$
$$558$$ 0 0
$$559$$ 346.410i 0.619696i
$$560$$ 969.948i 1.73205i
$$561$$ 0 0
$$562$$ 440.000 + 762.102i 0.782918 + 1.35605i
$$563$$ 262.500 + 151.554i 0.466252 + 0.269191i 0.714670 0.699462i $$-0.246577\pi$$
−0.248417 + 0.968653i $$0.579910\pi$$
$$564$$ 0 0
$$565$$ 259.000 + 448.601i 0.458407 + 0.793984i
$$566$$ −570.000 329.090i −1.00707 0.581430i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 50.0000 + 86.6025i 0.0878735 + 0.152201i 0.906612 0.421965i $$-0.138660\pi$$
−0.818739 + 0.574166i $$0.805326\pi$$
$$570$$ 0 0
$$571$$ 294.000 + 169.741i 0.514886 + 0.297270i 0.734840 0.678241i $$-0.237257\pi$$
−0.219954 + 0.975510i $$0.570591\pi$$
$$572$$ 692.820i 1.21122i
$$573$$ 0 0
$$574$$ 866.025i 1.50876i
$$575$$ 83.1384i 0.144589i
$$576$$ 0 0
$$577$$ −730.000 −1.26516 −0.632582 0.774493i $$-0.718005\pi$$
−0.632582 + 0.774493i $$0.718005\pi$$
$$578$$ 450.000 0.778547
$$579$$ 0 0
$$580$$ 280.000 0.482759
$$581$$ 127.500 220.836i 0.219449 0.380097i
$$582$$ 0 0
$$583$$ −352.500 + 203.516i −0.604631 + 0.349084i
$$584$$ 440.000 0.753425
$$585$$ 0 0
$$586$$ 218.000 377.587i 0.372014 0.644347i
$$587$$ 694.500 400.970i 1.18313 0.683083i 0.226397 0.974035i $$-0.427305\pi$$
0.956738 + 0.290952i $$0.0939720\pi$$
$$588$$ 0 0
$$589$$ −279.000 + 483.242i −0.473684 + 0.820445i
$$590$$ 420.000 242.487i 0.711864 0.410995i
$$591$$ 0 0
$$592$$ −160.000 −0.270270
$$593$$ −982.000 −1.65599 −0.827993 0.560738i $$-0.810517\pi$$
−0.827993 + 0.560738i $$0.810517\pi$$
$$594$$ 0 0
$$595$$ 484.974i 0.815083i
$$596$$ 230.000 398.372i 0.385906 0.668409i
$$597$$ 0 0
$$598$$ −120.000 + 69.2820i −0.200669 + 0.115856i
$$599$$ 195.000 + 112.583i 0.325543 + 0.187952i 0.653860 0.756615i $$-0.273148\pi$$
−0.328318 + 0.944567i $$0.606482\pi$$
$$600$$ 0 0
$$601$$ −125.500 217.372i −0.208819 0.361684i 0.742524 0.669819i $$-0.233629\pi$$
−0.951343 + 0.308135i $$0.900295\pi$$
$$602$$ 150.000 259.808i 0.249169 0.431574i
$$603$$ 0 0
$$604$$ 150.000 86.6025i 0.248344 0.143382i
$$605$$ 161.000 + 278.860i 0.266116 + 0.460926i
$$606$$ 0 0
$$607$$ 330.000 + 190.526i 0.543657 + 0.313881i 0.746560 0.665318i $$-0.231704\pi$$
−0.202903 + 0.979199i $$0.565037\pi$$
$$608$$ 332.554i 0.546963i
$$609$$ 0 0
$$610$$ −896.000 −1.46885
$$611$$ 1732.05i 2.83478i
$$612$$ 0 0
$$613$$ 650.000 1.06036 0.530179 0.847885i $$-0.322125\pi$$
0.530179 + 0.847885i $$0.322125\pi$$
$$614$$ 415.692i 0.677023i
$$615$$ 0 0
$$616$$ −300.000 + 519.615i −0.487013 + 0.843531i
$$617$$ −379.000 + 656.447i −0.614263 + 1.06393i 0.376251 + 0.926518i $$0.377213\pi$$
−0.990513 + 0.137416i $$0.956120\pi$$
$$618$$ 0 0
$$619$$ 150.000 86.6025i 0.242326 0.139907i −0.373919 0.927461i $$-0.621986\pi$$
0.616245 + 0.787554i $$0.288653\pi$$
$$620$$ 1302.00 751.710i 2.10000 1.21244i
$$621$$ 0 0
$$622$$ 510.000 + 294.449i 0.819936 + 0.473390i
$$623$$ 75.0000 43.3013i 0.120385 0.0695044i
$$624$$ 0 0
$$625$$ 324.500 562.050i 0.519200 0.899281i
$$626$$ 485.000 + 840.045i 0.774760 + 1.34192i
$$627$$ 0 0
$$628$$ −40.0000 + 69.2820i −0.0636943 + 0.110322i
$$629$$ −80.0000 −0.127186
$$630$$ 0 0
$$631$$ 119.512i 0.189400i −0.995506 0.0947001i $$-0.969811\pi$$
0.995506 0.0947001i $$-0.0301892\pi$$
$$632$$ −48.0000 + 27.7128i −0.0759494 + 0.0438494i
$$633$$ 0 0
$$634$$ −217.000 375.855i −0.342271 0.592831i
$$635$$ −157.500 90.9327i −0.248031 0.143201i
$$636$$ 0 0
$$637$$ 260.000 + 450.333i 0.408163 + 0.706960i
$$638$$ 150.000 + 86.6025i 0.235110 + 0.135741i
$$639$$ 0 0
$$640$$ −448.000 + 775.959i −0.700000 + 1.21244i
$$641$$ 455.000 + 788.083i 0.709828 + 1.22946i 0.964921 + 0.262542i $$0.0845609\pi$$
−0.255092 + 0.966917i $$0.582106\pi$$
$$642$$ 0 0
$$643$$ −30.0000 17.3205i −0.0466563 0.0269370i 0.476490 0.879180i $$-0.341909\pi$$
−0.523147 + 0.852243i $$0.675242\pi$$
$$644$$ 120.000 0.186335
$$645$$ 0 0
$$646$$ 166.277i 0.257395i
$$647$$ 914.523i 1.41348i 0.707472 + 0.706741i $$0.249835\pi$$
−0.707472 + 0.706741i $$0.750165\pi$$
$$648$$ 0 0
$$649$$ 300.000 0.462250
$$650$$ −960.000 −1.47692
$$651$$ 0 0
$$652$$ 415.692i 0.637565i
$$653$$ 51.5000 89.2006i 0.0788668 0.136601i −0.823894 0.566743i $$-0.808203\pi$$
0.902761 + 0.430142i $$0.141536\pi$$
$$654$$ 0 0
$$655$$ −997.500 + 575.907i −1.52290 + 0.879247i
$$656$$ −400.000 + 692.820i −0.609756 + 1.05613i
$$657$$ 0 0
$$658$$ −750.000 + 1299.04i −1.13982 + 1.97422i
$$659$$ −52.5000 + 30.3109i −0.0796662 + 0.0459953i −0.539304 0.842111i $$-0.681313\pi$$
0.459638 + 0.888106i $$0.347979\pi$$
$$660$$ 0 0
$$661$$ −289.000 + 500.563i −0.437216 + 0.757281i −0.997474 0.0710377i $$-0.977369\pi$$
0.560257 + 0.828319i $$0.310702\pi$$
$$662$$ −750.000 + 433.013i −1.13293 + 0.654098i
$$663$$ 0 0
$$664$$ 204.000 117.779i 0.307229 0.177379i
$$665$$ −630.000 −0.947368
$$666$$ 0 0
$$667$$ 34.6410i 0.0519356i
$$668$$ 852.000 + 491.902i 1.27545 + 0.736381i
$$669$$ 0 0
$$670$$ 1050.00 606.218i 1.56716 0.904803i
$$671$$ −480.000 277.128i −0.715350 0.413008i
$$672$$ 0 0
$$673$$ −422.500 731.791i −0.627786 1.08736i −0.987995 0.154486i $$-0.950628\pi$$
0.360209 0.932872i $$-0.382705\pi$$
$$674$$ −310.000 + 536.936i −0.459941 + 0.796641i
$$675$$ 0 0
$$676$$ −462.000 800.207i −0.683432 1.18374i
$$677$$ −577.000 999.393i −0.852290 1.47621i −0.879137 0.476569i $$-0.841880\pi$$
0.0268475 0.999640i $$-0.491453\pi$$
$$678$$ 0 0
$$679$$ −187.500 108.253i −0.276141 0.159430i
$$680$$ −224.000 + 387.979i −0.329412 + 0.570558i
$$681$$ 0 0
$$682$$ 930.000 1.36364
$$683$$ 187.061i 0.273882i 0.990579 + 0.136941i $$0.0437271\pi$$
−0.990579 + 0.136941i $$0.956273\pi$$
$$684$$ 0 0
$$685$$ −434.000 −0.633577
$$686$$ 398.372i 0.580717i
$$687$$ 0 0
$$688$$ 240.000 138.564i 0.348837 0.201401i
$$689$$ −470.000 + 814.064i −0.682148 + 1.18152i
$$690$$ 0 0
$$691$$ −426.000 + 245.951i −0.616498 + 0.355935i −0.775504 0.631342i $$-0.782504\pi$$
0.159006 + 0.987278i $$0.449171\pi$$
$$692$$ 254.000 + 439.941i 0.367052 + 0.635753i
$$693$$ 0 0
$$694$$ 375.000 + 216.506i 0.540346 + 0.311969i
$$695$$ 1050.00 606.218i 1.51079 0.872256i
$$696$$ 0 0
$$697$$ −200.000 + 346.410i −0.286944 + 0.497002i
$$698$$ 74.0000 + 128.172i 0.106017 + 0.183627i
$$699$$ 0 0
$$700$$ 720.000 + 415.692i 1.02857 + 0.593846i
$$701$$ 215.000 0.306705 0.153352 0.988172i $$-0.450993\pi$$
0.153352 + 0.988172i $$0.450993\pi$$
$$702$$ 0 0
$$703$$ 103.923i 0.147828i
$$704$$ −480.000 + 277.128i −0.681818 + 0.393648i
$$705$$ 0 0
$$706$$ −394.000 682.428i −0.558074 0.966612i
$$707$$ 1162.50 + 671.170i 1.64427 + 0.949321i
$$708$$ 0 0
$$709$$ 266.000 + 460.726i 0.375176 + 0.649824i 0.990353 0.138565i $$-0.0442488\pi$$
−0.615177 + 0.788389i $$0.710916\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 80.0000 0.112360
$$713$$ −93.0000 161.081i −0.130435 0.225920i
$$714$$ 0 0
$$715$$ −1050.00 606.218i −1.46853 0.847857i
$$716$$ 935.307i 1.30630i
$$717$$ 0 0
$$718$$ 1143.15i 1.59214i
$$719$$ 1143.15i 1.58992i −0.606661 0.794961i $$-0.707491\pi$$
0.606661 0.794961i $$-0.292509\pi$$
$$720$$ 0 0
$$721$$ 1200.00 1.66436
$$722$$ −506.000 −0.700831
$$723$$ 0 0
$$724$$ 224.000 0.309392
$$725$$ 120.000 207.846i 0.165517 0.286684i
$$726$$ 0 0
$$727$$ 1072.50 619.208i 1.47524 0.851731i 0.475630 0.879645i $$-0.342220\pi$$
0.999610 + 0.0279146i $$0.00888665\pi$$
$$728$$ 1385.64i 1.90335i
$$729$$ 0 0
$$730$$ 385.000 666.840i 0.527397 0.913479i
$$731$$ 120.000 69.2820i 0.164159 0.0947771i
$$732$$ 0 0
$$733$$ −475.000 + 822.724i −0.648022 + 1.12241i 0.335573 + 0.942014i $$0.391070\pi$$
−0.983595 + 0.180392i $$0.942263\pi$$
$$734$$ −975.000 + 562.917i −1.32834 + 0.766916i
$$735$$ 0 0
$$736$$ 96.0000 + 55.4256i 0.130435 + 0.0753066i
$$737$$ 750.000 1.01764
$$738$$ 0 0
$$739$$ 581.969i 0.787509i −0.919216 0.393754i $$-0.871176\pi$$
0.919216 0.393754i $$-0.128824\pi$$
$$740$$ −140.000 + 242.487i −0.189189 + 0.327685i
$$741$$ 0 0
$$742$$ 705.000 407.032i 0.950135 0.548561i
$$743$$ −750.000 433.013i −1.00942 0.582790i −0.0983991 0.995147i $$-0.531372\pi$$
−0.911022 + 0.412357i $$0.864706\pi$$
$$744$$ 0 0
$$745$$ −402.500 697.150i −0.540268 0.935772i
$$746$$ −40.0000 + 69.2820i −0.0536193 + 0.0928714i
$$747$$ 0 0
$$748$$ −240.000 + 138.564i −0.320856 + 0.185246i
$$749$$ −562.500 974.279i −0.751001 1.30077i
$$750$$ 0 0
$$751$$ −151.500 87.4686i −0.201731 0.116469i 0.395732 0.918366i $$-0.370491\pi$$
−0.597463 + 0.801897i $$0.703824\pi$$
$$752$$ −1200.00 + 692.820i −1.59574 + 0.921304i
$$753$$ 0 0
$$754$$ 400.000 0.530504
$$755$$ 303.109i 0.401469i
$$756$$ 0 0
$$757$$ 830.000 1.09643 0.548217 0.836336i $$-0.315307\pi$$
0.548217 + 0.836336i $$0.315307\pi$$
$$758$$ 1371.78i 1.80974i
$$759$$ 0 0
$$760$$ −504.000 290.985i −0.663158 0.382874i
$$761$$ −280.000 + 484.974i −0.367937 + 0.637285i −0.989243 0.146283i $$-0.953269\pi$$
0.621306 + 0.783568i $$0.286602\pi$$
$$762$$ 0 0
$$763$$ −1005.00 + 580.237i −1.31717 + 0.760468i
$$764$$ −120.000 + 69.2820i −0.157068 + 0.0906833i
$$765$$ 0 0
$$766$$ −624.000 360.267i −0.814621 0.470322i
$$767$$ 600.000 346.410i 0.782269 0.451643i
$$768$$ 0 0
$$769$$ 165.500 286.654i 0.215215 0.372763i −0.738124 0.674665i $$-0.764288\pi$$
0.953339 + 0.301902i $$0.0976216\pi$$
$$770$$ 525.000 + 909.327i 0.681818 + 1.18094i
$$771$$ 0 0
$$772$$ −130.000 + 225.167i −0.168394 + 0.291667i
$$773$$ −298.000 −0.385511 −0.192755 0.981247i $$-0.561742\pi$$
−0.192755 + 0.981247i $$0.561742\pi$$
$$774$$ 0 0
$$775$$ 1288.65i 1.66277i
$$776$$ −100.000 173.205i −0.128866 0.223202i
$$777$$ 0 0
$$778$$ −475.000 822.724i −0.610540 1.05749i
$$779$$ −450.000 259.808i −0.577664 0.333514i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 48.0000 + 27.7128i 0.0613811 + 0.0354384i
$$783$$ 0 0
$$784$$ 208.000 360.267i 0.265306 0.459524i
$$785$$ 70.0000 + 121.244i 0.0891720