Properties

 Label 637.2.f.a.393.1 Level $637$ Weight $2$ Character 637.393 Analytic conductor $5.086$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.f (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 393.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.393 Dual form 637.2.f.a.295.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-1.50000 + 2.59808i) q^{6} -3.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(1.50000 + 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} -3.00000 q^{12} +(1.00000 - 3.46410i) q^{13} +(4.50000 + 7.79423i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +6.00000 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{24} +4.00000 q^{25} +(-3.50000 + 0.866025i) q^{26} +9.00000 q^{27} +(-3.50000 - 6.06218i) q^{29} +(4.50000 - 7.79423i) q^{30} -3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(4.50000 - 7.79423i) q^{33} +2.00000 q^{34} +(3.00000 + 5.19615i) q^{36} +(-1.00000 - 1.73205i) q^{37} +1.00000 q^{38} +(-10.5000 + 2.59808i) q^{39} +9.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +3.00000 q^{44} +(9.00000 - 15.5885i) q^{45} -1.00000 q^{47} +(1.50000 - 2.59808i) q^{48} +(-2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +3.00000 q^{53} +(-4.50000 - 7.79423i) q^{54} +(-4.50000 - 7.79423i) q^{55} +3.00000 q^{57} +(-3.50000 + 6.06218i) q^{58} +(-2.00000 + 3.46410i) q^{59} +9.00000 q^{60} +(-6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} -9.00000 q^{66} +(1.50000 + 2.59808i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-6.50000 + 11.2583i) q^{71} +(9.00000 - 15.5885i) q^{72} +13.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-6.00000 - 10.3923i) q^{75} +(0.500000 + 0.866025i) q^{76} +(7.50000 + 7.79423i) q^{78} -3.00000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 - 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} -7.00000 q^{86} +(-10.5000 + 18.1865i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(3.00000 + 5.19615i) q^{89} -18.0000 q^{90} +(4.50000 + 7.79423i) q^{93} +(0.500000 + 0.866025i) q^{94} +(1.50000 - 2.59808i) q^{95} +15.0000 q^{96} +(-2.50000 + 4.33013i) q^{97} -18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10})$$ 2 * q - q^2 - 3 * q^3 + q^4 - 6 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9 $$2 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} - 6 q^{12} + 2 q^{13} + 9 q^{15} + q^{16} - 2 q^{17} + 12 q^{18} - q^{19} - 3 q^{20} + 3 q^{22} + 9 q^{24} + 8 q^{25} - 7 q^{26} + 18 q^{27} - 7 q^{29} + 9 q^{30} - 6 q^{31} - 5 q^{32} + 9 q^{33} + 4 q^{34} + 6 q^{36} - 2 q^{37} + 2 q^{38} - 21 q^{39} + 18 q^{40} + 3 q^{41} + 7 q^{43} + 6 q^{44} + 18 q^{45} - 2 q^{47} + 3 q^{48} - 4 q^{50} + 12 q^{51} - 5 q^{52} + 6 q^{53} - 9 q^{54} - 9 q^{55} + 6 q^{57} - 7 q^{58} - 4 q^{59} + 18 q^{60} - 13 q^{61} + 3 q^{62} + 14 q^{64} - 6 q^{65} - 18 q^{66} + 3 q^{67} + 2 q^{68} - 13 q^{71} + 18 q^{72} + 26 q^{73} - 2 q^{74} - 12 q^{75} + q^{76} + 15 q^{78} - 6 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{85} - 14 q^{86} - 21 q^{87} - 9 q^{88} + 6 q^{89} - 36 q^{90} + 9 q^{93} + q^{94} + 3 q^{95} + 30 q^{96} - 5 q^{97} - 36 q^{99}+O(q^{100})$$ 2 * q - q^2 - 3 * q^3 + q^4 - 6 * q^5 - 3 * q^6 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 - 6 * q^12 + 2 * q^13 + 9 * q^15 + q^16 - 2 * q^17 + 12 * q^18 - q^19 - 3 * q^20 + 3 * q^22 + 9 * q^24 + 8 * q^25 - 7 * q^26 + 18 * q^27 - 7 * q^29 + 9 * q^30 - 6 * q^31 - 5 * q^32 + 9 * q^33 + 4 * q^34 + 6 * q^36 - 2 * q^37 + 2 * q^38 - 21 * q^39 + 18 * q^40 + 3 * q^41 + 7 * q^43 + 6 * q^44 + 18 * q^45 - 2 * q^47 + 3 * q^48 - 4 * q^50 + 12 * q^51 - 5 * q^52 + 6 * q^53 - 9 * q^54 - 9 * q^55 + 6 * q^57 - 7 * q^58 - 4 * q^59 + 18 * q^60 - 13 * q^61 + 3 * q^62 + 14 * q^64 - 6 * q^65 - 18 * q^66 + 3 * q^67 + 2 * q^68 - 13 * q^71 + 18 * q^72 + 26 * q^73 - 2 * q^74 - 12 * q^75 + q^76 + 15 * q^78 - 6 * q^79 - 3 * q^80 - 9 * q^81 + 3 * q^82 + 6 * q^85 - 14 * q^86 - 21 * q^87 - 9 * q^88 + 6 * q^89 - 36 * q^90 + 9 * q^93 + q^94 + 3 * q^95 + 30 * q^96 - 5 * q^97 - 36 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i $$-0.281693\pi$$
−0.986869 + 0.161521i $$0.948360\pi$$
$$3$$ −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −3.00000 −1.34164 −0.670820 0.741620i $$-0.734058\pi$$
−0.670820 + 0.741620i $$0.734058\pi$$
$$6$$ −1.50000 + 2.59808i −0.612372 + 1.06066i
$$7$$ 0 0
$$8$$ −3.00000 −1.06066
$$9$$ −3.00000 + 5.19615i −1.00000 + 1.73205i
$$10$$ 1.50000 + 2.59808i 0.474342 + 0.821584i
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ −3.00000 −0.866025
$$13$$ 1.00000 3.46410i 0.277350 0.960769i
$$14$$ 0 0
$$15$$ 4.50000 + 7.79423i 1.16190 + 2.01246i
$$16$$ 0.500000 + 0.866025i 0.125000 + 0.216506i
$$17$$ −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i $$-0.911312\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 6.00000 1.41421
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ −1.50000 + 2.59808i −0.335410 + 0.580948i
$$21$$ 0 0
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ 4.50000 + 7.79423i 0.918559 + 1.59099i
$$25$$ 4.00000 0.800000
$$26$$ −3.50000 + 0.866025i −0.686406 + 0.169842i
$$27$$ 9.00000 1.73205
$$28$$ 0 0
$$29$$ −3.50000 6.06218i −0.649934 1.12572i −0.983138 0.182864i $$-0.941463\pi$$
0.333205 0.942855i $$-0.391870\pi$$
$$30$$ 4.50000 7.79423i 0.821584 1.42302i
$$31$$ −3.00000 −0.538816 −0.269408 0.963026i $$-0.586828\pi$$
−0.269408 + 0.963026i $$0.586828\pi$$
$$32$$ −2.50000 + 4.33013i −0.441942 + 0.765466i
$$33$$ 4.50000 7.79423i 0.783349 1.35680i
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 3.00000 + 5.19615i 0.500000 + 0.866025i
$$37$$ −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i $$-0.219235\pi$$
−0.936442 + 0.350823i $$0.885902\pi$$
$$38$$ 1.00000 0.162221
$$39$$ −10.5000 + 2.59808i −1.68135 + 0.416025i
$$40$$ 9.00000 1.42302
$$41$$ 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i $$-0.0913998\pi$$
−0.724797 + 0.688963i $$0.758066\pi$$
$$42$$ 0 0
$$43$$ 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i $$-0.654118\pi$$
0.999223 0.0394140i $$-0.0125491\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 9.00000 15.5885i 1.34164 2.32379i
$$46$$ 0 0
$$47$$ −1.00000 −0.145865 −0.0729325 0.997337i $$-0.523236\pi$$
−0.0729325 + 0.997337i $$0.523236\pi$$
$$48$$ 1.50000 2.59808i 0.216506 0.375000i
$$49$$ 0 0
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ 6.00000 0.840168
$$52$$ −2.50000 2.59808i −0.346688 0.360288i
$$53$$ 3.00000 0.412082 0.206041 0.978543i $$-0.433942\pi$$
0.206041 + 0.978543i $$0.433942\pi$$
$$54$$ −4.50000 7.79423i −0.612372 1.06066i
$$55$$ −4.50000 7.79423i −0.606780 1.05097i
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ −3.50000 + 6.06218i −0.459573 + 0.796003i
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 9.00000 1.16190
$$61$$ −6.50000 + 11.2583i −0.832240 + 1.44148i 0.0640184 + 0.997949i $$0.479608\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 1.50000 + 2.59808i 0.190500 + 0.329956i
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ −3.00000 + 10.3923i −0.372104 + 1.28901i
$$66$$ −9.00000 −1.10782
$$67$$ 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i $$-0.108004\pi$$
−0.759733 + 0.650236i $$0.774670\pi$$
$$68$$ 1.00000 + 1.73205i 0.121268 + 0.210042i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.50000 + 11.2583i −0.771408 + 1.33612i 0.165383 + 0.986229i $$0.447114\pi$$
−0.936791 + 0.349889i $$0.886219\pi$$
$$72$$ 9.00000 15.5885i 1.06066 1.83712i
$$73$$ 13.0000 1.52153 0.760767 0.649025i $$-0.224823\pi$$
0.760767 + 0.649025i $$0.224823\pi$$
$$74$$ −1.00000 + 1.73205i −0.116248 + 0.201347i
$$75$$ −6.00000 10.3923i −0.692820 1.20000i
$$76$$ 0.500000 + 0.866025i 0.0573539 + 0.0993399i
$$77$$ 0 0
$$78$$ 7.50000 + 7.79423i 0.849208 + 0.882523i
$$79$$ −3.00000 −0.337526 −0.168763 0.985657i $$-0.553977\pi$$
−0.168763 + 0.985657i $$0.553977\pi$$
$$80$$ −1.50000 2.59808i −0.167705 0.290474i
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 1.50000 2.59808i 0.165647 0.286910i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 3.00000 5.19615i 0.325396 0.563602i
$$86$$ −7.00000 −0.754829
$$87$$ −10.5000 + 18.1865i −1.12572 + 1.94980i
$$88$$ −4.50000 7.79423i −0.479702 0.830868i
$$89$$ 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i $$-0.0636557\pi$$
−0.662071 + 0.749441i $$0.730322\pi$$
$$90$$ −18.0000 −1.89737
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 4.50000 + 7.79423i 0.466628 + 0.808224i
$$94$$ 0.500000 + 0.866025i 0.0515711 + 0.0893237i
$$95$$ 1.50000 2.59808i 0.153897 0.266557i
$$96$$ 15.0000 1.53093
$$97$$ −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i $$-0.915026\pi$$
0.710742 + 0.703452i $$0.248359\pi$$
$$98$$ 0 0
$$99$$ −18.0000 −1.80907
$$100$$ 2.00000 3.46410i 0.200000 0.346410i
$$101$$ −2.50000 4.33013i −0.248759 0.430864i 0.714423 0.699715i $$-0.246689\pi$$
−0.963182 + 0.268851i $$0.913356\pi$$
$$102$$ −3.00000 5.19615i −0.297044 0.514496i
$$103$$ −5.00000 −0.492665 −0.246332 0.969185i $$-0.579225\pi$$
−0.246332 + 0.969185i $$0.579225\pi$$
$$104$$ −3.00000 + 10.3923i −0.294174 + 1.01905i
$$105$$ 0 0
$$106$$ −1.50000 2.59808i −0.145693 0.252347i
$$107$$ −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i $$-0.293050\pi$$
−0.992003 + 0.126217i $$0.959717\pi$$
$$108$$ 4.50000 7.79423i 0.433013 0.750000i
$$109$$ 7.00000 0.670478 0.335239 0.942133i $$-0.391183\pi$$
0.335239 + 0.942133i $$0.391183\pi$$
$$110$$ −4.50000 + 7.79423i −0.429058 + 0.743151i
$$111$$ −3.00000 + 5.19615i −0.284747 + 0.493197i
$$112$$ 0 0
$$113$$ −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i $$0.415962\pi$$
−0.966496 + 0.256681i $$0.917371\pi$$
$$114$$ −1.50000 2.59808i −0.140488 0.243332i
$$115$$ 0 0
$$116$$ −7.00000 −0.649934
$$117$$ 15.0000 + 15.5885i 1.38675 + 1.44115i
$$118$$ 4.00000 0.368230
$$119$$ 0 0
$$120$$ −13.5000 23.3827i −1.23238 2.13454i
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 13.0000 1.17696
$$123$$ 4.50000 7.79423i 0.405751 0.702782i
$$124$$ −1.50000 + 2.59808i −0.134704 + 0.233314i
$$125$$ 3.00000 0.268328
$$126$$ 0 0
$$127$$ −5.50000 9.52628i −0.488046 0.845321i 0.511859 0.859069i $$-0.328957\pi$$
−0.999905 + 0.0137486i $$0.995624\pi$$
$$128$$ 1.50000 + 2.59808i 0.132583 + 0.229640i
$$129$$ −21.0000 −1.84895
$$130$$ 10.5000 2.59808i 0.920911 0.227866i
$$131$$ −5.00000 −0.436852 −0.218426 0.975854i $$-0.570092\pi$$
−0.218426 + 0.975854i $$0.570092\pi$$
$$132$$ −4.50000 7.79423i −0.391675 0.678401i
$$133$$ 0 0
$$134$$ 1.50000 2.59808i 0.129580 0.224440i
$$135$$ −27.0000 −2.32379
$$136$$ 3.00000 5.19615i 0.257248 0.445566i
$$137$$ −5.00000 + 8.66025i −0.427179 + 0.739895i −0.996621 0.0821359i $$-0.973826\pi$$
0.569442 + 0.822031i $$0.307159\pi$$
$$138$$ 0 0
$$139$$ −7.50000 + 12.9904i −0.636142 + 1.10183i 0.350130 + 0.936701i $$0.386137\pi$$
−0.986272 + 0.165129i $$0.947196\pi$$
$$140$$ 0 0
$$141$$ 1.50000 + 2.59808i 0.126323 + 0.218797i
$$142$$ 13.0000 1.09094
$$143$$ 10.5000 2.59808i 0.878054 0.217262i
$$144$$ −6.00000 −0.500000
$$145$$ 10.5000 + 18.1865i 0.871978 + 1.51031i
$$146$$ −6.50000 11.2583i −0.537944 0.931746i
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i $$0.377278\pi$$
−0.990485 + 0.137619i $$0.956055\pi$$
$$150$$ −6.00000 + 10.3923i −0.489898 + 0.848528i
$$151$$ −21.0000 −1.70896 −0.854478 0.519488i $$-0.826123\pi$$
−0.854478 + 0.519488i $$0.826123\pi$$
$$152$$ 1.50000 2.59808i 0.121666 0.210732i
$$153$$ −6.00000 10.3923i −0.485071 0.840168i
$$154$$ 0 0
$$155$$ 9.00000 0.722897
$$156$$ −3.00000 + 10.3923i −0.240192 + 0.832050i
$$157$$ −19.0000 −1.51637 −0.758183 0.652042i $$-0.773912\pi$$
−0.758183 + 0.652042i $$0.773912\pi$$
$$158$$ 1.50000 + 2.59808i 0.119334 + 0.206692i
$$159$$ −4.50000 7.79423i −0.356873 0.618123i
$$160$$ 7.50000 12.9904i 0.592927 1.02698i
$$161$$ 0 0
$$162$$ −4.50000 + 7.79423i −0.353553 + 0.612372i
$$163$$ 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i $$-0.820864\pi$$
0.884943 + 0.465700i $$0.154198\pi$$
$$164$$ 3.00000 0.234261
$$165$$ −13.5000 + 23.3827i −1.05097 + 1.82034i
$$166$$ 0 0
$$167$$ −6.50000 11.2583i −0.502985 0.871196i −0.999994 0.00345033i $$-0.998902\pi$$
0.497009 0.867745i $$-0.334432\pi$$
$$168$$ 0 0
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ −6.00000 −0.460179
$$171$$ −3.00000 5.19615i −0.229416 0.397360i
$$172$$ −3.50000 6.06218i −0.266872 0.462237i
$$173$$ 9.50000 16.4545i 0.722272 1.25101i −0.237816 0.971310i $$-0.576431\pi$$
0.960087 0.279701i $$-0.0902353\pi$$
$$174$$ 21.0000 1.59201
$$175$$ 0 0
$$176$$ −1.50000 + 2.59808i −0.113067 + 0.195837i
$$177$$ 12.0000 0.901975
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −8.50000 14.7224i −0.635320 1.10041i −0.986447 0.164079i $$-0.947535\pi$$
0.351127 0.936328i $$-0.385798\pi$$
$$180$$ −9.00000 15.5885i −0.670820 1.16190i
$$181$$ 22.0000 1.63525 0.817624 0.575753i $$-0.195291\pi$$
0.817624 + 0.575753i $$0.195291\pi$$
$$182$$ 0 0
$$183$$ 39.0000 2.88296
$$184$$ 0 0
$$185$$ 3.00000 + 5.19615i 0.220564 + 0.382029i
$$186$$ 4.50000 7.79423i 0.329956 0.571501i
$$187$$ −6.00000 −0.438763
$$188$$ −0.500000 + 0.866025i −0.0364662 + 0.0631614i
$$189$$ 0 0
$$190$$ −3.00000 −0.217643
$$191$$ 8.50000 14.7224i 0.615038 1.06528i −0.375339 0.926887i $$-0.622474\pi$$
0.990378 0.138390i $$-0.0441928\pi$$
$$192$$ −10.5000 18.1865i −0.757772 1.31250i
$$193$$ −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i $$-0.247734\pi$$
−0.964059 + 0.265689i $$0.914400\pi$$
$$194$$ 5.00000 0.358979
$$195$$ 31.5000 7.79423i 2.25576 0.558156i
$$196$$ 0 0
$$197$$ 0.500000 + 0.866025i 0.0356235 + 0.0617018i 0.883287 0.468832i $$-0.155325\pi$$
−0.847664 + 0.530534i $$0.821992\pi$$
$$198$$ 9.00000 + 15.5885i 0.639602 + 1.10782i
$$199$$ −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i $$0.417466\pi$$
−0.965272 + 0.261245i $$0.915867\pi$$
$$200$$ −12.0000 −0.848528
$$201$$ 4.50000 7.79423i 0.317406 0.549762i
$$202$$ −2.50000 + 4.33013i −0.175899 + 0.304667i
$$203$$ 0 0
$$204$$ 3.00000 5.19615i 0.210042 0.363803i
$$205$$ −4.50000 7.79423i −0.314294 0.544373i
$$206$$ 2.50000 + 4.33013i 0.174183 + 0.301694i
$$207$$ 0 0
$$208$$ 3.50000 0.866025i 0.242681 0.0600481i
$$209$$ −3.00000 −0.207514
$$210$$ 0 0
$$211$$ −3.50000 6.06218i −0.240950 0.417338i 0.720035 0.693938i $$-0.244126\pi$$
−0.960985 + 0.276600i $$0.910792\pi$$
$$212$$ 1.50000 2.59808i 0.103020 0.178437i
$$213$$ 39.0000 2.67224
$$214$$ −4.00000 + 6.92820i −0.273434 + 0.473602i
$$215$$ −10.5000 + 18.1865i −0.716094 + 1.24031i
$$216$$ −27.0000 −1.83712
$$217$$ 0 0
$$218$$ −3.50000 6.06218i −0.237050 0.410582i
$$219$$ −19.5000 33.7750i −1.31769 2.28230i
$$220$$ −9.00000 −0.606780
$$221$$ 5.00000 + 5.19615i 0.336336 + 0.349531i
$$222$$ 6.00000 0.402694
$$223$$ −4.50000 7.79423i −0.301342 0.521940i 0.675098 0.737728i $$-0.264101\pi$$
−0.976440 + 0.215788i $$0.930768\pi$$
$$224$$ 0 0
$$225$$ −12.0000 + 20.7846i −0.800000 + 1.38564i
$$226$$ 15.0000 0.997785
$$227$$ −2.00000 + 3.46410i −0.132745 + 0.229920i −0.924734 0.380615i $$-0.875712\pi$$
0.791989 + 0.610535i $$0.209046\pi$$
$$228$$ 1.50000 2.59808i 0.0993399 0.172062i
$$229$$ 13.0000 0.859064 0.429532 0.903052i $$-0.358679\pi$$
0.429532 + 0.903052i $$0.358679\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 10.5000 + 18.1865i 0.689359 + 1.19400i
$$233$$ −21.0000 −1.37576 −0.687878 0.725826i $$-0.741458\pi$$
−0.687878 + 0.725826i $$0.741458\pi$$
$$234$$ 6.00000 20.7846i 0.392232 1.35873i
$$235$$ 3.00000 0.195698
$$236$$ 2.00000 + 3.46410i 0.130189 + 0.225494i
$$237$$ 4.50000 + 7.79423i 0.292306 + 0.506290i
$$238$$ 0 0
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ −4.50000 + 7.79423i −0.290474 + 0.503115i
$$241$$ −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i $$0.482594\pi$$
−0.892058 + 0.451920i $$0.850739\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ 0 0
$$244$$ 6.50000 + 11.2583i 0.416120 + 0.720741i
$$245$$ 0 0
$$246$$ −9.00000 −0.573819
$$247$$ 2.50000 + 2.59808i 0.159071 + 0.165312i
$$248$$ 9.00000 0.571501
$$249$$ 0 0
$$250$$ −1.50000 2.59808i −0.0948683 0.164317i
$$251$$ −11.5000 + 19.9186i −0.725874 + 1.25725i 0.232740 + 0.972539i $$0.425231\pi$$
−0.958613 + 0.284711i $$0.908102\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −5.50000 + 9.52628i −0.345101 + 0.597732i
$$255$$ −18.0000 −1.12720
$$256$$ 8.50000 14.7224i 0.531250 0.920152i
$$257$$ −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i $$-0.186535\pi$$
−0.895528 + 0.445005i $$0.853202\pi$$
$$258$$ 10.5000 + 18.1865i 0.653701 + 1.13224i
$$259$$ 0 0
$$260$$ 7.50000 + 7.79423i 0.465130 + 0.483378i
$$261$$ 42.0000 2.59973
$$262$$ 2.50000 + 4.33013i 0.154451 + 0.267516i
$$263$$ 13.5000 + 23.3827i 0.832446 + 1.44184i 0.896093 + 0.443866i $$0.146393\pi$$
−0.0636476 + 0.997972i $$0.520273\pi$$
$$264$$ −13.5000 + 23.3827i −0.830868 + 1.43910i
$$265$$ −9.00000 −0.552866
$$266$$ 0 0
$$267$$ 9.00000 15.5885i 0.550791 0.953998i
$$268$$ 3.00000 0.183254
$$269$$ 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i $$-0.648441\pi$$
0.998361 0.0572259i $$-0.0182255\pi$$
$$270$$ 13.5000 + 23.3827i 0.821584 + 1.42302i
$$271$$ −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i $$-0.328199\pi$$
−0.999870 + 0.0161307i $$0.994865\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 10.0000 0.604122
$$275$$ 6.00000 + 10.3923i 0.361814 + 0.626680i
$$276$$ 0 0
$$277$$ −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i $$0.396503\pi$$
−0.980373 + 0.197153i $$0.936830\pi$$
$$278$$ 15.0000 0.899640
$$279$$ 9.00000 15.5885i 0.538816 0.933257i
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 1.50000 2.59808i 0.0893237 0.154713i
$$283$$ 0.500000 + 0.866025i 0.0297219 + 0.0514799i 0.880504 0.474039i $$-0.157204\pi$$
−0.850782 + 0.525519i $$0.823871\pi$$
$$284$$ 6.50000 + 11.2583i 0.385704 + 0.668059i
$$285$$ −9.00000 −0.533114
$$286$$ −7.50000 7.79423i −0.443484 0.460882i
$$287$$ 0 0
$$288$$ −15.0000 25.9808i −0.883883 1.53093i
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 10.5000 18.1865i 0.616581 1.06795i
$$291$$ 15.0000 0.879316
$$292$$ 6.50000 11.2583i 0.380384 0.658844i
$$293$$ 5.50000 9.52628i 0.321313 0.556531i −0.659446 0.751752i $$-0.729209\pi$$
0.980759 + 0.195221i $$0.0625424\pi$$
$$294$$ 0 0
$$295$$ 6.00000 10.3923i 0.349334 0.605063i
$$296$$ 3.00000 + 5.19615i 0.174371 + 0.302020i
$$297$$ 13.5000 + 23.3827i 0.783349 + 1.35680i
$$298$$ 15.0000 0.868927
$$299$$ 0 0
$$300$$ −12.0000 −0.692820
$$301$$ 0 0
$$302$$ 10.5000 + 18.1865i 0.604207 + 1.04652i
$$303$$ −7.50000 + 12.9904i −0.430864 + 0.746278i
$$304$$ −1.00000 −0.0573539
$$305$$ 19.5000 33.7750i 1.11657 1.93395i
$$306$$ −6.00000 + 10.3923i −0.342997 + 0.594089i
$$307$$ −12.0000 −0.684876 −0.342438 0.939540i $$-0.611253\pi$$
−0.342438 + 0.939540i $$0.611253\pi$$
$$308$$ 0 0
$$309$$ 7.50000 + 12.9904i 0.426660 + 0.738997i
$$310$$ −4.50000 7.79423i −0.255583 0.442682i
$$311$$ 9.00000 0.510343 0.255172 0.966896i $$-0.417868\pi$$
0.255172 + 0.966896i $$0.417868\pi$$
$$312$$ 31.5000 7.79423i 1.78334 0.441261i
$$313$$ −19.0000 −1.07394 −0.536972 0.843600i $$-0.680432\pi$$
−0.536972 + 0.843600i $$0.680432\pi$$
$$314$$ 9.50000 + 16.4545i 0.536116 + 0.928580i
$$315$$ 0 0
$$316$$ −1.50000 + 2.59808i −0.0843816 + 0.146153i
$$317$$ −9.00000 −0.505490 −0.252745 0.967533i $$-0.581333\pi$$
−0.252745 + 0.967533i $$0.581333\pi$$
$$318$$ −4.50000 + 7.79423i −0.252347 + 0.437079i
$$319$$ 10.5000 18.1865i 0.587887 1.01825i
$$320$$ −21.0000 −1.17394
$$321$$ −12.0000 + 20.7846i −0.669775 + 1.16008i
$$322$$ 0 0
$$323$$ −1.00000 1.73205i −0.0556415 0.0963739i
$$324$$ −9.00000 −0.500000
$$325$$ 4.00000 13.8564i 0.221880 0.768615i
$$326$$ −1.00000 −0.0553849
$$327$$ −10.5000 18.1865i −0.580651 1.00572i
$$328$$ −4.50000 7.79423i −0.248471 0.430364i
$$329$$ 0 0
$$330$$ 27.0000 1.48630
$$331$$ 14.5000 25.1147i 0.796992 1.38043i −0.124574 0.992210i $$-0.539757\pi$$
0.921567 0.388221i $$-0.126910\pi$$
$$332$$ 0 0
$$333$$ 12.0000 0.657596
$$334$$ −6.50000 + 11.2583i −0.355664 + 0.616028i
$$335$$ −4.50000 7.79423i −0.245861 0.425844i
$$336$$ 0 0
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −0.500000 + 12.9904i −0.0271964 + 0.706584i
$$339$$ 45.0000 2.44406
$$340$$ −3.00000 5.19615i −0.162698 0.281801i
$$341$$ −4.50000 7.79423i −0.243689 0.422081i
$$342$$ −3.00000 + 5.19615i −0.162221 + 0.280976i
$$343$$ 0 0
$$344$$ −10.5000 + 18.1865i −0.566122 + 0.980552i
$$345$$ 0 0
$$346$$ −19.0000 −1.02145
$$347$$ 4.00000 6.92820i 0.214731 0.371925i −0.738458 0.674299i $$-0.764446\pi$$
0.953189 + 0.302374i $$0.0977791\pi$$
$$348$$ 10.5000 + 18.1865i 0.562859 + 0.974901i
$$349$$ 11.5000 + 19.9186i 0.615581 + 1.06622i 0.990282 + 0.139072i $$0.0444119\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 9.00000 31.1769i 0.480384 1.66410i
$$352$$ −15.0000 −0.799503
$$353$$ −12.5000 21.6506i −0.665308 1.15235i −0.979202 0.202889i $$-0.934967\pi$$
0.313894 0.949458i $$-0.398366\pi$$
$$354$$ −6.00000 10.3923i −0.318896 0.552345i
$$355$$ 19.5000 33.7750i 1.03495 1.79259i
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −8.50000 + 14.7224i −0.449239 + 0.778105i
$$359$$ 17.0000 0.897226 0.448613 0.893726i $$-0.351918\pi$$
0.448613 + 0.893726i $$0.351918\pi$$
$$360$$ −27.0000 + 46.7654i −1.42302 + 2.46475i
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ −11.0000 19.0526i −0.578147 1.00138i
$$363$$ −6.00000 −0.314918
$$364$$ 0 0
$$365$$ −39.0000 −2.04135
$$366$$ −19.5000 33.7750i −1.01928 1.76545i
$$367$$ −15.5000 26.8468i −0.809093 1.40139i −0.913493 0.406855i $$-0.866625\pi$$
0.104399 0.994535i $$-0.466708\pi$$
$$368$$ 0 0
$$369$$ −18.0000 −0.937043
$$370$$ 3.00000 5.19615i 0.155963 0.270135i
$$371$$ 0 0
$$372$$ 9.00000 0.466628
$$373$$ 4.50000 7.79423i 0.233001 0.403570i −0.725689 0.688023i $$-0.758479\pi$$
0.958690 + 0.284453i $$0.0918121\pi$$
$$374$$ 3.00000 + 5.19615i 0.155126 + 0.268687i
$$375$$ −4.50000 7.79423i −0.232379 0.402492i
$$376$$ 3.00000 0.154713
$$377$$ −24.5000 + 6.06218i −1.26181 + 0.312218i
$$378$$ 0 0
$$379$$ 16.5000 + 28.5788i 0.847548 + 1.46800i 0.883390 + 0.468639i $$0.155255\pi$$
−0.0358418 + 0.999357i $$0.511411\pi$$
$$380$$ −1.50000 2.59808i −0.0769484 0.133278i
$$381$$ −16.5000 + 28.5788i −0.845321 + 1.46414i
$$382$$ −17.0000 −0.869796
$$383$$ −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i $$0.346930\pi$$
−0.999088 + 0.0427020i $$0.986403\pi$$
$$384$$ 4.50000 7.79423i 0.229640 0.397748i
$$385$$ 0 0
$$386$$ −3.50000 + 6.06218i −0.178145 + 0.308557i
$$387$$ 21.0000 + 36.3731i 1.06749 + 1.84895i
$$388$$ 2.50000 + 4.33013i 0.126918 + 0.219829i
$$389$$ −33.0000 −1.67317 −0.836583 0.547840i $$-0.815450\pi$$
−0.836583 + 0.547840i $$0.815450\pi$$
$$390$$ −22.5000 23.3827i −1.13933 1.18403i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 7.50000 + 12.9904i 0.378325 + 0.655278i
$$394$$ 0.500000 0.866025i 0.0251896 0.0436297i
$$395$$ 9.00000 0.452839
$$396$$ −9.00000 + 15.5885i −0.452267 + 0.783349i
$$397$$ −0.500000 + 0.866025i −0.0250943 + 0.0434646i −0.878300 0.478110i $$-0.841322\pi$$
0.853206 + 0.521575i $$0.174655\pi$$
$$398$$ 20.0000 1.00251
$$399$$ 0 0
$$400$$ 2.00000 + 3.46410i 0.100000 + 0.173205i
$$401$$ 1.00000 + 1.73205i 0.0499376 + 0.0864945i 0.889914 0.456129i $$-0.150764\pi$$
−0.839976 + 0.542623i $$0.817431\pi$$
$$402$$ −9.00000 −0.448879
$$403$$ −3.00000 + 10.3923i −0.149441 + 0.517678i
$$404$$ −5.00000 −0.248759
$$405$$ 13.5000 + 23.3827i 0.670820 + 1.16190i
$$406$$ 0 0
$$407$$ 3.00000 5.19615i 0.148704 0.257564i
$$408$$ −18.0000 −0.891133
$$409$$ 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i $$-0.720830\pi$$
0.985558 + 0.169338i $$0.0541630\pi$$
$$410$$ −4.50000 + 7.79423i −0.222239 + 0.384930i
$$411$$ 30.0000 1.47979
$$412$$ −2.50000 + 4.33013i −0.123166 + 0.213330i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 12.5000 + 12.9904i 0.612863 + 0.636906i
$$417$$ 45.0000 2.20366
$$418$$ 1.50000 + 2.59808i 0.0733674 + 0.127076i
$$419$$ −12.5000 21.6506i −0.610665 1.05770i −0.991129 0.132907i $$-0.957569\pi$$
0.380464 0.924796i $$-0.375764\pi$$
$$420$$ 0 0
$$421$$ 18.0000 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$422$$ −3.50000 + 6.06218i −0.170377 + 0.295102i
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ −9.00000 −0.437079
$$425$$ −4.00000 + 6.92820i −0.194029 + 0.336067i
$$426$$ −19.5000 33.7750i −0.944778 1.63640i
$$427$$ 0 0
$$428$$ −8.00000 −0.386695
$$429$$ −22.5000 23.3827i −1.08631 1.12893i
$$430$$ 21.0000 1.01271
$$431$$ −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i $$-0.236215\pi$$
−0.953815 + 0.300395i $$0.902881\pi$$
$$432$$ 4.50000 + 7.79423i 0.216506 + 0.375000i
$$433$$ 13.5000 23.3827i 0.648769 1.12370i −0.334649 0.942343i $$-0.608618\pi$$
0.983417 0.181357i $$-0.0580490\pi$$
$$434$$ 0 0
$$435$$ 31.5000 54.5596i 1.51031 2.61593i
$$436$$ 3.50000 6.06218i 0.167620 0.290326i
$$437$$ 0 0
$$438$$ −19.5000 + 33.7750i −0.931746 + 1.61383i
$$439$$ −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i $$-0.291369\pi$$
−0.991322 + 0.131453i $$0.958036\pi$$
$$440$$ 13.5000 + 23.3827i 0.643587 + 1.11473i
$$441$$ 0 0
$$442$$ 2.00000 6.92820i 0.0951303 0.329541i
$$443$$ −11.0000 −0.522626 −0.261313 0.965254i $$-0.584155\pi$$
−0.261313 + 0.965254i $$0.584155\pi$$
$$444$$ 3.00000 + 5.19615i 0.142374 + 0.246598i
$$445$$ −9.00000 15.5885i −0.426641 0.738964i
$$446$$ −4.50000 + 7.79423i −0.213081 + 0.369067i
$$447$$ 45.0000 2.12843
$$448$$ 0 0
$$449$$ −7.50000 + 12.9904i −0.353947 + 0.613054i −0.986937 0.161106i $$-0.948494\pi$$
0.632990 + 0.774160i $$0.281827\pi$$
$$450$$ 24.0000 1.13137
$$451$$ −4.50000 + 7.79423i −0.211897 + 0.367016i
$$452$$ 7.50000 + 12.9904i 0.352770 + 0.611016i
$$453$$ 31.5000 + 54.5596i 1.48000 + 2.56343i
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ −9.00000 −0.421464
$$457$$ 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i $$-0.0283451\pi$$
−0.575036 + 0.818128i $$0.695012\pi$$
$$458$$ −6.50000 11.2583i −0.303725 0.526067i
$$459$$ −9.00000 + 15.5885i −0.420084 + 0.727607i
$$460$$ 0 0
$$461$$ 17.5000 30.3109i 0.815056 1.41172i −0.0942312 0.995550i $$-0.530039\pi$$
0.909288 0.416169i $$-0.136627\pi$$
$$462$$ 0 0
$$463$$ −8.00000 −0.371792 −0.185896 0.982569i $$-0.559519\pi$$
−0.185896 + 0.982569i $$0.559519\pi$$
$$464$$ 3.50000 6.06218i 0.162483 0.281430i
$$465$$ −13.5000 23.3827i −0.626048 1.08435i
$$466$$ 10.5000 + 18.1865i 0.486403 + 0.842475i
$$467$$ 7.00000 0.323921 0.161961 0.986797i $$-0.448218\pi$$
0.161961 + 0.986797i $$0.448218\pi$$
$$468$$ 21.0000 5.19615i 0.970725 0.240192i
$$469$$ 0 0
$$470$$ −1.50000 2.59808i −0.0691898 0.119840i
$$471$$ 28.5000 + 49.3634i 1.31321 + 2.27455i
$$472$$ 6.00000 10.3923i 0.276172 0.478345i
$$473$$ 21.0000 0.965581
$$474$$ 4.50000 7.79423i 0.206692 0.358001i
$$475$$ −2.00000 + 3.46410i −0.0917663 + 0.158944i
$$476$$ 0 0
$$477$$ −9.00000 + 15.5885i −0.412082 + 0.713746i
$$478$$ 2.00000 + 3.46410i 0.0914779 + 0.158444i
$$479$$ −17.5000 30.3109i −0.799595 1.38494i −0.919880 0.392200i $$-0.871714\pi$$
0.120284 0.992739i $$-0.461619\pi$$
$$480$$ −45.0000 −2.05396
$$481$$ −7.00000 + 1.73205i −0.319173 + 0.0789747i
$$482$$ 26.0000 1.18427
$$483$$ 0 0
$$484$$ −1.00000 1.73205i −0.0454545 0.0787296i
$$485$$ 7.50000 12.9904i 0.340557 0.589863i
$$486$$ 0 0
$$487$$ −8.00000 + 13.8564i −0.362515 + 0.627894i −0.988374 0.152042i $$-0.951415\pi$$
0.625859 + 0.779936i $$0.284748\pi$$
$$488$$ 19.5000 33.7750i 0.882724 1.52892i
$$489$$ −3.00000 −0.135665
$$490$$ 0 0
$$491$$ −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i $$-0.276576\pi$$
−0.984145 + 0.177365i $$0.943243\pi$$
$$492$$ −4.50000 7.79423i −0.202876 0.351391i
$$493$$ 14.0000 0.630528
$$494$$ 1.00000 3.46410i 0.0449921 0.155857i
$$495$$ 54.0000 2.42712
$$496$$ −1.50000 2.59808i −0.0673520 0.116657i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −31.0000 −1.38775 −0.693875 0.720095i $$-0.744098\pi$$
−0.693875 + 0.720095i $$0.744098\pi$$
$$500$$ 1.50000 2.59808i 0.0670820 0.116190i
$$501$$ −19.5000 + 33.7750i −0.871196 + 1.50896i
$$502$$ 23.0000 1.02654
$$503$$ −15.5000 + 26.8468i −0.691111 + 1.19704i 0.280363 + 0.959894i $$0.409545\pi$$
−0.971474 + 0.237145i $$0.923788\pi$$
$$504$$ 0 0
$$505$$ 7.50000 + 12.9904i 0.333746 + 0.578064i
$$506$$ 0 0
$$507$$ −1.50000 + 38.9711i −0.0666173 + 1.73077i
$$508$$ −11.0000 −0.488046
$$509$$ −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i $$-0.895025\pi$$
0.192599 0.981278i $$-0.438308\pi$$
$$510$$ 9.00000 + 15.5885i 0.398527 + 0.690268i
$$511$$ 0 0
$$512$$ −11.0000 −0.486136
$$513$$ −4.50000 + 7.79423i −0.198680 + 0.344124i
$$514$$ −1.00000 + 1.73205i −0.0441081 + 0.0763975i
$$515$$ 15.0000 0.660979
$$516$$ −10.5000 + 18.1865i −0.462237 + 0.800617i
$$517$$ −1.50000 2.59808i −0.0659699 0.114263i
$$518$$ 0 0
$$519$$ −57.0000 −2.50202
$$520$$ 9.00000 31.1769i 0.394676 1.36720i
$$521$$ 17.0000 0.744784 0.372392 0.928076i $$-0.378538\pi$$
0.372392 + 0.928076i $$0.378538\pi$$
$$522$$ −21.0000 36.3731i −0.919145 1.59201i
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ −2.50000 + 4.33013i −0.109213 + 0.189162i
$$525$$ 0 0
$$526$$ 13.5000 23.3827i 0.588628 1.01953i
$$527$$ 3.00000 5.19615i 0.130682 0.226348i
$$528$$ 9.00000 0.391675
$$529$$ 11.5000 19.9186i 0.500000 0.866025i
$$530$$ 4.50000 + 7.79423i 0.195468 + 0.338560i
$$531$$ −12.0000 20.7846i −0.520756 0.901975i
$$532$$ 0 0
$$533$$ 10.5000 2.59808i 0.454805 0.112535i
$$534$$ −18.0000 −0.778936
$$535$$ 12.0000 + 20.7846i 0.518805 + 0.898597i
$$536$$ −4.50000 7.79423i −0.194370 0.336659i
$$537$$ −25.5000 + 44.1673i −1.10041 + 1.90596i
$$538$$ −18.0000 −0.776035
$$539$$ 0 0
$$540$$ −13.5000 + 23.3827i −0.580948 + 1.00623i
$$541$$ −37.0000 −1.59075 −0.795377 0.606115i $$-0.792727\pi$$
−0.795377 + 0.606115i $$0.792727\pi$$
$$542$$ −8.00000 + 13.8564i −0.343629 + 0.595184i
$$543$$ −33.0000 57.1577i −1.41617 2.45287i
$$544$$ −5.00000 8.66025i −0.214373 0.371305i
$$545$$ −21.0000 −0.899541
$$546$$ 0 0
$$547$$ −28.0000 −1.19719 −0.598597 0.801050i $$-0.704275\pi$$
−0.598597 + 0.801050i $$0.704275\pi$$
$$548$$ 5.00000 + 8.66025i 0.213589 + 0.369948i
$$549$$ −39.0000 67.5500i −1.66448 2.88296i
$$550$$ 6.00000 10.3923i 0.255841 0.443129i
$$551$$ 7.00000 0.298210
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 22.0000 0.934690
$$555$$ 9.00000 15.5885i 0.382029 0.661693i
$$556$$ 7.50000 + 12.9904i 0.318071 + 0.550915i
$$557$$ −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i $$-0.186911\pi$$
−0.896053 + 0.443947i $$0.853578\pi$$
$$558$$ −18.0000 −0.762001
$$559$$ −17.5000 18.1865i −0.740171 0.769208i
$$560$$ 0 0
$$561$$ 9.00000 + 15.5885i 0.379980 + 0.658145i
$$562$$ 9.00000 + 15.5885i 0.379642 + 0.657559i
$$563$$ 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i $$-0.806471\pi$$
0.905088 + 0.425223i $$0.139804\pi$$
$$564$$ 3.00000 0.126323
$$565$$ 22.5000 38.9711i 0.946582 1.63953i
$$566$$ 0.500000 0.866025i 0.0210166 0.0364018i
$$567$$ 0 0
$$568$$ 19.5000 33.7750i 0.818202 1.41717i
$$569$$ −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i $$-0.233886\pi$$
−0.951592 + 0.307364i $$0.900553\pi$$
$$570$$ 4.50000 + 7.79423i 0.188484 + 0.326464i
$$571$$ 43.0000 1.79949 0.899747 0.436412i $$-0.143751\pi$$
0.899747 + 0.436412i $$0.143751\pi$$
$$572$$ 3.00000 10.3923i 0.125436 0.434524i
$$573$$ −51.0000 −2.13056
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −21.0000 + 36.3731i −0.875000 + 1.51554i
$$577$$ 1.00000 0.0416305 0.0208153 0.999783i $$-0.493374\pi$$
0.0208153 + 0.999783i $$0.493374\pi$$
$$578$$ 6.50000 11.2583i 0.270364 0.468285i
$$579$$ −10.5000 + 18.1865i −0.436365 + 0.755807i
$$580$$ 21.0000 0.871978
$$581$$ 0 0
$$582$$ −7.50000 12.9904i −0.310885 0.538469i
$$583$$ 4.50000 + 7.79423i 0.186371 + 0.322804i
$$584$$ −39.0000 −1.61383
$$585$$ −45.0000 46.7654i −1.86052 1.93351i
$$586$$ −11.0000 −0.454406
$$587$$ −16.5000 28.5788i −0.681028 1.17957i −0.974668 0.223659i $$-0.928200\pi$$
0.293640 0.955916i $$-0.405133\pi$$
$$588$$ 0 0
$$589$$ 1.50000 2.59808i 0.0618064 0.107052i
$$590$$ −12.0000 −0.494032
$$591$$ 1.50000 2.59808i 0.0617018 0.106871i
$$592$$ 1.00000 1.73205i 0.0410997 0.0711868i
$$593$$ −27.0000 −1.10876 −0.554379 0.832265i $$-0.687044\pi$$
−0.554379 + 0.832265i $$0.687044\pi$$
$$594$$ 13.5000 23.3827i 0.553912 0.959403i
$$595$$ 0 0
$$596$$ 7.50000 + 12.9904i 0.307212 + 0.532107i
$$597$$ 60.0000 2.45564
$$598$$ 0 0
$$599$$ −25.0000 −1.02147 −0.510736 0.859738i $$-0.670627\pi$$
−0.510736 + 0.859738i $$0.670627\pi$$
$$600$$ 18.0000 + 31.1769i 0.734847 + 1.27279i
$$601$$ 17.5000 + 30.3109i 0.713840 + 1.23641i 0.963405 + 0.268049i $$0.0863789\pi$$
−0.249565 + 0.968358i $$0.580288\pi$$
$$602$$ 0 0
$$603$$ −18.0000 −0.733017
$$604$$ −10.5000 + 18.1865i −0.427239 + 0.740000i
$$605$$ −3.00000 + 5.19615i −0.121967 + 0.211254i
$$606$$ 15.0000 0.609333
$$607$$ 5.50000 9.52628i 0.223238 0.386660i −0.732551 0.680712i $$-0.761671\pi$$
0.955789 + 0.294052i $$0.0950039\pi$$
$$608$$ −2.50000 4.33013i −0.101388 0.175610i
$$609$$ 0 0
$$610$$ −39.0000 −1.57906
$$611$$ −1.00000 + 3.46410i −0.0404557 + 0.140143i
$$612$$ −12.0000 −0.485071
$$613$$ 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i $$0.00179300\pi$$
−0.495114 + 0.868828i $$0.664874\pi$$
$$614$$ 6.00000 + 10.3923i 0.242140 + 0.419399i
$$615$$ −13.5000 + 23.3827i −0.544373 + 0.942881i
$$616$$ 0 0
$$617$$ 16.5000 28.5788i 0.664265 1.15054i −0.315219 0.949019i $$-0.602078\pi$$
0.979484 0.201522i $$-0.0645887\pi$$
$$618$$ 7.50000 12.9904i 0.301694 0.522550i
$$619$$ −11.0000 −0.442127 −0.221064 0.975259i $$-0.570953\pi$$
−0.221064 + 0.975259i $$0.570953\pi$$
$$620$$ 4.50000 7.79423i 0.180724 0.313024i
$$621$$ 0 0
$$622$$ −4.50000 7.79423i −0.180434 0.312520i
$$623$$ 0 0
$$624$$ −7.50000 7.79423i −0.300240 0.312019i
$$625$$ −29.0000 −1.16000
$$626$$ 9.50000 + 16.4545i 0.379696 + 0.657653i
$$627$$ 4.50000 + 7.79423i 0.179713 + 0.311272i
$$628$$ −9.50000 + 16.4545i −0.379091 + 0.656605i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ −12.5000 + 21.6506i −0.497617 + 0.861898i −0.999996 0.00274930i $$-0.999125\pi$$
0.502379 + 0.864647i $$0.332458\pi$$
$$632$$ 9.00000 0.358001
$$633$$ −10.5000 + 18.1865i −0.417338 + 0.722850i
$$634$$ 4.50000 + 7.79423i 0.178718 + 0.309548i
$$635$$ 16.5000 + 28.5788i 0.654783 + 1.13412i
$$636$$ −9.00000 −0.356873
$$637$$ 0 0
$$638$$ −21.0000 −0.831398
$$639$$ −39.0000 67.5500i −1.54282 2.67224i
$$640$$ −4.50000 7.79423i −0.177878 0.308094i
$$641$$ 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i $$-0.717651\pi$$
0.987200 + 0.159489i $$0.0509845\pi$$
$$642$$ 24.0000 0.947204
$$643$$ −9.50000 + 16.4545i −0.374643 + 0.648901i −0.990274 0.139134i $$-0.955568\pi$$
0.615630 + 0.788035i $$0.288902\pi$$
$$644$$ 0 0
$$645$$ 63.0000 2.48062
$$646$$ −1.00000 + 1.73205i −0.0393445 + 0.0681466i
$$647$$ 4.50000 + 7.79423i 0.176913 + 0.306423i 0.940822 0.338902i $$-0.110055\pi$$
−0.763908 + 0.645325i $$0.776722\pi$$
$$648$$ 13.5000 + 23.3827i 0.530330 + 0.918559i
$$649$$ −12.0000 −0.471041
$$650$$ −14.0000 + 3.46410i −0.549125 + 0.135873i
$$651$$ 0 0
$$652$$ −0.500000 0.866025i −0.0195815 0.0339162i
$$653$$ −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i $$-0.281232\pi$$
−0.986634 + 0.162951i $$0.947899\pi$$
$$654$$ −10.5000 + 18.1865i −0.410582 + 0.711150i
$$655$$ 15.0000 0.586098
$$656$$ −1.50000 + 2.59808i −0.0585652 + 0.101438i
$$657$$ −39.0000 + 67.5500i −1.52153 + 2.63538i
$$658$$ 0 0
$$659$$ −14.5000 + 25.1147i −0.564840 + 0.978331i 0.432225 + 0.901766i $$0.357729\pi$$
−0.997065 + 0.0765653i $$0.975605\pi$$
$$660$$ 13.5000 + 23.3827i 0.525487 + 0.910170i
$$661$$ −4.50000 7.79423i −0.175030 0.303160i 0.765142 0.643862i $$-0.222669\pi$$
−0.940172 + 0.340701i $$0.889335\pi$$
$$662$$ −29.0000 −1.12712
$$663$$ 6.00000 20.7846i 0.233021 0.807207i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −6.00000 10.3923i −0.232495 0.402694i
$$667$$ 0 0
$$668$$ −13.0000 −0.502985
$$669$$ −13.5000 + 23.3827i −0.521940 + 0.904027i
$$670$$ −4.50000 + 7.79423i −0.173850 + 0.301117i
$$671$$ −39.0000 −1.50558
$$672$$ 0 0
$$673$$ 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i $$0.123365\pi$$
−0.135615 + 0.990762i $$0.543301\pi$$
$$674$$ −7.00000 12.1244i −0.269630 0.467013i
$$675$$ 36.0000 1.38564
$$676$$ −11.5000 + 6.06218i −0.442308 + 0.233161i
$$677$$ −7.00000 −0.269032 −0.134516 0.990911i $$-0.542948\pi$$
−0.134516 + 0.990911i $$0.542948\pi$$
$$678$$ −22.5000 38.9711i −0.864107 1.49668i
$$679$$ 0 0
$$680$$ −9.00000 + 15.5885i −0.345134 + 0.597790i
$$681$$ 12.0000 0.459841
$$682$$ −4.50000 + 7.79423i −0.172314 + 0.298456i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ −6.00000 −0.229416
$$685$$ 15.0000 25.9808i 0.573121 0.992674i
$$686$$ 0 0
$$687$$ −19.5000 33.7750i −0.743971 1.28860i
$$688$$ 7.00000 0.266872
$$689$$ 3.00000 10.3923i 0.114291 0.395915i
$$690$$ 0 0
$$691$$ −2.00000 3.46410i −0.0760836 0.131781i 0.825473 0.564441i $$-0.190908\pi$$
−0.901557 + 0.432660i $$0.857575\pi$$
$$692$$ −9.50000 16.4545i −0.361136 0.625506i
$$693$$ 0 0
$$694$$ −8.00000 −0.303676
$$695$$ 22.5000 38.9711i 0.853474 1.47826i
$$696$$ 31.5000 54.5596i 1.19400 2.06808i
$$697$$ −6.00000 −0.227266
$$698$$ 11.5000 19.9186i 0.435281 0.753930i
$$699$$ 31.5000 + 54.5596i 1.19144 + 2.06363i
$$700$$ 0 0
$$701$$ 42.0000 1.58632 0.793159 0.609015i $$-0.208435\pi$$
0.793159 + 0.609015i $$0.208435\pi$$
$$702$$ −31.5000 + 7.79423i −1.18889 + 0.294174i
$$703$$ 2.00000 0.0754314
$$704$$ 10.5000 + 18.1865i 0.395734 + 0.685431i
$$705$$ −4.50000 7.79423i −0.169480 0.293548i
$$706$$ −12.5000 + 21.6506i −0.470444 + 0.814832i
$$707$$ 0 0
$$708$$ 6.00000 10.3923i 0.225494 0.390567i
$$709$$ −5.50000 + 9.52628i −0.206557 + 0.357767i −0.950628 0.310334i $$-0.899559\pi$$
0.744071 + 0.668101i $$0.232892\pi$$
$$710$$ −39.0000 −1.46364
$$711$$ 9.00000 15.5885i 0.337526 0.584613i
$$712$$ −9.00000 15.5885i −0.337289 0.584202i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −31.5000 + 7.79423i −1.17803 + 0.291488i
$$716$$ −17.0000 −0.635320
$$717$$ 6.00000 + 10.3923i 0.224074 + 0.388108i
$$718$$ −8.50000 14.7224i −0.317217 0.549436i
$$719$$ −4.50000 + 7.79423i −0.167822 + 0.290676i −0.937654 0.347571i $$-0.887007\pi$$
0.769832 + 0.638247i $$0.220340\pi$$
$$720$$ 18.0000 0.670820
$$721$$ 0 0
$$722$$ 9.00000 15.5885i 0.334945 0.580142i
$$723$$ 78.0000 2.90085
$$724$$ 11.0000 19.0526i 0.408812 0.708083i
$$725$$ −14.0000 24.2487i −0.519947 0.900575i
$$726$$ 3.00000 + 5.19615i 0.111340 + 0.192847i
$$727$$ 8.00000 0.296704 0.148352 0.988935i $$-0.452603\pi$$
0.148352 + 0.988935i $$0.452603\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 19.5000 + 33.7750i 0.721727 + 1.25007i
$$731$$ 7.00000 + 12.1244i 0.258904 + 0.448435i
$$732$$ 19.5000 33.7750i 0.720741 1.24836i
$$733$$ 9.00000 0.332423 0.166211 0.986090i $$-0.446847\pi$$
0.166211 + 0.986090i $$0.446847\pi$$
$$734$$ −15.5000 + 26.8468i −0.572115 + 0.990933i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4.50000 + 7.79423i −0.165760 + 0.287104i
$$738$$ 9.00000 + 15.5885i 0.331295 + 0.573819i
$$739$$ −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i $$-0.172522\pi$$
−0.875075 + 0.483987i $$0.839188\pi$$
$$740$$ 6.00000 0.220564
$$741$$ 3.00000 10.3923i 0.110208 0.381771i
$$742$$ 0 0
$$743$$ −25.5000 44.1673i −0.935504 1.62034i −0.773732 0.633513i $$-0.781612\pi$$
−0.161772 0.986828i $$-0.551721\pi$$
$$744$$ −13.5000 23.3827i −0.494934 0.857251i
$$745$$ 22.5000 38.9711i 0.824336 1.42779i
$$746$$ −9.00000 −0.329513
$$747$$ 0 0
$$748$$ −3.00000 + 5.19615i −0.109691 + 0.189990i
$$749$$ 0 0
$$750$$ −4.50000 + 7.79423i −0.164317 + 0.284605i
$$751$$ −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i $$-0.995991\pi$$
0.489053 0.872254i $$-0.337342\pi$$
$$752$$ −0.500000 0.866025i −0.0182331 0.0315807i
$$753$$ 69.0000 2.51450
$$754$$ 17.5000 + 18.1865i 0.637312 + 0.662314i
$$755$$ 63.0000 2.29280
$$756$$ 0 0
$$757$$ −1.50000 2.59808i −0.0545184 0.0944287i 0.837478 0.546471i $$-0.184029\pi$$
−0.891997 + 0.452042i $$0.850696\pi$$
$$758$$ 16.5000 28.5788i 0.599307 1.03803i
$$759$$ 0 0
$$760$$ −4.50000 + 7.79423i −0.163232 + 0.282726i
$$761$$ −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i $$-0.885491\pi$$
0.772863 + 0.634573i $$0.218824\pi$$
$$762$$ 33.0000 1.19546
$$763$$ 0 0
$$764$$ −8.50000 14.7224i −0.307519 0.532639i
$$765$$ 18.0000 + 31.1769i 0.650791 + 1.12720i
$$766$$ 21.0000 0.758761
$$767$$ 10.0000 + 10.3923i 0.361079 + 0.375244i
$$768$$ −51.0000 −1.84030
$$769$$ 9.50000 + 16.4545i 0.342579 + 0.593364i 0.984911 0.173063i $$-0.0553663\pi$$
−0.642332 + 0.766426i $$0.722033\pi$$
$$770$$ 0 0
$$771$$ −3.00000 + 5.19615i −0.108042 + 0.187135i
$$772$$ −7.00000 −0.251936
$$773$$ −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i $$-0.867747\pi$$
0.807018 + 0.590527i $$0.201080\pi$$
$$774$$ 21.0000 36.3731i 0.754829 1.30740i
$$775$$ −12.0000 −0.431053
$$776$$ 7.50000 12.9904i 0.269234 0.466328i
$$777$$ 0 0
$$778$$ 16.5000 + 28.5788i 0.591554 + 1.02460i
$$779$$ −3.00000 −0.107486
$$780$$ 9.00000 31.1769i 0.322252 1.11631i