# Properties

 Label 65.2.d.a.64.1 Level $65$ Weight $2$ Character 65.64 Analytic conductor $0.519$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$65 = 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 65.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.519027613138$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 64.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 65.64 Dual form 65.2.d.a.64.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -2.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{6} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -2.00000i q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{6} +3.00000 q^{8} -1.00000 q^{9} +(1.00000 + 2.00000i) q^{10} -2.00000i q^{11} +2.00000i q^{12} +(3.00000 + 2.00000i) q^{13} +(-4.00000 + 2.00000i) q^{15} -1.00000 q^{16} +1.00000 q^{18} +6.00000i q^{19} +(1.00000 + 2.00000i) q^{20} +2.00000i q^{22} -6.00000i q^{23} -6.00000i q^{24} +(-3.00000 + 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} -4.00000i q^{27} +6.00000 q^{29} +(4.00000 - 2.00000i) q^{30} -6.00000i q^{31} -5.00000 q^{32} -4.00000 q^{33} +1.00000 q^{36} +6.00000 q^{37} -6.00000i q^{38} +(4.00000 - 6.00000i) q^{39} +(-3.00000 - 6.00000i) q^{40} +8.00000i q^{41} +6.00000i q^{43} +2.00000i q^{44} +(1.00000 + 2.00000i) q^{45} +6.00000i q^{46} -8.00000 q^{47} +2.00000i q^{48} -7.00000 q^{49} +(3.00000 - 4.00000i) q^{50} +(-3.00000 - 2.00000i) q^{52} +12.0000i q^{53} +4.00000i q^{54} +(-4.00000 + 2.00000i) q^{55} +12.0000 q^{57} -6.00000 q^{58} -2.00000i q^{59} +(4.00000 - 2.00000i) q^{60} +6.00000 q^{61} +6.00000i q^{62} +7.00000 q^{64} +(1.00000 - 8.00000i) q^{65} +4.00000 q^{66} +12.0000 q^{67} -12.0000 q^{69} +2.00000i q^{71} -3.00000 q^{72} -6.00000 q^{73} -6.00000 q^{74} +(8.00000 + 6.00000i) q^{75} -6.00000i q^{76} +(-4.00000 + 6.00000i) q^{78} +(1.00000 + 2.00000i) q^{80} -11.0000 q^{81} -8.00000i q^{82} -4.00000 q^{83} -6.00000i q^{86} -12.0000i q^{87} -6.00000i q^{88} +8.00000i q^{89} +(-1.00000 - 2.00000i) q^{90} +6.00000i q^{92} -12.0000 q^{93} +8.00000 q^{94} +(12.0000 - 6.00000i) q^{95} +10.0000i q^{96} -6.00000 q^{97} +7.00000 q^{98} +2.00000i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 6 q^{8} - 2 q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 6 * q^8 - 2 * q^9 $$2 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 6 q^{8} - 2 q^{9} + 2 q^{10} + 6 q^{13} - 8 q^{15} - 2 q^{16} + 2 q^{18} + 2 q^{20} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 8 q^{30} - 10 q^{32} - 8 q^{33} + 2 q^{36} + 12 q^{37} + 8 q^{39} - 6 q^{40} + 2 q^{45} - 16 q^{47} - 14 q^{49} + 6 q^{50} - 6 q^{52} - 8 q^{55} + 24 q^{57} - 12 q^{58} + 8 q^{60} + 12 q^{61} + 14 q^{64} + 2 q^{65} + 8 q^{66} + 24 q^{67} - 24 q^{69} - 6 q^{72} - 12 q^{73} - 12 q^{74} + 16 q^{75} - 8 q^{78} + 2 q^{80} - 22 q^{81} - 8 q^{83} - 2 q^{90} - 24 q^{93} + 16 q^{94} + 24 q^{95} - 12 q^{97} + 14 q^{98}+O(q^{100})$$ 2 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 6 * q^8 - 2 * q^9 + 2 * q^10 + 6 * q^13 - 8 * q^15 - 2 * q^16 + 2 * q^18 + 2 * q^20 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 8 * q^30 - 10 * q^32 - 8 * q^33 + 2 * q^36 + 12 * q^37 + 8 * q^39 - 6 * q^40 + 2 * q^45 - 16 * q^47 - 14 * q^49 + 6 * q^50 - 6 * q^52 - 8 * q^55 + 24 * q^57 - 12 * q^58 + 8 * q^60 + 12 * q^61 + 14 * q^64 + 2 * q^65 + 8 * q^66 + 24 * q^67 - 24 * q^69 - 6 * q^72 - 12 * q^73 - 12 * q^74 + 16 * q^75 - 8 * q^78 + 2 * q^80 - 22 * q^81 - 8 * q^83 - 2 * q^90 - 24 * q^93 + 16 * q^94 + 24 * q^95 - 12 * q^97 + 14 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$41$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107 −0.353553 0.935414i $$-0.615027\pi$$
−0.353553 + 0.935414i $$0.615027\pi$$
$$3$$ 2.00000i 1.15470i −0.816497 0.577350i $$-0.804087\pi$$
0.816497 0.577350i $$-0.195913\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −1.00000 2.00000i −0.447214 0.894427i
$$6$$ 2.00000i 0.816497i
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 3.00000 1.06066
$$9$$ −1.00000 −0.333333
$$10$$ 1.00000 + 2.00000i 0.316228 + 0.632456i
$$11$$ 2.00000i 0.603023i −0.953463 0.301511i $$-0.902509\pi$$
0.953463 0.301511i $$-0.0974911\pi$$
$$12$$ 2.00000i 0.577350i
$$13$$ 3.00000 + 2.00000i 0.832050 + 0.554700i
$$14$$ 0 0
$$15$$ −4.00000 + 2.00000i −1.03280 + 0.516398i
$$16$$ −1.00000 −0.250000
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 6.00000i 1.37649i 0.725476 + 0.688247i $$0.241620\pi$$
−0.725476 + 0.688247i $$0.758380\pi$$
$$20$$ 1.00000 + 2.00000i 0.223607 + 0.447214i
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 6.00000i 1.25109i −0.780189 0.625543i $$-0.784877\pi$$
0.780189 0.625543i $$-0.215123\pi$$
$$24$$ 6.00000i 1.22474i
$$25$$ −3.00000 + 4.00000i −0.600000 + 0.800000i
$$26$$ −3.00000 2.00000i −0.588348 0.392232i
$$27$$ 4.00000i 0.769800i
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 4.00000 2.00000i 0.730297 0.365148i
$$31$$ 6.00000i 1.07763i −0.842424 0.538816i $$-0.818872\pi$$
0.842424 0.538816i $$-0.181128\pi$$
$$32$$ −5.00000 −0.883883
$$33$$ −4.00000 −0.696311
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ 6.00000i 0.973329i
$$39$$ 4.00000 6.00000i 0.640513 0.960769i
$$40$$ −3.00000 6.00000i −0.474342 0.948683i
$$41$$ 8.00000i 1.24939i 0.780869 + 0.624695i $$0.214777\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 6.00000i 0.914991i 0.889212 + 0.457496i $$0.151253\pi$$
−0.889212 + 0.457496i $$0.848747\pi$$
$$44$$ 2.00000i 0.301511i
$$45$$ 1.00000 + 2.00000i 0.149071 + 0.298142i
$$46$$ 6.00000i 0.884652i
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 2.00000i 0.288675i
$$49$$ −7.00000 −1.00000
$$50$$ 3.00000 4.00000i 0.424264 0.565685i
$$51$$ 0 0
$$52$$ −3.00000 2.00000i −0.416025 0.277350i
$$53$$ 12.0000i 1.64833i 0.566352 + 0.824163i $$0.308354\pi$$
−0.566352 + 0.824163i $$0.691646\pi$$
$$54$$ 4.00000i 0.544331i
$$55$$ −4.00000 + 2.00000i −0.539360 + 0.269680i
$$56$$ 0 0
$$57$$ 12.0000 1.58944
$$58$$ −6.00000 −0.787839
$$59$$ 2.00000i 0.260378i −0.991489 0.130189i $$-0.958442\pi$$
0.991489 0.130189i $$-0.0415584\pi$$
$$60$$ 4.00000 2.00000i 0.516398 0.258199i
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 6.00000i 0.762001i
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 1.00000 8.00000i 0.124035 0.992278i
$$66$$ 4.00000 0.492366
$$67$$ 12.0000 1.46603 0.733017 0.680211i $$-0.238112\pi$$
0.733017 + 0.680211i $$0.238112\pi$$
$$68$$ 0 0
$$69$$ −12.0000 −1.44463
$$70$$ 0 0
$$71$$ 2.00000i 0.237356i 0.992933 + 0.118678i $$0.0378657\pi$$
−0.992933 + 0.118678i $$0.962134\pi$$
$$72$$ −3.00000 −0.353553
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ −6.00000 −0.697486
$$75$$ 8.00000 + 6.00000i 0.923760 + 0.692820i
$$76$$ 6.00000i 0.688247i
$$77$$ 0 0
$$78$$ −4.00000 + 6.00000i −0.452911 + 0.679366i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 1.00000 + 2.00000i 0.111803 + 0.223607i
$$81$$ −11.0000 −1.22222
$$82$$ 8.00000i 0.883452i
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 6.00000i 0.646997i
$$87$$ 12.0000i 1.28654i
$$88$$ 6.00000i 0.639602i
$$89$$ 8.00000i 0.847998i 0.905663 + 0.423999i $$0.139374\pi$$
−0.905663 + 0.423999i $$0.860626\pi$$
$$90$$ −1.00000 2.00000i −0.105409 0.210819i
$$91$$ 0 0
$$92$$ 6.00000i 0.625543i
$$93$$ −12.0000 −1.24434
$$94$$ 8.00000 0.825137
$$95$$ 12.0000 6.00000i 1.23117 0.615587i
$$96$$ 10.0000i 1.02062i
$$97$$ −6.00000 −0.609208 −0.304604 0.952479i $$-0.598524\pi$$
−0.304604 + 0.952479i $$0.598524\pi$$
$$98$$ 7.00000 0.707107
$$99$$ 2.00000i 0.201008i
$$100$$ 3.00000 4.00000i 0.300000 0.400000i
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 6.00000i 0.591198i −0.955312 0.295599i $$-0.904481\pi$$
0.955312 0.295599i $$-0.0955191\pi$$
$$104$$ 9.00000 + 6.00000i 0.882523 + 0.588348i
$$105$$ 0 0
$$106$$ 12.0000i 1.16554i
$$107$$ 6.00000i 0.580042i 0.957020 + 0.290021i $$0.0936623\pi$$
−0.957020 + 0.290021i $$0.906338\pi$$
$$108$$ 4.00000i 0.384900i
$$109$$ 12.0000i 1.14939i −0.818367 0.574696i $$-0.805120\pi$$
0.818367 0.574696i $$-0.194880\pi$$
$$110$$ 4.00000 2.00000i 0.381385 0.190693i
$$111$$ 12.0000i 1.13899i
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ −12.0000 −1.12390
$$115$$ −12.0000 + 6.00000i −1.11901 + 0.559503i
$$116$$ −6.00000 −0.557086
$$117$$ −3.00000 2.00000i −0.277350 0.184900i
$$118$$ 2.00000i 0.184115i
$$119$$ 0 0
$$120$$ −12.0000 + 6.00000i −1.09545 + 0.547723i
$$121$$ 7.00000 0.636364
$$122$$ −6.00000 −0.543214
$$123$$ 16.0000 1.44267
$$124$$ 6.00000i 0.538816i
$$125$$ 11.0000 + 2.00000i 0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 2.00000i 0.177471i 0.996055 + 0.0887357i $$0.0282826\pi$$
−0.996055 + 0.0887357i $$0.971717\pi$$
$$128$$ 3.00000 0.265165
$$129$$ 12.0000 1.05654
$$130$$ −1.00000 + 8.00000i −0.0877058 + 0.701646i
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ −8.00000 + 4.00000i −0.688530 + 0.344265i
$$136$$ 0 0
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ 12.0000 1.02151
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 0 0
$$141$$ 16.0000i 1.34744i
$$142$$ 2.00000i 0.167836i
$$143$$ 4.00000 6.00000i 0.334497 0.501745i
$$144$$ 1.00000 0.0833333
$$145$$ −6.00000 12.0000i −0.498273 0.996546i
$$146$$ 6.00000 0.496564
$$147$$ 14.0000i 1.15470i
$$148$$ −6.00000 −0.493197
$$149$$ 20.0000i 1.63846i −0.573462 0.819232i $$-0.694400\pi$$
0.573462 0.819232i $$-0.305600\pi$$
$$150$$ −8.00000 6.00000i −0.653197 0.489898i
$$151$$ 18.0000i 1.46482i 0.680864 + 0.732410i $$0.261604\pi$$
−0.680864 + 0.732410i $$0.738396\pi$$
$$152$$ 18.0000i 1.45999i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −12.0000 + 6.00000i −0.963863 + 0.481932i
$$156$$ −4.00000 + 6.00000i −0.320256 + 0.480384i
$$157$$ 12.0000i 0.957704i −0.877896 0.478852i $$-0.841053\pi$$
0.877896 0.478852i $$-0.158947\pi$$
$$158$$ 0 0
$$159$$ 24.0000 1.90332
$$160$$ 5.00000 + 10.0000i 0.395285 + 0.790569i
$$161$$ 0 0
$$162$$ 11.0000 0.864242
$$163$$ 12.0000 0.939913 0.469956 0.882690i $$-0.344270\pi$$
0.469956 + 0.882690i $$0.344270\pi$$
$$164$$ 8.00000i 0.624695i
$$165$$ 4.00000 + 8.00000i 0.311400 + 0.622799i
$$166$$ 4.00000 0.310460
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ 5.00000 + 12.0000i 0.384615 + 0.923077i
$$170$$ 0 0
$$171$$ 6.00000i 0.458831i
$$172$$ 6.00000i 0.457496i
$$173$$ 12.0000i 0.912343i −0.889892 0.456172i $$-0.849220\pi$$
0.889892 0.456172i $$-0.150780\pi$$
$$174$$ 12.0000i 0.909718i
$$175$$ 0 0
$$176$$ 2.00000i 0.150756i
$$177$$ −4.00000 −0.300658
$$178$$ 8.00000i 0.599625i
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ −1.00000 2.00000i −0.0745356 0.149071i
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ 12.0000i 0.887066i
$$184$$ 18.0000i 1.32698i
$$185$$ −6.00000 12.0000i −0.441129 0.882258i
$$186$$ 12.0000 0.879883
$$187$$ 0 0
$$188$$ 8.00000 0.583460
$$189$$ 0 0
$$190$$ −12.0000 + 6.00000i −0.870572 + 0.435286i
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 14.0000i 1.01036i
$$193$$ −6.00000 −0.431889 −0.215945 0.976406i $$-0.569283\pi$$
−0.215945 + 0.976406i $$0.569283\pi$$
$$194$$ 6.00000 0.430775
$$195$$ −16.0000 2.00000i −1.14578 0.143223i
$$196$$ 7.00000 0.500000
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 2.00000i 0.142134i
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ −9.00000 + 12.0000i −0.636396 + 0.848528i
$$201$$ 24.0000i 1.69283i
$$202$$ −6.00000 −0.422159
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 16.0000 8.00000i 1.11749 0.558744i
$$206$$ 6.00000i 0.418040i
$$207$$ 6.00000i 0.417029i
$$208$$ −3.00000 2.00000i −0.208013 0.138675i
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 12.0000i 0.824163i
$$213$$ 4.00000 0.274075
$$214$$ 6.00000i 0.410152i
$$215$$ 12.0000 6.00000i 0.818393 0.409197i
$$216$$ 12.0000i 0.816497i
$$217$$ 0 0
$$218$$ 12.0000i 0.812743i
$$219$$ 12.0000i 0.810885i
$$220$$ 4.00000 2.00000i 0.269680 0.134840i
$$221$$ 0 0
$$222$$ 12.0000i 0.805387i
$$223$$ 24.0000 1.60716 0.803579 0.595198i $$-0.202926\pi$$
0.803579 + 0.595198i $$0.202926\pi$$
$$224$$ 0 0
$$225$$ 3.00000 4.00000i 0.200000 0.266667i
$$226$$ 0 0
$$227$$ −4.00000 −0.265489 −0.132745 0.991150i $$-0.542379\pi$$
−0.132745 + 0.991150i $$0.542379\pi$$
$$228$$ −12.0000 −0.794719
$$229$$ 12.0000i 0.792982i 0.918039 + 0.396491i $$0.129772\pi$$
−0.918039 + 0.396491i $$0.870228\pi$$
$$230$$ 12.0000 6.00000i 0.791257 0.395628i
$$231$$ 0 0
$$232$$ 18.0000 1.18176
$$233$$ 24.0000i 1.57229i 0.618041 + 0.786146i $$0.287927\pi$$
−0.618041 + 0.786146i $$0.712073\pi$$
$$234$$ 3.00000 + 2.00000i 0.196116 + 0.130744i
$$235$$ 8.00000 + 16.0000i 0.521862 + 1.04372i
$$236$$ 2.00000i 0.130189i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 10.0000i 0.646846i 0.946254 + 0.323423i $$0.104834\pi$$
−0.946254 + 0.323423i $$0.895166\pi$$
$$240$$ 4.00000 2.00000i 0.258199 0.129099i
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −7.00000 −0.449977
$$243$$ 10.0000i 0.641500i
$$244$$ −6.00000 −0.384111
$$245$$ 7.00000 + 14.0000i 0.447214 + 0.894427i
$$246$$ −16.0000 −1.02012
$$247$$ −12.0000 + 18.0000i −0.763542 + 1.14531i
$$248$$ 18.0000i 1.14300i
$$249$$ 8.00000i 0.506979i
$$250$$ −11.0000 2.00000i −0.695701 0.126491i
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 2.00000i 0.125491i
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ −12.0000 −0.747087
$$259$$ 0 0
$$260$$ −1.00000 + 8.00000i −0.0620174 + 0.496139i
$$261$$ −6.00000 −0.371391
$$262$$ 12.0000 0.741362
$$263$$ 6.00000i 0.369976i −0.982741 0.184988i $$-0.940775\pi$$
0.982741 0.184988i $$-0.0592246\pi$$
$$264$$ −12.0000 −0.738549
$$265$$ 24.0000 12.0000i 1.47431 0.737154i
$$266$$ 0 0
$$267$$ 16.0000 0.979184
$$268$$ −12.0000 −0.733017
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 8.00000 4.00000i 0.486864 0.243432i
$$271$$ 6.00000i 0.364474i −0.983255 0.182237i $$-0.941666\pi$$
0.983255 0.182237i $$-0.0583338\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 8.00000 + 6.00000i 0.482418 + 0.361814i
$$276$$ 12.0000 0.722315
$$277$$ 12.0000i 0.721010i 0.932757 + 0.360505i $$0.117396\pi$$
−0.932757 + 0.360505i $$0.882604\pi$$
$$278$$ 4.00000 0.239904
$$279$$ 6.00000i 0.359211i
$$280$$ 0 0
$$281$$ 8.00000i 0.477240i −0.971113 0.238620i $$-0.923305\pi$$
0.971113 0.238620i $$-0.0766950\pi$$
$$282$$ 16.0000i 0.952786i
$$283$$ 22.0000i 1.30776i 0.756596 + 0.653882i $$0.226861\pi$$
−0.756596 + 0.653882i $$0.773139\pi$$
$$284$$ 2.00000i 0.118678i
$$285$$ −12.0000 24.0000i −0.710819 1.42164i
$$286$$ −4.00000 + 6.00000i −0.236525 + 0.354787i
$$287$$ 0 0
$$288$$ 5.00000 0.294628
$$289$$ 17.0000 1.00000
$$290$$ 6.00000 + 12.0000i 0.352332 + 0.704664i
$$291$$ 12.0000i 0.703452i
$$292$$ 6.00000 0.351123
$$293$$ −26.0000 −1.51894 −0.759468 0.650545i $$-0.774541\pi$$
−0.759468 + 0.650545i $$0.774541\pi$$
$$294$$ 14.0000i 0.816497i
$$295$$ −4.00000 + 2.00000i −0.232889 + 0.116445i
$$296$$ 18.0000 1.04623
$$297$$ −8.00000 −0.464207
$$298$$ 20.0000i 1.15857i
$$299$$ 12.0000 18.0000i 0.693978 1.04097i
$$300$$ −8.00000 6.00000i −0.461880 0.346410i
$$301$$ 0 0
$$302$$ 18.0000i 1.03578i
$$303$$ 12.0000i 0.689382i
$$304$$ 6.00000i 0.344124i
$$305$$ −6.00000 12.0000i −0.343559 0.687118i
$$306$$ 0 0
$$307$$ 12.0000 0.684876 0.342438 0.939540i $$-0.388747\pi$$
0.342438 + 0.939540i $$0.388747\pi$$
$$308$$ 0 0
$$309$$ −12.0000 −0.682656
$$310$$ 12.0000 6.00000i 0.681554 0.340777i
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 12.0000 18.0000i 0.679366 1.01905i
$$313$$ 8.00000i 0.452187i −0.974106 0.226093i $$-0.927405\pi$$
0.974106 0.226093i $$-0.0725954\pi$$
$$314$$ 12.0000i 0.677199i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.00000 −0.112331 −0.0561656 0.998421i $$-0.517887\pi$$
−0.0561656 + 0.998421i $$0.517887\pi$$
$$318$$ −24.0000 −1.34585
$$319$$ 12.0000i 0.671871i
$$320$$ −7.00000 14.0000i −0.391312 0.782624i
$$321$$ 12.0000 0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 11.0000 0.611111
$$325$$ −17.0000 + 6.00000i −0.942990 + 0.332820i
$$326$$ −12.0000 −0.664619
$$327$$ −24.0000 −1.32720
$$328$$ 24.0000i 1.32518i
$$329$$ 0 0
$$330$$ −4.00000 8.00000i −0.220193 0.440386i
$$331$$ 30.0000i 1.64895i 0.565899 + 0.824475i $$0.308529\pi$$
−0.565899 + 0.824475i $$0.691471\pi$$
$$332$$ 4.00000 0.219529
$$333$$ −6.00000 −0.328798
$$334$$ 16.0000 0.875481
$$335$$ −12.0000 24.0000i −0.655630 1.31126i
$$336$$ 0 0
$$337$$ 32.0000i 1.74315i −0.490261 0.871576i $$-0.663099\pi$$
0.490261 0.871576i $$-0.336901\pi$$
$$338$$ −5.00000 12.0000i −0.271964 0.652714i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −12.0000 −0.649836
$$342$$ 6.00000i 0.324443i
$$343$$ 0 0
$$344$$ 18.0000i 0.970495i
$$345$$ 12.0000 + 24.0000i 0.646058 + 1.29212i
$$346$$ 12.0000i 0.645124i
$$347$$ 6.00000i 0.322097i 0.986947 + 0.161048i $$0.0514875\pi$$
−0.986947 + 0.161048i $$0.948512\pi$$
$$348$$ 12.0000i 0.643268i
$$349$$ 12.0000i 0.642345i −0.947021 0.321173i $$-0.895923\pi$$
0.947021 0.321173i $$-0.104077\pi$$
$$350$$ 0 0
$$351$$ 8.00000 12.0000i 0.427008 0.640513i
$$352$$ 10.0000i 0.533002i
$$353$$ −14.0000 −0.745145 −0.372572 0.928003i $$-0.621524\pi$$
−0.372572 + 0.928003i $$0.621524\pi$$
$$354$$ 4.00000 0.212598
$$355$$ 4.00000 2.00000i 0.212298 0.106149i
$$356$$ 8.00000i 0.423999i
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 2.00000i 0.105556i 0.998606 + 0.0527780i $$0.0168076\pi$$
−0.998606 + 0.0527780i $$0.983192\pi$$
$$360$$ 3.00000 + 6.00000i 0.158114 + 0.316228i
$$361$$ −17.0000 −0.894737
$$362$$ 2.00000 0.105118
$$363$$ 14.0000i 0.734809i
$$364$$ 0 0
$$365$$ 6.00000 + 12.0000i 0.314054 + 0.628109i
$$366$$ 12.0000i 0.627250i
$$367$$ 18.0000i 0.939592i 0.882775 + 0.469796i $$0.155673\pi$$
−0.882775 + 0.469796i $$0.844327\pi$$
$$368$$ 6.00000i 0.312772i
$$369$$ 8.00000i 0.416463i
$$370$$ 6.00000 + 12.0000i 0.311925 + 0.623850i
$$371$$ 0 0
$$372$$ 12.0000 0.622171
$$373$$ 4.00000i 0.207112i −0.994624 0.103556i $$-0.966978\pi$$
0.994624 0.103556i $$-0.0330221\pi$$
$$374$$ 0 0
$$375$$ 4.00000 22.0000i 0.206559 1.13608i
$$376$$ −24.0000 −1.23771
$$377$$ 18.0000 + 12.0000i 0.927047 + 0.618031i
$$378$$ 0 0
$$379$$ 18.0000i 0.924598i −0.886724 0.462299i $$-0.847025\pi$$
0.886724 0.462299i $$-0.152975\pi$$
$$380$$ −12.0000 + 6.00000i −0.615587 + 0.307794i
$$381$$ 4.00000 0.204926
$$382$$ 0 0
$$383$$ 8.00000 0.408781 0.204390 0.978889i $$-0.434479\pi$$
0.204390 + 0.978889i $$0.434479\pi$$
$$384$$ 6.00000i 0.306186i
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ 6.00000i 0.304997i
$$388$$ 6.00000 0.304604
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 16.0000 + 2.00000i 0.810191 + 0.101274i
$$391$$ 0 0
$$392$$ −21.0000 −1.06066
$$393$$ 24.0000i 1.21064i
$$394$$ 2.00000 0.100759
$$395$$ 0 0
$$396$$ 2.00000i 0.100504i
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ 24.0000 1.20301
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 16.0000i 0.799002i −0.916733 0.399501i $$-0.869183\pi$$
0.916733 0.399501i $$-0.130817\pi$$
$$402$$ 24.0000i 1.19701i
$$403$$ 12.0000 18.0000i 0.597763 0.896644i
$$404$$ −6.00000 −0.298511
$$405$$ 11.0000 + 22.0000i 0.546594 + 1.09319i
$$406$$ 0 0
$$407$$ 12.0000i 0.594818i
$$408$$ 0 0
$$409$$ 24.0000i 1.18672i 0.804936 + 0.593362i $$0.202200\pi$$
−0.804936 + 0.593362i $$0.797800\pi$$
$$410$$ −16.0000 + 8.00000i −0.790184 + 0.395092i
$$411$$ 4.00000i 0.197305i
$$412$$ 6.00000i 0.295599i
$$413$$ 0 0
$$414$$ 6.00000i 0.294884i
$$415$$ 4.00000 + 8.00000i 0.196352 + 0.392705i
$$416$$ −15.0000 10.0000i −0.735436 0.490290i
$$417$$ 8.00000i 0.391762i
$$418$$ −12.0000 −0.586939
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 36.0000i 1.75453i −0.480004 0.877266i $$-0.659365\pi$$
0.480004 0.877266i $$-0.340635\pi$$
$$422$$ 12.0000 0.584151
$$423$$ 8.00000 0.388973
$$424$$ 36.0000i 1.74831i
$$425$$ 0 0
$$426$$ −4.00000 −0.193801
$$427$$ 0 0
$$428$$ 6.00000i 0.290021i
$$429$$ −12.0000 8.00000i −0.579365 0.386244i
$$430$$ −12.0000 + 6.00000i −0.578691 + 0.289346i
$$431$$ 10.0000i 0.481683i 0.970564 + 0.240842i $$0.0774234\pi$$
−0.970564 + 0.240842i $$0.922577\pi$$
$$432$$ 4.00000i 0.192450i
$$433$$ 16.0000i 0.768911i −0.923144 0.384455i $$-0.874389\pi$$
0.923144 0.384455i $$-0.125611\pi$$
$$434$$ 0 0
$$435$$ −24.0000 + 12.0000i −1.15071 + 0.575356i
$$436$$ 12.0000i 0.574696i
$$437$$ 36.0000 1.72211
$$438$$ 12.0000i 0.573382i
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ −12.0000 + 6.00000i −0.572078 + 0.286039i
$$441$$ 7.00000 0.333333
$$442$$ 0 0
$$443$$ 6.00000i 0.285069i 0.989790 + 0.142534i $$0.0455251\pi$$
−0.989790 + 0.142534i $$0.954475\pi$$
$$444$$ 12.0000i 0.569495i
$$445$$ 16.0000 8.00000i 0.758473 0.379236i
$$446$$ −24.0000 −1.13643
$$447$$ −40.0000 −1.89194
$$448$$ 0 0
$$449$$ 16.0000i 0.755087i 0.925992 + 0.377543i $$0.123231\pi$$
−0.925992 + 0.377543i $$0.876769\pi$$
$$450$$ −3.00000 + 4.00000i −0.141421 + 0.188562i
$$451$$ 16.0000 0.753411
$$452$$ 0 0
$$453$$ 36.0000 1.69143
$$454$$ 4.00000 0.187729
$$455$$ 0 0
$$456$$ 36.0000 1.68585
$$457$$ −30.0000 −1.40334 −0.701670 0.712502i $$-0.747562\pi$$
−0.701670 + 0.712502i $$0.747562\pi$$
$$458$$ 12.0000i 0.560723i
$$459$$ 0 0
$$460$$ 12.0000 6.00000i 0.559503 0.279751i
$$461$$ 4.00000i 0.186299i 0.995652 + 0.0931493i $$0.0296934\pi$$
−0.995652 + 0.0931493i $$0.970307\pi$$
$$462$$ 0 0
$$463$$ −24.0000 −1.11537 −0.557687 0.830051i $$-0.688311\pi$$
−0.557687 + 0.830051i $$0.688311\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 12.0000 + 24.0000i 0.556487 + 1.11297i
$$466$$ 24.0000i 1.11178i
$$467$$ 18.0000i 0.832941i −0.909149 0.416470i $$-0.863267\pi$$
0.909149 0.416470i $$-0.136733\pi$$
$$468$$ 3.00000 + 2.00000i 0.138675 + 0.0924500i
$$469$$ 0 0
$$470$$ −8.00000 16.0000i −0.369012 0.738025i
$$471$$ −24.0000 −1.10586
$$472$$ 6.00000i 0.276172i
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ −24.0000 18.0000i −1.10120 0.825897i
$$476$$ 0 0
$$477$$ 12.0000i 0.549442i
$$478$$ 10.0000i 0.457389i
$$479$$ 22.0000i 1.00521i −0.864517 0.502603i $$-0.832376\pi$$
0.864517 0.502603i $$-0.167624\pi$$
$$480$$ 20.0000 10.0000i 0.912871 0.456435i
$$481$$ 18.0000 + 12.0000i 0.820729 + 0.547153i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ 6.00000 + 12.0000i 0.272446 + 0.544892i
$$486$$ 10.0000i 0.453609i
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 18.0000 0.814822
$$489$$ 24.0000i 1.08532i
$$490$$ −7.00000 14.0000i −0.316228 0.632456i
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ −16.0000 −0.721336
$$493$$ 0 0
$$494$$ 12.0000 18.0000i 0.539906 0.809858i
$$495$$ 4.00000 2.00000i 0.179787 0.0898933i
$$496$$ 6.00000i 0.269408i
$$497$$ 0 0
$$498$$ 8.00000i 0.358489i
$$499$$ 6.00000i 0.268597i 0.990941 + 0.134298i $$0.0428781\pi$$
−0.990941 + 0.134298i $$0.957122\pi$$
$$500$$ −11.0000 2.00000i −0.491935 0.0894427i
$$501$$ 32.0000i 1.42965i
$$502$$ −12.0000 −0.535586
$$503$$ 6.00000i 0.267527i −0.991013 0.133763i $$-0.957294\pi$$
0.991013 0.133763i $$-0.0427062\pi$$
$$504$$ 0 0
$$505$$ −6.00000 12.0000i −0.266996 0.533993i
$$506$$ 12.0000 0.533465
$$507$$ 24.0000 10.0000i 1.06588 0.444116i
$$508$$ 2.00000i 0.0887357i
$$509$$ 20.0000i 0.886484i 0.896402 + 0.443242i $$0.146172\pi$$
−0.896402 + 0.443242i $$0.853828\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 11.0000 0.486136
$$513$$ 24.0000 1.05963
$$514$$ 0 0
$$515$$ −12.0000 + 6.00000i −0.528783 + 0.264392i
$$516$$ −12.0000 −0.528271
$$517$$ 16.0000i 0.703679i
$$518$$ 0 0
$$519$$ −24.0000 −1.05348
$$520$$ 3.00000 24.0000i 0.131559 1.05247i
$$521$$ −30.0000 −1.31432 −0.657162 0.753749i $$-0.728243\pi$$
−0.657162 + 0.753749i $$0.728243\pi$$
$$522$$ 6.00000 0.262613
$$523$$ 42.0000i 1.83653i −0.395964 0.918266i $$-0.629590\pi$$
0.395964 0.918266i $$-0.370410\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 6.00000i 0.261612i
$$527$$ 0 0
$$528$$ 4.00000 0.174078
$$529$$ −13.0000 −0.565217
$$530$$ −24.0000 + 12.0000i −1.04249 + 0.521247i
$$531$$ 2.00000i 0.0867926i
$$532$$ 0 0
$$533$$ −16.0000 + 24.0000i −0.693037 + 1.03956i
$$534$$ −16.0000 −0.692388
$$535$$ 12.0000 6.00000i 0.518805 0.259403i
$$536$$ 36.0000 1.55496
$$537$$ 24.0000i 1.03568i
$$538$$ 18.0000 0.776035
$$539$$ 14.0000i 0.603023i
$$540$$ 8.00000 4.00000i 0.344265 0.172133i
$$541$$ 12.0000i 0.515920i −0.966156 0.257960i $$-0.916950\pi$$
0.966156 0.257960i $$-0.0830503\pi$$
$$542$$ 6.00000i 0.257722i
$$543$$ 4.00000i 0.171656i
$$544$$ 0 0
$$545$$ −24.0000 + 12.0000i −1.02805 + 0.514024i
$$546$$ 0 0
$$547$$ 18.0000i 0.769624i −0.922995 0.384812i $$-0.874266\pi$$
0.922995 0.384812i $$-0.125734\pi$$
$$548$$ −2.00000 −0.0854358
$$549$$ −6.00000 −0.256074
$$550$$ −8.00000 6.00000i −0.341121 0.255841i
$$551$$ 36.0000i 1.53365i
$$552$$ −36.0000 −1.53226
$$553$$ 0 0
$$554$$ 12.0000i 0.509831i
$$555$$ −24.0000 + 12.0000i −1.01874 + 0.509372i
$$556$$ 4.00000 0.169638
$$557$$ 14.0000 0.593199 0.296600 0.955002i $$-0.404147\pi$$
0.296600 + 0.955002i $$0.404147\pi$$
$$558$$ 6.00000i 0.254000i
$$559$$ −12.0000 + 18.0000i −0.507546 + 0.761319i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 8.00000i 0.337460i
$$563$$ 30.0000i 1.26435i 0.774826 + 0.632175i $$0.217837\pi$$
−0.774826 + 0.632175i $$0.782163\pi$$
$$564$$ 16.0000i 0.673722i
$$565$$ 0 0
$$566$$ 22.0000i 0.924729i
$$567$$ 0 0
$$568$$ 6.00000i 0.251754i
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 12.0000 + 24.0000i 0.502625 + 1.00525i
$$571$$ 12.0000 0.502184 0.251092 0.967963i $$-0.419210\pi$$
0.251092 + 0.967963i $$0.419210\pi$$
$$572$$ −4.00000 + 6.00000i −0.167248 + 0.250873i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 24.0000 + 18.0000i 1.00087 + 0.750652i
$$576$$ −7.00000 −0.291667
$$577$$ 18.0000 0.749350 0.374675 0.927156i $$-0.377754\pi$$
0.374675 + 0.927156i $$0.377754\pi$$
$$578$$ −17.0000 −0.707107
$$579$$ 12.0000i 0.498703i
$$580$$ 6.00000 + 12.0000i 0.249136 + 0.498273i
$$581$$ 0 0
$$582$$ 12.0000i 0.497416i
$$583$$ 24.0000 0.993978
$$584$$ −18.0000 −0.744845
$$585$$ −1.00000 + 8.00000i −0.0413449 + 0.330759i
$$586$$ 26.0000 1.07405
$$587$$ 20.0000 0.825488 0.412744 0.910847i $$-0.364570\pi$$
0.412744 + 0.910847i $$0.364570\pi$$
$$588$$ 14.0000i 0.577350i
$$589$$ 36.0000 1.48335
$$590$$ 4.00000 2.00000i 0.164677 0.0823387i
$$591$$ 4.00000i 0.164538i
$$592$$ −6.00000 −0.246598
$$593$$ −22.0000 −0.903432 −0.451716 0.892162i $$-0.649188\pi$$
−0.451716 + 0.892162i $$0.649188\pi$$
$$594$$ 8.00000 0.328244
$$595$$ 0 0
$$596$$ 20.0000i 0.819232i
$$597$$ 48.0000i 1.96451i
$$598$$ −12.0000 + 18.0000i −0.490716 + 0.736075i
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 24.0000 + 18.0000i 0.979796 + 0.734847i
$$601$$ −6.00000 −0.244745 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$602$$ 0 0
$$603$$ −12.0000 −0.488678
$$604$$ 18.0000i 0.732410i
$$605$$ −7.00000 14.0000i −0.284590 0.569181i
$$606$$ 12.0000i 0.487467i
$$607$$ 18.0000i 0.730597i 0.930890 + 0.365299i $$0.119033\pi$$
−0.930890 + 0.365299i $$0.880967\pi$$
$$608$$ 30.0000i 1.21666i
$$609$$ 0 0
$$610$$ 6.00000 + 12.0000i 0.242933 + 0.485866i
$$611$$ −24.0000 16.0000i −0.970936 0.647291i
$$612$$ 0 0
$$613$$ 30.0000 1.21169 0.605844 0.795583i $$-0.292835\pi$$
0.605844 + 0.795583i $$0.292835\pi$$
$$614$$ −12.0000 −0.484281
$$615$$ −16.0000 32.0000i −0.645182 1.29036i
$$616$$ 0 0
$$617$$ 34.0000 1.36879 0.684394 0.729112i $$-0.260067\pi$$
0.684394 + 0.729112i $$0.260067\pi$$
$$618$$ 12.0000 0.482711
$$619$$ 18.0000i 0.723481i −0.932279 0.361741i $$-0.882183\pi$$
0.932279 0.361741i $$-0.117817\pi$$
$$620$$ 12.0000 6.00000i 0.481932 0.240966i
$$621$$ −24.0000 −0.963087
$$622$$ −24.0000 −0.962312
$$623$$ 0 0
$$624$$ −4.00000 + 6.00000i −0.160128 + 0.240192i
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 8.00000i 0.319744i
$$627$$ 24.0000i 0.958468i
$$628$$ 12.0000i 0.478852i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 30.0000i 1.19428i −0.802137 0.597141i $$-0.796303\pi$$
0.802137 0.597141i $$-0.203697\pi$$
$$632$$ 0 0
$$633$$ 24.0000i 0.953914i
$$634$$ 2.00000 0.0794301
$$635$$ 4.00000 2.00000i 0.158735 0.0793676i
$$636$$ −24.0000 −0.951662
$$637$$ −21.0000 14.0000i −0.832050 0.554700i
$$638$$ 12.0000i 0.475085i
$$639$$ 2.00000i 0.0791188i
$$640$$ −3.00000 6.00000i −0.118585 0.237171i
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ −12.0000 −0.473602
$$643$$ −36.0000 −1.41970 −0.709851 0.704352i $$-0.751238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$644$$ 0 0
$$645$$ −12.0000 24.0000i −0.472500 0.944999i
$$646$$ 0 0
$$647$$ 6.00000i 0.235884i −0.993020 0.117942i $$-0.962370\pi$$
0.993020 0.117942i $$-0.0376297\pi$$
$$648$$ −33.0000 −1.29636
$$649$$ −4.00000 −0.157014
$$650$$ 17.0000 6.00000i 0.666795 0.235339i
$$651$$ 0 0
$$652$$ −12.0000 −0.469956
$$653$$ 36.0000i 1.40879i 0.709809 + 0.704394i $$0.248781\pi$$
−0.709809 + 0.704394i $$0.751219\pi$$
$$654$$ 24.0000 0.938474
$$655$$ 12.0000 + 24.0000i 0.468879 + 0.937758i
$$656$$ 8.00000i 0.312348i
$$657$$ 6.00000 0.234082
$$658$$ 0 0
$$659$$ 36.0000 1.40236 0.701180 0.712984i $$-0.252657\pi$$
0.701180 + 0.712984i $$0.252657\pi$$
$$660$$ −4.00000 8.00000i −0.155700 0.311400i
$$661$$ 12.0000i 0.466746i 0.972387 + 0.233373i $$0.0749763\pi$$
−0.972387 + 0.233373i $$0.925024\pi$$
$$662$$ 30.0000i 1.16598i
$$663$$ 0 0
$$664$$ −12.0000 −0.465690
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ 36.0000i 1.39393i
$$668$$ 16.0000 0.619059
$$669$$ 48.0000i 1.85579i
$$670$$ 12.0000 + 24.0000i 0.463600 + 0.927201i
$$671$$ 12.0000i 0.463255i
$$672$$ 0 0
$$673$$ 48.0000i 1.85026i −0.379646 0.925132i $$-0.623954\pi$$
0.379646 0.925132i $$-0.376046\pi$$
$$674$$ 32.0000i 1.23259i
$$675$$ 16.0000 + 12.0000i 0.615840 + 0.461880i
$$676$$ −5.00000 12.0000i −0.192308 0.461538i
$$677$$ 36.0000i 1.38359i −0.722093 0.691796i $$-0.756820\pi$$
0.722093 0.691796i $$-0.243180\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 8.00000i 0.306561i
$$682$$ 12.0000 0.459504
$$683$$ −44.0000 −1.68361 −0.841807 0.539779i $$-0.818508\pi$$
−0.841807 + 0.539779i $$0.818508\pi$$
$$684$$ 6.00000i 0.229416i
$$685$$ −2.00000 4.00000i −0.0764161 0.152832i
$$686$$ 0 0
$$687$$ 24.0000 0.915657
$$688$$ 6.00000i 0.228748i
$$689$$ −24.0000 + 36.0000i −0.914327 + 1.37149i
$$690$$ −12.0000 24.0000i −0.456832 0.913664i
$$691$$ 42.0000i 1.59776i −0.601494 0.798878i $$-0.705427\pi$$
0.601494 0.798878i $$-0.294573\pi$$
$$692$$ 12.0000i 0.456172i
$$693$$ 0 0
$$694$$ 6.00000i 0.227757i
$$695$$ 4.00000 + 8.00000i 0.151729 + 0.303457i
$$696$$ 36.0000i 1.36458i
$$697$$ 0 0
$$698$$ 12.0000i 0.454207i
$$699$$ 48.0000 1.81553
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ −8.00000 + 12.0000i −0.301941 + 0.452911i
$$703$$ 36.0000i 1.35777i
$$704$$ 14.0000i 0.527645i
$$705$$ 32.0000 16.0000i 1.20519 0.602595i
$$706$$ 14.0000 0.526897
$$707$$ 0 0
$$708$$ 4.00000 0.150329
$$709$$ 12.0000i 0.450669i 0.974281 + 0.225335i $$0.0723476\pi$$
−0.974281 + 0.225335i $$0.927652\pi$$
$$710$$ −4.00000 + 2.00000i −0.150117 + 0.0750587i
$$711$$ 0 0
$$712$$ 24.0000i 0.899438i
$$713$$ −36.0000 −1.34821
$$714$$ 0 0
$$715$$ −16.0000 2.00000i −0.598366 0.0747958i
$$716$$ 12.0000 0.448461
$$717$$ 20.0000 0.746914
$$718$$ 2.00000i 0.0746393i
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ −1.00000 2.00000i −0.0372678 0.0745356i
$$721$$ 0 0
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ 2.00000 0.0743294
$$725$$ −18.0000 + 24.0000i −0.668503 + 0.891338i
$$726$$ 14.0000i 0.519589i
$$727$$ 26.0000i 0.964287i 0.876092 + 0.482143i $$0.160142\pi$$
−0.876092 + 0.482143i $$0.839858\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ −6.00000 12.0000i −0.222070 0.444140i
$$731$$ 0 0
$$732$$ 12.0000i 0.443533i
$$733$$ −42.0000 −1.55131 −0.775653 0.631160i $$-0.782579\pi$$
−0.775653 + 0.631160i $$0.782579\pi$$
$$734$$ 18.0000i 0.664392i
$$735$$ 28.0000 14.0000i 1.03280 0.516398i
$$736$$ 30.0000i 1.10581i
$$737$$ 24.0000i 0.884051i
$$738$$ 8.00000i 0.294484i
$$739$$ 6.00000i 0.220714i 0.993892 + 0.110357i $$0.0351994\pi$$
−0.993892 + 0.110357i $$0.964801\pi$$
$$740$$ 6.00000 + 12.0000i 0.220564 + 0.441129i
$$741$$ 36.0000 + 24.0000i 1.32249 + 0.881662i
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ −36.0000 −1.31982
$$745$$ −40.0000 + 20.0000i −1.46549 + 0.732743i
$$746$$ 4.00000i 0.146450i
$$747$$ 4.00000 0.146352
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −4.00000 + 22.0000i −0.146059 + 0.803326i
$$751$$ −32.0000 −1.16770 −0.583848 0.811863i $$-0.698454\pi$$
−0.583848 + 0.811863i $$0.698454\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 24.0000i 0.874609i
$$754$$ −18.0000 12.0000i −0.655521 0.437014i
$$755$$ 36.0000 18.0000i 1.31017 0.655087i
$$756$$ 0 0
$$757$$ 20.0000i 0.726912i −0.931611 0.363456i $$-0.881597\pi$$
0.931611 0.363456i $$-0.118403\pi$$
$$758$$ 18.0000i 0.653789i
$$759$$ 24.0000i 0.871145i
$$760$$ 36.0000 18.0000i 1.30586 0.652929i
$$761$$ 40.0000i 1.45000i 0.688749 + 0.724999i $$0.258160\pi$$
−0.688749 + 0.724999i $$0.741840\pi$$
$$762$$ −4.00000 −0.144905
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −8.00000 −0.289052
$$767$$ 4.00000 6.00000i 0.144432 0.216647i
$$768$$ 34.0000i 1.22687i
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 6.00000 0.215945
$$773$$ 38.0000 1.36677 0.683383 0.730061i $$-0.260508\pi$$
0.683383 + 0.730061i $$0.260508\pi$$
$$774$$ 6.00000i 0.215666i
$$775$$ 24.0000 + 18.0000i 0.862105 + 0.646579i
$$776$$ −18.0000 −0.646162
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ −48.0000 −1.71978
$$780$$ 16.0000 + 2.00000i 0.572892 + 0.0716115i
$$781$$ 4.00000 0.143131
$$782$$ 0 0
$$783$$ 24.0000i 0.857690i
$$784$$ 7.00000 0.250000
$$785$$ −24.0000 + 12.0000i −0.856597 + 0.428298i
$$786$$ 24.0000i 0.856052i
$$787$$ 12.0000 0.427754 0.213877 0.976861i $$-0.431391\pi$$
0.213877 + 0.976861i $$0.431391\pi$$
$$788$$ 2.00000 0.0712470
$$789$$ −12.0000 −0.427211
$$790$$ 0