Properties

 Label 170.2.d.a.169.2 Level 170 Weight 2 Character 170.169 Analytic conductor 1.357 Analytic rank 0 Dimension 2 CM no Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$170 = 2 \cdot 5 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 170.d (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$1.35745683436$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 169.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 170.169 Dual form 170.2.d.a.169.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -1.00000i q^{6} -2.00000 q^{7} -1.00000i q^{8} -2.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -1.00000i q^{6} -2.00000 q^{7} -1.00000i q^{8} -2.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} +1.00000 q^{12} +1.00000i q^{13} -2.00000i q^{14} +(2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -2.00000i q^{18} -5.00000 q^{19} +(2.00000 - 1.00000i) q^{20} +2.00000 q^{21} +4.00000 q^{23} +1.00000i q^{24} +(3.00000 - 4.00000i) q^{25} -1.00000 q^{26} +5.00000 q^{27} +2.00000 q^{28} +9.00000i q^{29} +(1.00000 + 2.00000i) q^{30} -5.00000i q^{31} +1.00000i q^{32} +(-4.00000 - 1.00000i) q^{34} +(4.00000 - 2.00000i) q^{35} +2.00000 q^{36} -2.00000 q^{37} -5.00000i q^{38} -1.00000i q^{39} +(1.00000 + 2.00000i) q^{40} +10.0000i q^{41} +2.00000i q^{42} +6.00000i q^{43} +(4.00000 - 2.00000i) q^{45} +4.00000i q^{46} -7.00000i q^{47} -1.00000 q^{48} -3.00000 q^{49} +(4.00000 + 3.00000i) q^{50} +(1.00000 - 4.00000i) q^{51} -1.00000i q^{52} +1.00000i q^{53} +5.00000i q^{54} +2.00000i q^{56} +5.00000 q^{57} -9.00000 q^{58} -5.00000 q^{59} +(-2.00000 + 1.00000i) q^{60} -5.00000i q^{61} +5.00000 q^{62} +4.00000 q^{63} -1.00000 q^{64} +(-1.00000 - 2.00000i) q^{65} -2.00000i q^{67} +(1.00000 - 4.00000i) q^{68} -4.00000 q^{69} +(2.00000 + 4.00000i) q^{70} -5.00000i q^{71} +2.00000i q^{72} -11.0000 q^{73} -2.00000i q^{74} +(-3.00000 + 4.00000i) q^{75} +5.00000 q^{76} +1.00000 q^{78} -16.0000i q^{79} +(-2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -10.0000 q^{82} +6.00000i q^{83} -2.00000 q^{84} +(-2.00000 - 9.00000i) q^{85} -6.00000 q^{86} -9.00000i q^{87} +5.00000 q^{89} +(2.00000 + 4.00000i) q^{90} -2.00000i q^{91} -4.00000 q^{92} +5.00000i q^{93} +7.00000 q^{94} +(10.0000 - 5.00000i) q^{95} -1.00000i q^{96} -7.00000 q^{97} -3.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{7} - 4q^{9} + O(q^{10})$$ $$2q - 2q^{3} - 2q^{4} - 4q^{5} - 4q^{7} - 4q^{9} - 2q^{10} + 2q^{12} + 4q^{15} + 2q^{16} - 2q^{17} - 10q^{19} + 4q^{20} + 4q^{21} + 8q^{23} + 6q^{25} - 2q^{26} + 10q^{27} + 4q^{28} + 2q^{30} - 8q^{34} + 8q^{35} + 4q^{36} - 4q^{37} + 2q^{40} + 8q^{45} - 2q^{48} - 6q^{49} + 8q^{50} + 2q^{51} + 10q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{62} + 8q^{63} - 2q^{64} - 2q^{65} + 2q^{68} - 8q^{69} + 4q^{70} - 22q^{73} - 6q^{75} + 10q^{76} + 2q^{78} - 4q^{80} + 2q^{81} - 20q^{82} - 4q^{84} - 4q^{85} - 12q^{86} + 10q^{89} + 4q^{90} - 8q^{92} + 14q^{94} + 20q^{95} - 14q^{97} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$$.

 $$n$$ $$71$$ $$137$$ $$\chi(n)$$ $$-1$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ −1.00000 −0.577350 −0.288675 0.957427i $$-0.593215\pi$$
−0.288675 + 0.957427i $$0.593215\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −2.00000 + 1.00000i −0.894427 + 0.447214i
$$6$$ 1.00000i 0.408248i
$$7$$ −2.00000 −0.755929 −0.377964 0.925820i $$-0.623376\pi$$
−0.377964 + 0.925820i $$0.623376\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −2.00000 −0.666667
$$10$$ −1.00000 2.00000i −0.316228 0.632456i
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 1.00000i 0.277350i 0.990338 + 0.138675i $$0.0442844\pi$$
−0.990338 + 0.138675i $$0.955716\pi$$
$$14$$ 2.00000i 0.534522i
$$15$$ 2.00000 1.00000i 0.516398 0.258199i
$$16$$ 1.00000 0.250000
$$17$$ −1.00000 + 4.00000i −0.242536 + 0.970143i
$$18$$ 2.00000i 0.471405i
$$19$$ −5.00000 −1.14708 −0.573539 0.819178i $$-0.694430\pi$$
−0.573539 + 0.819178i $$0.694430\pi$$
$$20$$ 2.00000 1.00000i 0.447214 0.223607i
$$21$$ 2.00000 0.436436
$$22$$ 0 0
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ −1.00000 −0.196116
$$27$$ 5.00000 0.962250
$$28$$ 2.00000 0.377964
$$29$$ 9.00000i 1.67126i 0.549294 + 0.835629i $$0.314897\pi$$
−0.549294 + 0.835629i $$0.685103\pi$$
$$30$$ 1.00000 + 2.00000i 0.182574 + 0.365148i
$$31$$ 5.00000i 0.898027i −0.893525 0.449013i $$-0.851776\pi$$
0.893525 0.449013i $$-0.148224\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ −4.00000 1.00000i −0.685994 0.171499i
$$35$$ 4.00000 2.00000i 0.676123 0.338062i
$$36$$ 2.00000 0.333333
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ 5.00000i 0.811107i
$$39$$ 1.00000i 0.160128i
$$40$$ 1.00000 + 2.00000i 0.158114 + 0.316228i
$$41$$ 10.0000i 1.56174i 0.624695 + 0.780869i $$0.285223\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 2.00000i 0.308607i
$$43$$ 6.00000i 0.914991i 0.889212 + 0.457496i $$0.151253\pi$$
−0.889212 + 0.457496i $$0.848747\pi$$
$$44$$ 0 0
$$45$$ 4.00000 2.00000i 0.596285 0.298142i
$$46$$ 4.00000i 0.589768i
$$47$$ 7.00000i 1.02105i −0.859861 0.510527i $$-0.829450\pi$$
0.859861 0.510527i $$-0.170550\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −3.00000 −0.428571
$$50$$ 4.00000 + 3.00000i 0.565685 + 0.424264i
$$51$$ 1.00000 4.00000i 0.140028 0.560112i
$$52$$ 1.00000i 0.138675i
$$53$$ 1.00000i 0.137361i 0.997639 + 0.0686803i $$0.0218788\pi$$
−0.997639 + 0.0686803i $$0.978121\pi$$
$$54$$ 5.00000i 0.680414i
$$55$$ 0 0
$$56$$ 2.00000i 0.267261i
$$57$$ 5.00000 0.662266
$$58$$ −9.00000 −1.18176
$$59$$ −5.00000 −0.650945 −0.325472 0.945552i $$-0.605523\pi$$
−0.325472 + 0.945552i $$0.605523\pi$$
$$60$$ −2.00000 + 1.00000i −0.258199 + 0.129099i
$$61$$ 5.00000i 0.640184i −0.947386 0.320092i $$-0.896286\pi$$
0.947386 0.320092i $$-0.103714\pi$$
$$62$$ 5.00000 0.635001
$$63$$ 4.00000 0.503953
$$64$$ −1.00000 −0.125000
$$65$$ −1.00000 2.00000i −0.124035 0.248069i
$$66$$ 0 0
$$67$$ 2.00000i 0.244339i −0.992509 0.122169i $$-0.961015\pi$$
0.992509 0.122169i $$-0.0389851\pi$$
$$68$$ 1.00000 4.00000i 0.121268 0.485071i
$$69$$ −4.00000 −0.481543
$$70$$ 2.00000 + 4.00000i 0.239046 + 0.478091i
$$71$$ 5.00000i 0.593391i −0.954972 0.296695i $$-0.904115\pi$$
0.954972 0.296695i $$-0.0958846\pi$$
$$72$$ 2.00000i 0.235702i
$$73$$ −11.0000 −1.28745 −0.643726 0.765256i $$-0.722612\pi$$
−0.643726 + 0.765256i $$0.722612\pi$$
$$74$$ 2.00000i 0.232495i
$$75$$ −3.00000 + 4.00000i −0.346410 + 0.461880i
$$76$$ 5.00000 0.573539
$$77$$ 0 0
$$78$$ 1.00000 0.113228
$$79$$ 16.0000i 1.80014i −0.435745 0.900070i $$-0.643515\pi$$
0.435745 0.900070i $$-0.356485\pi$$
$$80$$ −2.00000 + 1.00000i −0.223607 + 0.111803i
$$81$$ 1.00000 0.111111
$$82$$ −10.0000 −1.10432
$$83$$ 6.00000i 0.658586i 0.944228 + 0.329293i $$0.106810\pi$$
−0.944228 + 0.329293i $$0.893190\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ −2.00000 9.00000i −0.216930 0.976187i
$$86$$ −6.00000 −0.646997
$$87$$ 9.00000i 0.964901i
$$88$$ 0 0
$$89$$ 5.00000 0.529999 0.264999 0.964249i $$-0.414628\pi$$
0.264999 + 0.964249i $$0.414628\pi$$
$$90$$ 2.00000 + 4.00000i 0.210819 + 0.421637i
$$91$$ 2.00000i 0.209657i
$$92$$ −4.00000 −0.417029
$$93$$ 5.00000i 0.518476i
$$94$$ 7.00000 0.721995
$$95$$ 10.0000 5.00000i 1.02598 0.512989i
$$96$$ 1.00000i 0.102062i
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ 3.00000i 0.303046i
$$99$$ 0 0
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ −8.00000 −0.796030 −0.398015 0.917379i $$-0.630301\pi$$
−0.398015 + 0.917379i $$0.630301\pi$$
$$102$$ 4.00000 + 1.00000i 0.396059 + 0.0990148i
$$103$$ 16.0000i 1.57653i 0.615338 + 0.788263i $$0.289020\pi$$
−0.615338 + 0.788263i $$0.710980\pi$$
$$104$$ 1.00000 0.0980581
$$105$$ −4.00000 + 2.00000i −0.390360 + 0.195180i
$$106$$ −1.00000 −0.0971286
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −5.00000 −0.481125
$$109$$ 9.00000i 0.862044i 0.902342 + 0.431022i $$0.141847\pi$$
−0.902342 + 0.431022i $$0.858153\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ −2.00000 −0.188982
$$113$$ 9.00000 0.846649 0.423324 0.905978i $$-0.360863\pi$$
0.423324 + 0.905978i $$0.360863\pi$$
$$114$$ 5.00000i 0.468293i
$$115$$ −8.00000 + 4.00000i −0.746004 + 0.373002i
$$116$$ 9.00000i 0.835629i
$$117$$ 2.00000i 0.184900i
$$118$$ 5.00000i 0.460287i
$$119$$ 2.00000 8.00000i 0.183340 0.733359i
$$120$$ −1.00000 2.00000i −0.0912871 0.182574i
$$121$$ 11.0000 1.00000
$$122$$ 5.00000 0.452679
$$123$$ 10.0000i 0.901670i
$$124$$ 5.00000i 0.449013i
$$125$$ −2.00000 + 11.0000i −0.178885 + 0.983870i
$$126$$ 4.00000i 0.356348i
$$127$$ 7.00000i 0.621150i −0.950549 0.310575i $$-0.899478\pi$$
0.950549 0.310575i $$-0.100522\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 6.00000i 0.528271i
$$130$$ 2.00000 1.00000i 0.175412 0.0877058i
$$131$$ 20.0000i 1.74741i 0.486458 + 0.873704i $$0.338289\pi$$
−0.486458 + 0.873704i $$0.661711\pi$$
$$132$$ 0 0
$$133$$ 10.0000 0.867110
$$134$$ 2.00000 0.172774
$$135$$ −10.0000 + 5.00000i −0.860663 + 0.430331i
$$136$$ 4.00000 + 1.00000i 0.342997 + 0.0857493i
$$137$$ 2.00000i 0.170872i −0.996344 0.0854358i $$-0.972772\pi$$
0.996344 0.0854358i $$-0.0272282\pi$$
$$138$$ 4.00000i 0.340503i
$$139$$ 14.0000i 1.18746i 0.804663 + 0.593732i $$0.202346\pi$$
−0.804663 + 0.593732i $$0.797654\pi$$
$$140$$ −4.00000 + 2.00000i −0.338062 + 0.169031i
$$141$$ 7.00000i 0.589506i
$$142$$ 5.00000 0.419591
$$143$$ 0 0
$$144$$ −2.00000 −0.166667
$$145$$ −9.00000 18.0000i −0.747409 1.49482i
$$146$$ 11.0000i 0.910366i
$$147$$ 3.00000 0.247436
$$148$$ 2.00000 0.164399
$$149$$ 20.0000 1.63846 0.819232 0.573462i $$-0.194400\pi$$
0.819232 + 0.573462i $$0.194400\pi$$
$$150$$ −4.00000 3.00000i −0.326599 0.244949i
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 5.00000i 0.405554i
$$153$$ 2.00000 8.00000i 0.161690 0.646762i
$$154$$ 0 0
$$155$$ 5.00000 + 10.0000i 0.401610 + 0.803219i
$$156$$ 1.00000i 0.0800641i
$$157$$ 18.0000i 1.43656i 0.695756 + 0.718278i $$0.255069\pi$$
−0.695756 + 0.718278i $$0.744931\pi$$
$$158$$ 16.0000 1.27289
$$159$$ 1.00000i 0.0793052i
$$160$$ −1.00000 2.00000i −0.0790569 0.158114i
$$161$$ −8.00000 −0.630488
$$162$$ 1.00000i 0.0785674i
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 10.0000i 0.780869i
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ 18.0000 1.39288 0.696441 0.717614i $$-0.254766\pi$$
0.696441 + 0.717614i $$0.254766\pi$$
$$168$$ 2.00000i 0.154303i
$$169$$ 12.0000 0.923077
$$170$$ 9.00000 2.00000i 0.690268 0.153393i
$$171$$ 10.0000 0.764719
$$172$$ 6.00000i 0.457496i
$$173$$ −16.0000 −1.21646 −0.608229 0.793762i $$-0.708120\pi$$
−0.608229 + 0.793762i $$0.708120\pi$$
$$174$$ 9.00000 0.682288
$$175$$ −6.00000 + 8.00000i −0.453557 + 0.604743i
$$176$$ 0 0
$$177$$ 5.00000 0.375823
$$178$$ 5.00000i 0.374766i
$$179$$ 20.0000 1.49487 0.747435 0.664335i $$-0.231285\pi$$
0.747435 + 0.664335i $$0.231285\pi$$
$$180$$ −4.00000 + 2.00000i −0.298142 + 0.149071i
$$181$$ 10.0000i 0.743294i −0.928374 0.371647i $$-0.878793\pi$$
0.928374 0.371647i $$-0.121207\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 5.00000i 0.369611i
$$184$$ 4.00000i 0.294884i
$$185$$ 4.00000 2.00000i 0.294086 0.147043i
$$186$$ −5.00000 −0.366618
$$187$$ 0 0
$$188$$ 7.00000i 0.510527i
$$189$$ −10.0000 −0.727393
$$190$$ 5.00000 + 10.0000i 0.362738 + 0.725476i
$$191$$ −18.0000 −1.30243 −0.651217 0.758891i $$-0.725741\pi$$
−0.651217 + 0.758891i $$0.725741\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 14.0000 1.00774 0.503871 0.863779i $$-0.331909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 7.00000i 0.502571i
$$195$$ 1.00000 + 2.00000i 0.0716115 + 0.143223i
$$196$$ 3.00000 0.214286
$$197$$ 8.00000 0.569976 0.284988 0.958531i $$-0.408010\pi$$
0.284988 + 0.958531i $$0.408010\pi$$
$$198$$ 0 0
$$199$$ 1.00000i 0.0708881i −0.999372 0.0354441i $$-0.988715\pi$$
0.999372 0.0354441i $$-0.0112846\pi$$
$$200$$ −4.00000 3.00000i −0.282843 0.212132i
$$201$$ 2.00000i 0.141069i
$$202$$ 8.00000i 0.562878i
$$203$$ 18.0000i 1.26335i
$$204$$ −1.00000 + 4.00000i −0.0700140 + 0.280056i
$$205$$ −10.0000 20.0000i −0.698430 1.39686i
$$206$$ −16.0000 −1.11477
$$207$$ −8.00000 −0.556038
$$208$$ 1.00000i 0.0693375i
$$209$$ 0 0
$$210$$ −2.00000 4.00000i −0.138013 0.276026i
$$211$$ 20.0000i 1.37686i 0.725304 + 0.688428i $$0.241699\pi$$
−0.725304 + 0.688428i $$0.758301\pi$$
$$212$$ 1.00000i 0.0686803i
$$213$$ 5.00000i 0.342594i
$$214$$ 12.0000i 0.820303i
$$215$$ −6.00000 12.0000i −0.409197 0.818393i
$$216$$ 5.00000i 0.340207i
$$217$$ 10.0000i 0.678844i
$$218$$ −9.00000 −0.609557
$$219$$ 11.0000 0.743311
$$220$$ 0 0
$$221$$ −4.00000 1.00000i −0.269069 0.0672673i
$$222$$ 2.00000i 0.134231i
$$223$$ 9.00000i 0.602685i −0.953516 0.301342i $$-0.902565\pi$$
0.953516 0.301342i $$-0.0974347\pi$$
$$224$$ 2.00000i 0.133631i
$$225$$ −6.00000 + 8.00000i −0.400000 + 0.533333i
$$226$$ 9.00000i 0.598671i
$$227$$ −27.0000 −1.79205 −0.896026 0.444001i $$-0.853559\pi$$
−0.896026 + 0.444001i $$0.853559\pi$$
$$228$$ −5.00000 −0.331133
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ −4.00000 8.00000i −0.263752 0.527504i
$$231$$ 0 0
$$232$$ 9.00000 0.590879
$$233$$ −21.0000 −1.37576 −0.687878 0.725826i $$-0.741458\pi$$
−0.687878 + 0.725826i $$0.741458\pi$$
$$234$$ 2.00000 0.130744
$$235$$ 7.00000 + 14.0000i 0.456630 + 0.913259i
$$236$$ 5.00000 0.325472
$$237$$ 16.0000i 1.03931i
$$238$$ 8.00000 + 2.00000i 0.518563 + 0.129641i
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 2.00000 1.00000i 0.129099 0.0645497i
$$241$$ 10.0000i 0.644157i −0.946713 0.322078i $$-0.895619\pi$$
0.946713 0.322078i $$-0.104381\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ −16.0000 −1.02640
$$244$$ 5.00000i 0.320092i
$$245$$ 6.00000 3.00000i 0.383326 0.191663i
$$246$$ 10.0000 0.637577
$$247$$ 5.00000i 0.318142i
$$248$$ −5.00000 −0.317500
$$249$$ 6.00000i 0.380235i
$$250$$ −11.0000 2.00000i −0.695701 0.126491i
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ −4.00000 −0.251976
$$253$$ 0 0
$$254$$ 7.00000 0.439219
$$255$$ 2.00000 + 9.00000i 0.125245 + 0.563602i
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000i 1.12281i 0.827541 + 0.561405i $$0.189739\pi$$
−0.827541 + 0.561405i $$0.810261\pi$$
$$258$$ 6.00000 0.373544
$$259$$ 4.00000 0.248548
$$260$$ 1.00000 + 2.00000i 0.0620174 + 0.124035i
$$261$$ 18.0000i 1.11417i
$$262$$ −20.0000 −1.23560
$$263$$ 21.0000i 1.29492i 0.762101 + 0.647458i $$0.224168\pi$$
−0.762101 + 0.647458i $$0.775832\pi$$
$$264$$ 0 0
$$265$$ −1.00000 2.00000i −0.0614295 0.122859i
$$266$$ 10.0000i 0.613139i
$$267$$ −5.00000 −0.305995
$$268$$ 2.00000i 0.122169i
$$269$$ 1.00000i 0.0609711i −0.999535 0.0304855i $$-0.990295\pi$$
0.999535 0.0304855i $$-0.00970535\pi$$
$$270$$ −5.00000 10.0000i −0.304290 0.608581i
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ −1.00000 + 4.00000i −0.0606339 + 0.242536i
$$273$$ 2.00000i 0.121046i
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ 4.00000 0.240772
$$277$$ 18.0000 1.08152 0.540758 0.841178i $$-0.318138\pi$$
0.540758 + 0.841178i $$0.318138\pi$$
$$278$$ −14.0000 −0.839664
$$279$$ 10.0000i 0.598684i
$$280$$ −2.00000 4.00000i −0.119523 0.239046i
$$281$$ −23.0000 −1.37206 −0.686032 0.727571i $$-0.740649\pi$$
−0.686032 + 0.727571i $$0.740649\pi$$
$$282$$ −7.00000 −0.416844
$$283$$ −21.0000 −1.24832 −0.624160 0.781296i $$-0.714559\pi$$
−0.624160 + 0.781296i $$0.714559\pi$$
$$284$$ 5.00000i 0.296695i
$$285$$ −10.0000 + 5.00000i −0.592349 + 0.296174i
$$286$$ 0 0
$$287$$ 20.0000i 1.18056i
$$288$$ 2.00000i 0.117851i
$$289$$ −15.0000 8.00000i −0.882353 0.470588i
$$290$$ 18.0000 9.00000i 1.05700 0.528498i
$$291$$ 7.00000 0.410347
$$292$$ 11.0000 0.643726
$$293$$ 29.0000i 1.69420i −0.531435 0.847099i $$-0.678347\pi$$
0.531435 0.847099i $$-0.321653\pi$$
$$294$$ 3.00000i 0.174964i
$$295$$ 10.0000 5.00000i 0.582223 0.291111i
$$296$$ 2.00000i 0.116248i
$$297$$ 0 0
$$298$$ 20.0000i 1.15857i
$$299$$ 4.00000i 0.231326i
$$300$$ 3.00000 4.00000i 0.173205 0.230940i
$$301$$ 12.0000i 0.691669i
$$302$$ 8.00000i 0.460348i
$$303$$ 8.00000 0.459588
$$304$$ −5.00000 −0.286770
$$305$$ 5.00000 + 10.0000i 0.286299 + 0.572598i
$$306$$ 8.00000 + 2.00000i 0.457330 + 0.114332i
$$307$$ 2.00000i 0.114146i −0.998370 0.0570730i $$-0.981823\pi$$
0.998370 0.0570730i $$-0.0181768\pi$$
$$308$$ 0 0
$$309$$ 16.0000i 0.910208i
$$310$$ −10.0000 + 5.00000i −0.567962 + 0.283981i
$$311$$ 20.0000i 1.13410i −0.823685 0.567048i $$-0.808085\pi$$
0.823685 0.567048i $$-0.191915\pi$$
$$312$$ −1.00000 −0.0566139
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ −18.0000 −1.01580
$$315$$ −8.00000 + 4.00000i −0.450749 + 0.225374i
$$316$$ 16.0000i 0.900070i
$$317$$ −12.0000 −0.673987 −0.336994 0.941507i $$-0.609410\pi$$
−0.336994 + 0.941507i $$0.609410\pi$$
$$318$$ 1.00000 0.0560772
$$319$$ 0 0
$$320$$ 2.00000 1.00000i 0.111803 0.0559017i
$$321$$ 12.0000 0.669775
$$322$$ 8.00000i 0.445823i
$$323$$ 5.00000 20.0000i 0.278207 1.11283i
$$324$$ −1.00000 −0.0555556
$$325$$ 4.00000 + 3.00000i 0.221880 + 0.166410i
$$326$$ 4.00000i 0.221540i
$$327$$ 9.00000i 0.497701i
$$328$$ 10.0000 0.552158
$$329$$ 14.0000i 0.771845i
$$330$$ 0 0
$$331$$ 7.00000 0.384755 0.192377 0.981321i $$-0.438380\pi$$
0.192377 + 0.981321i $$0.438380\pi$$
$$332$$ 6.00000i 0.329293i
$$333$$ 4.00000 0.219199
$$334$$ 18.0000i 0.984916i
$$335$$ 2.00000 + 4.00000i 0.109272 + 0.218543i
$$336$$ 2.00000 0.109109
$$337$$ 23.0000 1.25289 0.626445 0.779466i $$-0.284509\pi$$
0.626445 + 0.779466i $$0.284509\pi$$
$$338$$ 12.0000i 0.652714i
$$339$$ −9.00000 −0.488813
$$340$$ 2.00000 + 9.00000i 0.108465 + 0.488094i
$$341$$ 0 0
$$342$$ 10.0000i 0.540738i
$$343$$ 20.0000 1.07990
$$344$$ 6.00000 0.323498
$$345$$ 8.00000 4.00000i 0.430706 0.215353i
$$346$$ 16.0000i 0.860165i
$$347$$ 23.0000 1.23470 0.617352 0.786687i $$-0.288205\pi$$
0.617352 + 0.786687i $$0.288205\pi$$
$$348$$ 9.00000i 0.482451i
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ −8.00000 6.00000i −0.427618 0.320713i
$$351$$ 5.00000i 0.266880i
$$352$$ 0 0
$$353$$ 4.00000i 0.212899i −0.994318 0.106449i $$-0.966052\pi$$
0.994318 0.106449i $$-0.0339482\pi$$
$$354$$ 5.00000i 0.265747i
$$355$$ 5.00000 + 10.0000i 0.265372 + 0.530745i
$$356$$ −5.00000 −0.264999
$$357$$ −2.00000 + 8.00000i −0.105851 + 0.423405i
$$358$$ 20.0000i 1.05703i
$$359$$ −30.0000 −1.58334 −0.791670 0.610949i $$-0.790788\pi$$
−0.791670 + 0.610949i $$0.790788\pi$$
$$360$$ −2.00000 4.00000i −0.105409 0.210819i
$$361$$ 6.00000 0.315789
$$362$$ 10.0000 0.525588
$$363$$ −11.0000 −0.577350
$$364$$ 2.00000i 0.104828i
$$365$$ 22.0000 11.0000i 1.15153 0.575766i
$$366$$ −5.00000 −0.261354
$$367$$ −2.00000 −0.104399 −0.0521996 0.998637i $$-0.516623\pi$$
−0.0521996 + 0.998637i $$0.516623\pi$$
$$368$$ 4.00000 0.208514
$$369$$ 20.0000i 1.04116i
$$370$$ 2.00000 + 4.00000i 0.103975 + 0.207950i
$$371$$ 2.00000i 0.103835i
$$372$$ 5.00000i 0.259238i
$$373$$ 34.0000i 1.76045i −0.474554 0.880227i $$-0.657390\pi$$
0.474554 0.880227i $$-0.342610\pi$$
$$374$$ 0 0
$$375$$ 2.00000 11.0000i 0.103280 0.568038i
$$376$$ −7.00000 −0.360997
$$377$$ −9.00000 −0.463524
$$378$$ 10.0000i 0.514344i
$$379$$ 4.00000i 0.205466i 0.994709 + 0.102733i $$0.0327588\pi$$
−0.994709 + 0.102733i $$0.967241\pi$$
$$380$$ −10.0000 + 5.00000i −0.512989 + 0.256495i
$$381$$ 7.00000i 0.358621i
$$382$$ 18.0000i 0.920960i
$$383$$ 31.0000i 1.58403i 0.610504 + 0.792013i $$0.290967\pi$$
−0.610504 + 0.792013i $$0.709033\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 0 0
$$386$$ 14.0000i 0.712581i
$$387$$ 12.0000i 0.609994i
$$388$$ 7.00000 0.355371
$$389$$ −10.0000 −0.507020 −0.253510 0.967333i $$-0.581585\pi$$
−0.253510 + 0.967333i $$0.581585\pi$$
$$390$$ −2.00000 + 1.00000i −0.101274 + 0.0506370i
$$391$$ −4.00000 + 16.0000i −0.202289 + 0.809155i
$$392$$ 3.00000i 0.151523i
$$393$$ 20.0000i 1.00887i
$$394$$ 8.00000i 0.403034i
$$395$$ 16.0000 + 32.0000i 0.805047 + 1.61009i
$$396$$ 0 0
$$397$$ 18.0000 0.903394 0.451697 0.892171i $$-0.350819\pi$$
0.451697 + 0.892171i $$0.350819\pi$$
$$398$$ 1.00000 0.0501255
$$399$$ −10.0000 −0.500626
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 10.0000i 0.499376i 0.968326 + 0.249688i $$0.0803281\pi$$
−0.968326 + 0.249688i $$0.919672\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ 5.00000 0.249068
$$404$$ 8.00000 0.398015
$$405$$ −2.00000 + 1.00000i −0.0993808 + 0.0496904i
$$406$$ 18.0000 0.893325
$$407$$ 0 0
$$408$$ −4.00000 1.00000i −0.198030 0.0495074i
$$409$$ −25.0000 −1.23617 −0.618085 0.786111i $$-0.712091\pi$$
−0.618085 + 0.786111i $$0.712091\pi$$
$$410$$ 20.0000 10.0000i 0.987730 0.493865i
$$411$$ 2.00000i 0.0986527i
$$412$$ 16.0000i 0.788263i
$$413$$ 10.0000 0.492068
$$414$$ 8.00000i 0.393179i
$$415$$ −6.00000 12.0000i −0.294528 0.589057i
$$416$$ −1.00000 −0.0490290
$$417$$ 14.0000i 0.685583i
$$418$$ 0 0
$$419$$ 24.0000i 1.17248i 0.810139 + 0.586238i $$0.199392\pi$$
−0.810139 + 0.586238i $$0.800608\pi$$
$$420$$ 4.00000 2.00000i 0.195180 0.0975900i
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ −20.0000 −0.973585
$$423$$ 14.0000i 0.680703i
$$424$$ 1.00000 0.0485643
$$425$$ 13.0000 + 16.0000i 0.630593 + 0.776114i
$$426$$ −5.00000 −0.242251
$$427$$ 10.0000i 0.483934i
$$428$$ 12.0000 0.580042
$$429$$ 0 0
$$430$$ 12.0000 6.00000i 0.578691 0.289346i
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 5.00000 0.240563
$$433$$ 6.00000i 0.288342i 0.989553 + 0.144171i $$0.0460515\pi$$
−0.989553 + 0.144171i $$0.953949\pi$$
$$434$$ −10.0000 −0.480015
$$435$$ 9.00000 + 18.0000i 0.431517 + 0.863034i
$$436$$ 9.00000i 0.431022i
$$437$$ −20.0000 −0.956730
$$438$$ 11.0000i 0.525600i
$$439$$ 24.0000i 1.14546i 0.819745 + 0.572729i $$0.194115\pi$$
−0.819745 + 0.572729i $$0.805885\pi$$
$$440$$ 0 0
$$441$$ 6.00000 0.285714
$$442$$ 1.00000 4.00000i 0.0475651 0.190261i
$$443$$ 26.0000i 1.23530i 0.786454 + 0.617649i $$0.211915\pi$$
−0.786454 + 0.617649i $$0.788085\pi$$
$$444$$ −2.00000 −0.0949158
$$445$$ −10.0000 + 5.00000i −0.474045 + 0.237023i
$$446$$ 9.00000 0.426162
$$447$$ −20.0000 −0.945968
$$448$$ 2.00000 0.0944911
$$449$$ 16.0000i 0.755087i −0.925992 0.377543i $$-0.876769\pi$$
0.925992 0.377543i $$-0.123231\pi$$
$$450$$ −8.00000 6.00000i −0.377124 0.282843i
$$451$$ 0 0
$$452$$ −9.00000 −0.423324
$$453$$ 8.00000 0.375873
$$454$$ 27.0000i 1.26717i
$$455$$ 2.00000 + 4.00000i 0.0937614 + 0.187523i
$$456$$ 5.00000i 0.234146i
$$457$$ 18.0000i 0.842004i 0.907060 + 0.421002i $$0.138322\pi$$
−0.907060 + 0.421002i $$0.861678\pi$$
$$458$$ 0 0
$$459$$ −5.00000 + 20.0000i −0.233380 + 0.933520i
$$460$$ 8.00000 4.00000i 0.373002 0.186501i
$$461$$ 32.0000 1.49039 0.745194 0.666847i $$-0.232357\pi$$
0.745194 + 0.666847i $$0.232357\pi$$
$$462$$ 0 0
$$463$$ 29.0000i 1.34774i −0.738848 0.673872i $$-0.764630\pi$$
0.738848 0.673872i $$-0.235370\pi$$
$$464$$ 9.00000i 0.417815i
$$465$$ −5.00000 10.0000i −0.231869 0.463739i
$$466$$ 21.0000i 0.972806i
$$467$$ 12.0000i 0.555294i −0.960683 0.277647i $$-0.910445\pi$$
0.960683 0.277647i $$-0.0895545\pi$$
$$468$$ 2.00000i 0.0924500i
$$469$$ 4.00000i 0.184703i
$$470$$ −14.0000 + 7.00000i −0.645772 + 0.322886i
$$471$$ 18.0000i 0.829396i
$$472$$ 5.00000i 0.230144i
$$473$$ 0 0
$$474$$ −16.0000 −0.734904
$$475$$ −15.0000 + 20.0000i −0.688247 + 0.917663i
$$476$$ −2.00000 + 8.00000i −0.0916698 + 0.366679i
$$477$$ 2.00000i 0.0915737i
$$478$$ 0 0
$$479$$ 21.0000i 0.959514i −0.877401 0.479757i $$-0.840725\pi$$
0.877401 0.479757i $$-0.159275\pi$$
$$480$$ 1.00000 + 2.00000i 0.0456435 + 0.0912871i
$$481$$ 2.00000i 0.0911922i
$$482$$ 10.0000 0.455488
$$483$$ 8.00000 0.364013
$$484$$ −11.0000 −0.500000
$$485$$ 14.0000 7.00000i 0.635707 0.317854i
$$486$$ 16.0000i 0.725775i
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ −5.00000 −0.226339
$$489$$ −4.00000 −0.180886
$$490$$ 3.00000 + 6.00000i 0.135526 + 0.271052i
$$491$$ −33.0000 −1.48927 −0.744635 0.667472i $$-0.767376\pi$$
−0.744635 + 0.667472i $$0.767376\pi$$
$$492$$ 10.0000i 0.450835i
$$493$$ −36.0000 9.00000i −1.62136 0.405340i
$$494$$ 5.00000 0.224961
$$495$$ 0 0
$$496$$ 5.00000i 0.224507i
$$497$$ 10.0000i 0.448561i
$$498$$ 6.00000 0.268866
$$499$$ 6.00000i 0.268597i −0.990941 0.134298i $$-0.957122\pi$$
0.990941 0.134298i $$-0.0428781\pi$$
$$500$$ 2.00000 11.0000i 0.0894427 0.491935i
$$501$$ −18.0000 −0.804181
$$502$$ 8.00000i 0.357057i
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 4.00000i 0.178174i
$$505$$ 16.0000 8.00000i 0.711991 0.355995i
$$506$$ 0 0
$$507$$ −12.0000 −0.532939
$$508$$ 7.00000i 0.310575i
$$509$$ −20.0000 −0.886484 −0.443242 0.896402i $$-0.646172\pi$$
−0.443242 + 0.896402i $$0.646172\pi$$
$$510$$ −9.00000 + 2.00000i −0.398527 + 0.0885615i
$$511$$ 22.0000 0.973223
$$512$$ 1.00000i 0.0441942i
$$513$$ −25.0000 −1.10378
$$514$$ −18.0000 −0.793946
$$515$$ −16.0000 32.0000i −0.705044 1.41009i
$$516$$ 6.00000i 0.264135i
$$517$$ 0 0
$$518$$ 4.00000i 0.175750i
$$519$$ 16.0000 0.702322
$$520$$ −2.00000 + 1.00000i −0.0877058 + 0.0438529i
$$521$$ 40.0000i 1.75243i 0.481919 + 0.876216i $$0.339940\pi$$
−0.481919 + 0.876216i $$0.660060\pi$$
$$522$$ 18.0000 0.787839
$$523$$ 34.0000i 1.48672i −0.668894 0.743358i $$-0.733232\pi$$
0.668894 0.743358i $$-0.266768\pi$$
$$524$$ 20.0000i 0.873704i
$$525$$ 6.00000 8.00000i 0.261861 0.349149i
$$526$$ −21.0000 −0.915644
$$527$$ 20.0000 + 5.00000i 0.871214 + 0.217803i
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ 2.00000 1.00000i 0.0868744 0.0434372i
$$531$$ 10.0000 0.433963
$$532$$ −10.0000 −0.433555
$$533$$ −10.0000 −0.433148
$$534$$ 5.00000i 0.216371i
$$535$$ 24.0000 12.0000i 1.03761 0.518805i
$$536$$ −2.00000 −0.0863868
$$537$$ −20.0000 −0.863064
$$538$$ 1.00000 0.0431131
$$539$$ 0 0
$$540$$ 10.0000 5.00000i 0.430331 0.215166i
$$541$$ 10.0000i 0.429934i 0.976621 + 0.214967i $$0.0689643\pi$$
−0.976621 + 0.214967i $$0.931036\pi$$
$$542$$ 22.0000i 0.944981i
$$543$$ 10.0000i 0.429141i
$$544$$ −4.00000 1.00000i −0.171499 0.0428746i
$$545$$ −9.00000 18.0000i −0.385518 0.771035i
$$546$$ −2.00000 −0.0855921
$$547$$ 13.0000 0.555840 0.277920 0.960604i $$-0.410355\pi$$
0.277920 + 0.960604i $$0.410355\pi$$
$$548$$ 2.00000i 0.0854358i
$$549$$ 10.0000i 0.426790i
$$550$$ 0 0
$$551$$ 45.0000i 1.91706i
$$552$$ 4.00000i 0.170251i
$$553$$ 32.0000i 1.36078i
$$554$$ 18.0000i 0.764747i
$$555$$ −4.00000 + 2.00000i −0.169791 + 0.0848953i
$$556$$ 14.0000i 0.593732i
$$557$$ 3.00000i 0.127114i 0.997978 + 0.0635570i $$0.0202445\pi$$
−0.997978 + 0.0635570i $$0.979756\pi$$
$$558$$ −10.0000 −0.423334
$$559$$ −6.00000 −0.253773
$$560$$ 4.00000 2.00000i 0.169031 0.0845154i
$$561$$ 0 0
$$562$$ 23.0000i 0.970196i
$$563$$ 24.0000i 1.01148i −0.862686 0.505740i $$-0.831220\pi$$
0.862686 0.505740i $$-0.168780\pi$$
$$564$$ 7.00000i 0.294753i
$$565$$ −18.0000 + 9.00000i −0.757266 + 0.378633i
$$566$$ 21.0000i 0.882696i
$$567$$ −2.00000 −0.0839921
$$568$$ −5.00000 −0.209795
$$569$$ 15.0000 0.628833 0.314416 0.949285i $$-0.398191\pi$$
0.314416 + 0.949285i $$0.398191\pi$$
$$570$$ −5.00000 10.0000i −0.209427 0.418854i
$$571$$ 20.0000i 0.836974i 0.908223 + 0.418487i $$0.137439\pi$$
−0.908223 + 0.418487i $$0.862561\pi$$
$$572$$ 0 0
$$573$$ 18.0000 0.751961
$$574$$ 20.0000 0.834784
$$575$$ 12.0000 16.0000i 0.500435 0.667246i
$$576$$ 2.00000 0.0833333
$$577$$ 28.0000i 1.16566i 0.812596 + 0.582828i $$0.198054\pi$$
−0.812596 + 0.582828i $$0.801946\pi$$
$$578$$ 8.00000 15.0000i 0.332756 0.623918i
$$579$$ −14.0000 −0.581820
$$580$$ 9.00000 + 18.0000i 0.373705 + 0.747409i
$$581$$ 12.0000i 0.497844i
$$582$$ 7.00000i 0.290159i
$$583$$ 0 0
$$584$$ 11.0000i 0.455183i
$$585$$ 2.00000 + 4.00000i 0.0826898 + 0.165380i
$$586$$ 29.0000 1.19798
$$587$$ 12.0000i 0.495293i −0.968850 0.247647i $$-0.920343\pi$$
0.968850 0.247647i $$-0.0796572\pi$$
$$588$$ −3.00000 −0.123718
$$589$$ 25.0000i 1.03011i
$$590$$ 5.00000 + 10.0000i 0.205847 + 0.411693i
$$591$$ −8.00000 −0.329076
$$592$$ −2.00000 −0.0821995
$$593$$ 6.00000i 0.246390i 0.992382 + 0.123195i $$0.0393141\pi$$
−0.992382 + 0.123195i $$0.960686\pi$$
$$594$$ 0 0
$$595$$ 4.00000 + 18.0000i 0.163984 + 0.737928i
$$596$$ −20.0000 −0.819232
$$597$$ 1.00000i 0.0409273i
$$598$$ −4.00000 −0.163572
$$599$$ 20.0000 0.817178 0.408589 0.912719i $$-0.366021\pi$$
0.408589 + 0.912719i $$0.366021\pi$$
$$600$$ 4.00000 + 3.00000i 0.163299 + 0.122474i
$$601$$ 30.0000i 1.22373i 0.790964 + 0.611863i $$0.209580\pi$$
−0.790964 + 0.611863i $$0.790420\pi$$
$$602$$ 12.0000 0.489083
$$603$$ 4.00000i 0.162893i
$$604$$ 8.00000 0.325515
$$605$$ −22.0000 + 11.0000i −0.894427 + 0.447214i
$$606$$ 8.00000i 0.324978i
$$607$$ 38.0000 1.54237 0.771186 0.636610i $$-0.219664\pi$$
0.771186 + 0.636610i $$0.219664\pi$$
$$608$$ 5.00000i 0.202777i
$$609$$ 18.0000i 0.729397i
$$610$$ −10.0000 + 5.00000i −0.404888 + 0.202444i
$$611$$ 7.00000 0.283190
$$612$$ −2.00000 + 8.00000i −0.0808452 + 0.323381i
$$613$$ 41.0000i 1.65597i 0.560747 + 0.827987i $$0.310514\pi$$
−0.560747 + 0.827987i $$0.689486\pi$$
$$614$$ 2.00000 0.0807134
$$615$$ 10.0000 + 20.0000i 0.403239 + 0.806478i
$$616$$ 0 0
$$617$$ 33.0000 1.32853 0.664265 0.747497i $$-0.268745\pi$$
0.664265 + 0.747497i $$0.268745\pi$$
$$618$$ 16.0000 0.643614
$$619$$ 26.0000i 1.04503i −0.852631 0.522514i $$-0.824994\pi$$
0.852631 0.522514i $$-0.175006\pi$$
$$620$$ −5.00000 10.0000i −0.200805 0.401610i
$$621$$ 20.0000 0.802572
$$622$$ 20.0000 0.801927
$$623$$ −10.0000 −0.400642
$$624$$ 1.00000i 0.0400320i
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 14.0000i 0.559553i
$$627$$ 0 0
$$628$$ 18.0000i 0.718278i
$$629$$ 2.00000 8.00000i 0.0797452 0.318981i
$$630$$ −4.00000 8.00000i −0.159364 0.318728i
$$631$$ 2.00000 0.0796187 0.0398094 0.999207i $$-0.487325\pi$$
0.0398094 + 0.999207i $$0.487325\pi$$
$$632$$ −16.0000 −0.636446
$$633$$ 20.0000i 0.794929i
$$634$$ 12.0000i 0.476581i
$$635$$ 7.00000 + 14.0000i 0.277787 + 0.555573i
$$636$$ 1.00000i 0.0396526i
$$637$$ 3.00000i 0.118864i
$$638$$ 0 0
$$639$$ 10.0000i 0.395594i
$$640$$ 1.00000 + 2.00000i 0.0395285 + 0.0790569i
$$641$$ 10.0000i 0.394976i 0.980305 + 0.197488i $$0.0632784\pi$$
−0.980305 + 0.197488i $$0.936722\pi$$
$$642$$ 12.0000i 0.473602i
$$643$$ −36.0000 −1.41970 −0.709851 0.704352i $$-0.751238\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$644$$ 8.00000 0.315244
$$645$$ 6.00000 + 12.0000i 0.236250 + 0.472500i
$$646$$ 20.0000 + 5.00000i 0.786889 + 0.196722i
$$647$$ 37.0000i 1.45462i −0.686309 0.727310i $$-0.740770\pi$$
0.686309 0.727310i $$-0.259230\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ 0 0
$$650$$ −3.00000 + 4.00000i −0.117670 + 0.156893i
$$651$$ 10.0000i 0.391931i
$$652$$ −4.00000 −0.156652
$$653$$ 24.0000 0.939193 0.469596 0.882881i $$-0.344399\pi$$
0.469596 + 0.882881i $$0.344399\pi$$
$$654$$ 9.00000 0.351928
$$655$$ −20.0000 40.0000i −0.781465 1.56293i
$$656$$ 10.0000i 0.390434i
$$657$$ 22.0000 0.858302
$$658$$ −14.0000 −0.545777
$$659$$ −5.00000 −0.194772 −0.0973862 0.995247i $$-0.531048\pi$$
−0.0973862 + 0.995247i $$0.531048\pi$$
$$660$$ 0 0
$$661$$ −8.00000 −0.311164 −0.155582 0.987823i $$-0.549725\pi$$
−0.155582 + 0.987823i $$0.549725\pi$$
$$662$$ 7.00000i 0.272063i
$$663$$ 4.00000 + 1.00000i 0.155347 + 0.0388368i
$$664$$ 6.00000 0.232845
$$665$$ −20.0000 + 10.0000i −0.775567 + 0.387783i
$$666$$ 4.00000i 0.154997i
$$667$$ 36.0000i 1.39393i
$$668$$ −18.0000 −0.696441
$$669$$ 9.00000i 0.347960i
$$670$$ −4.00000 + 2.00000i −0.154533 + 0.0772667i
$$671$$ 0 0
$$672$$ 2.00000i 0.0771517i
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 23.0000i 0.885927i
$$675$$ 15.0000 20.0000i 0.577350 0.769800i
$$676$$ −12.0000 −0.461538
$$677$$ −2.00000 −0.0768662 −0.0384331 0.999261i $$-0.512237\pi$$
−0.0384331 + 0.999261i $$0.512237\pi$$
$$678$$ 9.00000i 0.345643i
$$679$$ 14.0000 0.537271
$$680$$ −9.00000 + 2.00000i −0.345134 + 0.0766965i
$$681$$ 27.0000 1.03464
$$682$$ 0 0
$$683$$ 39.0000 1.49229 0.746147 0.665782i $$-0.231902\pi$$
0.746147 + 0.665782i $$0.231902\pi$$
$$684$$ −10.0000 −0.382360
$$685$$ 2.00000 + 4.00000i 0.0764161 + 0.152832i
$$686$$ 20.0000i 0.763604i
$$687$$ 0 0
$$688$$ 6.00000i 0.228748i
$$689$$ −1.00000 −0.0380970
$$690$$ 4.00000 + 8.00000i 0.152277 + 0.304555i
$$691$$ 30.0000i 1.14125i −0.821209 0.570627i $$-0.806700\pi$$
0.821209 0.570627i $$-0.193300\pi$$
$$692$$ 16.0000 0.608229
$$693$$ 0 0
$$694$$ 23.0000i 0.873068i
$$695$$ −14.0000 28.0000i −0.531050 1.06210i
$$696$$ −9.00000 −0.341144
$$697$$ −40.0000 10.0000i −1.51511 0.378777i
$$698$$ 10.0000i 0.378506i
$$699$$ 21.0000 0.794293
$$700$$ 6.00000 8.00000i 0.226779 0.302372i
$$701$$ −48.0000 −1.81293 −0.906467 0.422276i $$-0.861231\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 10.0000 0.377157
$$704$$ 0 0
$$705$$ −7.00000 14.0000i −0.263635 0.527271i
$$706$$ 4.00000 0.150542
$$707$$ 16.0000 0.601742
$$708$$ −5.00000 −0.187912
$$709$$ 31.0000i 1.16423i −0.813107 0.582115i $$-0.802225\pi$$
0.813107 0.582115i $$-0.197775\pi$$
$$710$$ −10.0000 + 5.00000i −0.375293 + 0.187647i
$$711$$ 32.0000i 1.20009i
$$712$$ 5.00000i 0.187383i
$$713$$ 20.0000i 0.749006i
$$714$$ −8.00000 2.00000i −0.299392 0.0748481i
$$715$$ 0 0
$$716$$ −20.0000 −0.747435
$$717$$ 0 0
$$718$$ 30.0000i 1.11959i
$$719$$ 51.0000i 1.90198i −0.309223 0.950990i $$-0.600069\pi$$
0.309223 0.950990i $$-0.399931\pi$$
$$720$$ 4.00000 2.00000i 0.149071 0.0745356i
$$721$$ 32.0000i 1.19174i
$$722$$ 6.00000i 0.223297i
$$723$$ 10.0000i 0.371904i
$$724$$ 10.0000i 0.371647i
$$725$$ 36.0000 + 27.0000i 1.33701 + 1.00275i
$$726$$ 11.0000i 0.408248i
$$727$$ 33.0000i 1.22390i 0.790896 + 0.611951i $$0.209615\pi$$
−0.790896 + 0.611951i $$0.790385\pi$$
$$728$$ −2.00000 −0.0741249
$$729$$ 13.0000 0.481481
$$730$$ 11.0000 + 22.0000i 0.407128 + 0.814257i
$$731$$ −24.0000 6.00000i −0.887672 0.221918i
$$732$$ 5.00000i 0.184805i
$$733$$ 6.00000i 0.221615i 0.993842 + 0.110808i $$0.0353437\pi$$
−0.993842 + 0.110808i $$0.964656\pi$$
$$734$$ 2.00000i 0.0738213i
$$735$$ −6.00000 + 3.00000i −0.221313 + 0.110657i
$$736$$ 4.00000i 0.147442i
$$737$$ 0 0
$$738$$ 20.0000 0.736210
$$739$$ −15.0000 −0.551784 −0.275892 0.961189i $$-0.588973\pi$$
−0.275892 + 0.961189i $$0.588973\pi$$
$$740$$ −4.00000 + 2.00000i −0.147043 + 0.0735215i
$$741$$ 5.00000i 0.183680i
$$742$$ 2.00000 0.0734223
$$743$$ 34.0000 1.24734 0.623670 0.781688i $$-0.285641\pi$$
0.623670 + 0.781688i $$0.285641\pi$$
$$744$$ 5.00000 0.183309
$$745$$ −40.0000 + 20.0000i −1.46549 + 0.732743i
$$746$$ 34.0000 1.24483
$$747$$ 12.0000i 0.439057i
$$748$$ 0 0
$$749$$ 24.0000 0.876941
$$750$$ 11.0000 + 2.00000i 0.401663 + 0.0730297i
$$751$$ 25.0000i 0.912263i 0.889912 + 0.456131i $$0.150765\pi$$
−0.889912 + 0.456131i $$0.849235\pi$$
$$752$$ 7.00000i 0.255264i
$$753$$ 8.00000 0.291536
$$754$$ 9.00000i 0.327761i
$$755$$ 16.0000 8.00000i 0.582300 0.291150i
$$756$$ 10.0000 0.363696
$$757$$ 13.0000i 0.472493i 0.971693 + 0.236247i $$0.0759173\pi$$
−0.971693 + 0.236247i $$0.924083\pi$$
$$758$$ −4.00000 −0.145287
$$759$$ 0 0
$$760$$ −5.00000 10.0000i −0.181369 0.362738i
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ −7.00000 −0.253583
$$763$$ 18.0000i 0.651644i
$$764$$ 18.0000 0.651217
$$765$$ 4.00000 + 18.0000i 0.144620 + 0.650791i
$$766$$ −31.0000 −1.12008
$$767$$ 5.00000i 0.180540i
$$768$$ −1.00000 −0.0360844
$$769$$ 35.0000 1.26213 0.631066 0.775729i $$-0.282618\pi$$
0.631066 + 0.775729i $$0.282618\pi$$
$$770$$ 0 0
$$771$$ 18.0000i 0.648254i
$$772$$ −14.0000 −0.503871
$$773$$ 26.0000i 0.935155i 0.883952 + 0.467578i $$0.154873\pi$$
−0.883952 + 0.467578i $$0.845127\pi$$
$$774$$ 12.0000 0.431331
$$775$$ −20.0000 15.0000i −0.718421 0.538816i
$$776$$ 7.00000i 0.251285i
$$777$$ −4.00000 −0.143499
$$778$$ 10.0000i 0.358517i
$$779$$ 50.0000i 1.79144i
$$780$$ −1.00000 2.00000i −0.0358057 0.0716115i
$$781$$ 0 0
$$782$$ −16.0000 4.00000i −0.572159 0.143040i
$$783$$ 45.0000i 1.60817i
$$784$$ −3.00000 −0.107143
$$785$$ −18.0000 36.0000i −0.642448 1.28490i
$$786$$ 20.0000 0.713376
$$787$$ −7.00000 −0.249523 −0.124762 0.992187i $$-0.539817\pi$$
−0.124762 + 0.992187i $$0.539817\pi$$
$$788$$ −8.00000 −0.284988
$$789$$ 21.0000i 0.747620i
$$790$$ −32.0000 + 16.0000i −1.13851 + 0.569254i
$$791$$ −18.0000 −0.640006
$$792$$ 0 0
$$793$$ 5.00000 0.177555
$$794$$ 18.0000i 0.638796i
$$795$$ 1.00000 + 2.00000i 0.0354663 + 0.0709327i
$$796$$ 1.00000i 0.0354441i
$$797$$ 2.00000i 0.0708436i −0.999372 0.0354218i $$-0.988723\pi$$
0.999372 0.0354218i $$-0.0112775\pi$$
$$798$$ 10.0000i 0.353996i
$$799$$ 28.0000 + 7.00000i 0.990569 + 0.247642i
$$800$$ 4.00000 + 3.00000i 0.141421 + 0.106066i
$$801$$ −10.0000 −0.353333
$$802$$ −10.0000 −0.353112
$$803$$ 0