# Properties

 Label 570.2.m.b.37.1 Level $570$ Weight $2$ Character 570.37 Analytic conductor $4.551$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ Defining polynomial: $$x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{9}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 37.1 Root $$0.339574 - 0.339574i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.37 Dual form 570.2.m.b.493.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.367533 - 2.20566i) q^{10} -4.80832 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.531491 - 0.531491i) q^{13} +1.03038 q^{14} +(-2.20566 + 0.367533i) q^{15} -1.00000 q^{16} +(-3.72984 - 3.72984i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.90517 + 3.24961i) q^{19} +(1.81952 + 1.29975i) q^{20} -1.03038i q^{21} +(3.39999 - 3.39999i) q^{22} +(-4.07973 + 4.07973i) q^{23} +1.00000i q^{24} +(-1.62130 - 4.72984i) q^{25} +0.751642 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.728588 + 0.728588i) q^{28} -0.494819 q^{29} +(1.29975 - 1.81952i) q^{30} -8.62312i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.39999 - 3.39999i) q^{33} +5.27479 q^{34} +(2.27266 - 0.378698i) q^{35} +1.00000 q^{36} +(-5.47836 + 5.47836i) q^{37} +(-4.35209 - 0.243552i) q^{38} -0.751642i q^{39} +(-2.20566 + 0.367533i) q^{40} +5.82553i q^{41} +(0.728588 + 0.728588i) q^{42} +(-3.04079 + 3.04079i) q^{43} +4.80832i q^{44} +(-1.81952 - 1.29975i) q^{45} -5.76961i q^{46} +(0.910451 + 0.910451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -5.93832i q^{49} +(4.49094 + 2.19807i) q^{50} -5.27479i q^{51} +(-0.531491 + 0.531491i) q^{52} +(-3.53266 - 3.53266i) q^{53} -1.00000i q^{54} +(6.24961 - 8.74883i) q^{55} -1.03038i q^{56} +(-0.243552 + 4.35209i) q^{57} +(0.349890 - 0.349890i) q^{58} +12.1307 q^{59} +(0.367533 + 2.20566i) q^{60} -5.32419 q^{61} +(6.09747 + 6.09747i) q^{62} +(0.728588 - 0.728588i) q^{63} +1.00000i q^{64} +(1.65786 - 0.276253i) q^{65} +4.80832 q^{66} +(-9.19128 + 9.19128i) q^{67} +(-3.72984 + 3.72984i) q^{68} -5.76961 q^{69} +(-1.33924 + 1.87480i) q^{70} +2.06076i q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.31160 - 3.31160i) q^{73} -7.74758i q^{74} +(2.19807 - 4.49094i) q^{75} +(3.24961 - 2.90517i) q^{76} +(3.50328 + 3.50328i) q^{77} +(0.531491 + 0.531491i) q^{78} -2.77074 q^{79} +(1.29975 - 1.81952i) q^{80} -1.00000 q^{81} +(-4.11927 - 4.11927i) q^{82} +(-3.57770 + 3.57770i) q^{83} -1.03038 q^{84} +(11.6344 - 1.93866i) q^{85} -4.30033i q^{86} +(-0.349890 - 0.349890i) q^{87} +(-3.39999 - 3.39999i) q^{88} -1.08630 q^{89} +(2.20566 - 0.367533i) q^{90} +0.774476i q^{91} +(4.07973 + 4.07973i) q^{92} +(6.09747 - 6.09747i) q^{93} -1.28757 q^{94} +(-9.68873 + 1.06234i) q^{95} +1.00000 q^{96} +(-2.81665 + 2.81665i) q^{97} +(4.19903 + 4.19903i) q^{98} -4.80832i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10})$$ $$20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 0.707107i −0.500000 + 0.500000i
$$3$$ 0.707107 + 0.707107i 0.408248 + 0.408248i
$$4$$ 1.00000i 0.500000i
$$5$$ −1.29975 + 1.81952i −0.581266 + 0.813714i
$$6$$ −1.00000 −0.408248
$$7$$ −0.728588 0.728588i −0.275380 0.275380i 0.555881 0.831262i $$-0.312381\pi$$
−0.831262 + 0.555881i $$0.812381\pi$$
$$8$$ 0.707107 + 0.707107i 0.250000 + 0.250000i
$$9$$ 1.00000i 0.333333i
$$10$$ −0.367533 2.20566i −0.116224 0.697490i
$$11$$ −4.80832 −1.44976 −0.724881 0.688874i $$-0.758105\pi$$
−0.724881 + 0.688874i $$0.758105\pi$$
$$12$$ 0.707107 0.707107i 0.204124 0.204124i
$$13$$ −0.531491 0.531491i −0.147409 0.147409i 0.629550 0.776960i $$-0.283239\pi$$
−0.776960 + 0.629550i $$0.783239\pi$$
$$14$$ 1.03038 0.275380
$$15$$ −2.20566 + 0.367533i −0.569498 + 0.0948965i
$$16$$ −1.00000 −0.250000
$$17$$ −3.72984 3.72984i −0.904619 0.904619i 0.0912125 0.995831i $$-0.470926\pi$$
−0.995831 + 0.0912125i $$0.970926\pi$$
$$18$$ −0.707107 0.707107i −0.166667 0.166667i
$$19$$ 2.90517 + 3.24961i 0.666493 + 0.745511i
$$20$$ 1.81952 + 1.29975i 0.406857 + 0.290633i
$$21$$ 1.03038i 0.224847i
$$22$$ 3.39999 3.39999i 0.724881 0.724881i
$$23$$ −4.07973 + 4.07973i −0.850682 + 0.850682i −0.990217 0.139535i $$-0.955439\pi$$
0.139535 + 0.990217i $$0.455439\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ −1.62130 4.72984i −0.324260 0.945968i
$$26$$ 0.751642 0.147409
$$27$$ −0.707107 + 0.707107i −0.136083 + 0.136083i
$$28$$ −0.728588 + 0.728588i −0.137690 + 0.137690i
$$29$$ −0.494819 −0.0918856 −0.0459428 0.998944i $$-0.514629\pi$$
−0.0459428 + 0.998944i $$0.514629\pi$$
$$30$$ 1.29975 1.81952i 0.237301 0.332197i
$$31$$ 8.62312i 1.54876i −0.632722 0.774379i $$-0.718062\pi$$
0.632722 0.774379i $$-0.281938\pi$$
$$32$$ 0.707107 0.707107i 0.125000 0.125000i
$$33$$ −3.39999 3.39999i −0.591863 0.591863i
$$34$$ 5.27479 0.904619
$$35$$ 2.27266 0.378698i 0.384150 0.0640117i
$$36$$ 1.00000 0.166667
$$37$$ −5.47836 + 5.47836i −0.900637 + 0.900637i −0.995491 0.0948538i $$-0.969762\pi$$
0.0948538 + 0.995491i $$0.469762\pi$$
$$38$$ −4.35209 0.243552i −0.706002 0.0395093i
$$39$$ 0.751642i 0.120359i
$$40$$ −2.20566 + 0.367533i −0.348745 + 0.0581120i
$$41$$ 5.82553i 0.909794i 0.890544 + 0.454897i $$0.150324\pi$$
−0.890544 + 0.454897i $$0.849676\pi$$
$$42$$ 0.728588 + 0.728588i 0.112424 + 0.112424i
$$43$$ −3.04079 + 3.04079i −0.463716 + 0.463716i −0.899871 0.436155i $$-0.856340\pi$$
0.436155 + 0.899871i $$0.356340\pi$$
$$44$$ 4.80832i 0.724881i
$$45$$ −1.81952 1.29975i −0.271238 0.193755i
$$46$$ 5.76961i 0.850682i
$$47$$ 0.910451 + 0.910451i 0.132803 + 0.132803i 0.770384 0.637581i $$-0.220065\pi$$
−0.637581 + 0.770384i $$0.720065\pi$$
$$48$$ −0.707107 0.707107i −0.102062 0.102062i
$$49$$ 5.93832i 0.848331i
$$50$$ 4.49094 + 2.19807i 0.635114 + 0.310854i
$$51$$ 5.27479i 0.738618i
$$52$$ −0.531491 + 0.531491i −0.0737046 + 0.0737046i
$$53$$ −3.53266 3.53266i −0.485248 0.485248i 0.421555 0.906803i $$-0.361484\pi$$
−0.906803 + 0.421555i $$0.861484\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ 6.24961 8.74883i 0.842697 1.17969i
$$56$$ 1.03038i 0.137690i
$$57$$ −0.243552 + 4.35209i −0.0322592 + 0.576448i
$$58$$ 0.349890 0.349890i 0.0459428 0.0459428i
$$59$$ 12.1307 1.57928 0.789641 0.613569i $$-0.210267\pi$$
0.789641 + 0.613569i $$0.210267\pi$$
$$60$$ 0.367533 + 2.20566i 0.0474483 + 0.284749i
$$61$$ −5.32419 −0.681692 −0.340846 0.940119i $$-0.610713\pi$$
−0.340846 + 0.940119i $$0.610713\pi$$
$$62$$ 6.09747 + 6.09747i 0.774379 + 0.774379i
$$63$$ 0.728588 0.728588i 0.0917935 0.0917935i
$$64$$ 1.00000i 0.125000i
$$65$$ 1.65786 0.276253i 0.205633 0.0342650i
$$66$$ 4.80832 0.591863
$$67$$ −9.19128 + 9.19128i −1.12289 + 1.12289i −0.131590 + 0.991304i $$0.542008\pi$$
−0.991304 + 0.131590i $$0.957992\pi$$
$$68$$ −3.72984 + 3.72984i −0.452309 + 0.452309i
$$69$$ −5.76961 −0.694579
$$70$$ −1.33924 + 1.87480i −0.160069 + 0.224081i
$$71$$ 2.06076i 0.244567i 0.992495 + 0.122284i $$0.0390217\pi$$
−0.992495 + 0.122284i $$0.960978\pi$$
$$72$$ −0.707107 + 0.707107i −0.0833333 + 0.0833333i
$$73$$ 3.31160 3.31160i 0.387594 0.387594i −0.486235 0.873828i $$-0.661630\pi$$
0.873828 + 0.486235i $$0.161630\pi$$
$$74$$ 7.74758i 0.900637i
$$75$$ 2.19807 4.49094i 0.253811 0.518569i
$$76$$ 3.24961 2.90517i 0.372756 0.333246i
$$77$$ 3.50328 + 3.50328i 0.399236 + 0.399236i
$$78$$ 0.531491 + 0.531491i 0.0601795 + 0.0601795i
$$79$$ −2.77074 −0.311733 −0.155866 0.987778i $$-0.549817\pi$$
−0.155866 + 0.987778i $$0.549817\pi$$
$$80$$ 1.29975 1.81952i 0.145316 0.203428i
$$81$$ −1.00000 −0.111111
$$82$$ −4.11927 4.11927i −0.454897 0.454897i
$$83$$ −3.57770 + 3.57770i −0.392703 + 0.392703i −0.875650 0.482947i $$-0.839567\pi$$
0.482947 + 0.875650i $$0.339567\pi$$
$$84$$ −1.03038 −0.112424
$$85$$ 11.6344 1.93866i 1.26192 0.210277i
$$86$$ 4.30033i 0.463716i
$$87$$ −0.349890 0.349890i −0.0375122 0.0375122i
$$88$$ −3.39999 3.39999i −0.362441 0.362441i
$$89$$ −1.08630 −0.115147 −0.0575736 0.998341i $$-0.518336\pi$$
−0.0575736 + 0.998341i $$0.518336\pi$$
$$90$$ 2.20566 0.367533i 0.232497 0.0387414i
$$91$$ 0.774476i 0.0811872i
$$92$$ 4.07973 + 4.07973i 0.425341 + 0.425341i
$$93$$ 6.09747 6.09747i 0.632278 0.632278i
$$94$$ −1.28757 −0.132803
$$95$$ −9.68873 + 1.06234i −0.994042 + 0.108994i
$$96$$ 1.00000 0.102062
$$97$$ −2.81665 + 2.81665i −0.285988 + 0.285988i −0.835491 0.549503i $$-0.814817\pi$$
0.549503 + 0.835491i $$0.314817\pi$$
$$98$$ 4.19903 + 4.19903i 0.424166 + 0.424166i
$$99$$ 4.80832i 0.483254i
$$100$$ −4.72984 + 1.62130i −0.472984 + 0.162130i
$$101$$ −14.0592 −1.39894 −0.699470 0.714662i $$-0.746581\pi$$
−0.699470 + 0.714662i $$0.746581\pi$$
$$102$$ 3.72984 + 3.72984i 0.369309 + 0.369309i
$$103$$ 6.63327 + 6.63327i 0.653596 + 0.653596i 0.953857 0.300261i $$-0.0970739\pi$$
−0.300261 + 0.953857i $$0.597074\pi$$
$$104$$ 0.751642i 0.0737046i
$$105$$ 1.87480 + 1.33924i 0.182961 + 0.130696i
$$106$$ 4.99593 0.485248
$$107$$ −1.54262 + 1.54262i −0.149131 + 0.149131i −0.777730 0.628599i $$-0.783629\pi$$
0.628599 + 0.777730i $$0.283629\pi$$
$$108$$ 0.707107 + 0.707107i 0.0680414 + 0.0680414i
$$109$$ 18.4286 1.76514 0.882569 0.470183i $$-0.155812\pi$$
0.882569 + 0.470183i $$0.155812\pi$$
$$110$$ 1.76721 + 10.6055i 0.168497 + 1.01119i
$$111$$ −7.74758 −0.735367
$$112$$ 0.728588 + 0.728588i 0.0688451 + 0.0688451i
$$113$$ 5.25913 + 5.25913i 0.494738 + 0.494738i 0.909795 0.415058i $$-0.136239\pi$$
−0.415058 + 0.909795i $$0.636239\pi$$
$$114$$ −2.90517 3.24961i −0.272095 0.304354i
$$115$$ −2.12052 12.7258i −0.197740 1.18668i
$$116$$ 0.494819i 0.0459428i
$$117$$ 0.531491 0.531491i 0.0491364 0.0491364i
$$118$$ −8.57770 + 8.57770i −0.789641 + 0.789641i
$$119$$ 5.43503i 0.498229i
$$120$$ −1.81952 1.29975i −0.166099 0.118650i
$$121$$ 12.1199 1.10181
$$122$$ 3.76477 3.76477i 0.340846 0.340846i
$$123$$ −4.11927 + 4.11927i −0.371422 + 0.371422i
$$124$$ −8.62312 −0.774379
$$125$$ 10.7133 + 3.19762i 0.958229 + 0.286004i
$$126$$ 1.03038i 0.0917935i
$$127$$ −9.35800 + 9.35800i −0.830388 + 0.830388i −0.987570 0.157181i $$-0.949759\pi$$
0.157181 + 0.987570i $$0.449759\pi$$
$$128$$ −0.707107 0.707107i −0.0625000 0.0625000i
$$129$$ −4.30033 −0.378623
$$130$$ −0.976946 + 1.36763i −0.0856839 + 0.119949i
$$131$$ 12.6267 1.10320 0.551601 0.834108i $$-0.314017\pi$$
0.551601 + 0.834108i $$0.314017\pi$$
$$132$$ −3.39999 + 3.39999i −0.295931 + 0.295931i
$$133$$ 0.250951 4.48430i 0.0217602 0.388838i
$$134$$ 12.9984i 1.12289i
$$135$$ −0.367533 2.20566i −0.0316322 0.189833i
$$136$$ 5.27479i 0.452309i
$$137$$ 0.378698 + 0.378698i 0.0323544 + 0.0323544i 0.723099 0.690745i $$-0.242717\pi$$
−0.690745 + 0.723099i $$0.742717\pi$$
$$138$$ 4.07973 4.07973i 0.347290 0.347290i
$$139$$ 22.7942i 1.93338i 0.255957 + 0.966688i $$0.417609\pi$$
−0.255957 + 0.966688i $$0.582391\pi$$
$$140$$ −0.378698 2.27266i −0.0320058 0.192075i
$$141$$ 1.28757i 0.108433i
$$142$$ −1.45718 1.45718i −0.122284 0.122284i
$$143$$ 2.55558 + 2.55558i 0.213708 + 0.213708i
$$144$$ 1.00000i 0.0833333i
$$145$$ 0.643141 0.900333i 0.0534100 0.0747686i
$$146$$ 4.68331i 0.387594i
$$147$$ 4.19903 4.19903i 0.346330 0.346330i
$$148$$ 5.47836 + 5.47836i 0.450319 + 0.450319i
$$149$$ 15.8801i 1.30095i 0.759529 + 0.650473i $$0.225429\pi$$
−0.759529 + 0.650473i $$0.774571\pi$$
$$150$$ 1.62130 + 4.72984i 0.132379 + 0.386190i
$$151$$ 13.3507i 1.08646i 0.839583 + 0.543231i $$0.182799\pi$$
−0.839583 + 0.543231i $$0.817201\pi$$
$$152$$ −0.243552 + 4.35209i −0.0197547 + 0.353001i
$$153$$ 3.72984 3.72984i 0.301540 0.301540i
$$154$$ −4.95439 −0.399236
$$155$$ 15.6899 + 11.2079i 1.26025 + 0.900240i
$$156$$ −0.751642 −0.0601795
$$157$$ 11.7372 + 11.7372i 0.936727 + 0.936727i 0.998114 0.0613870i $$-0.0195524\pi$$
−0.0613870 + 0.998114i $$0.519552\pi$$
$$158$$ 1.95921 1.95921i 0.155866 0.155866i
$$159$$ 4.99593i 0.396203i
$$160$$ 0.367533 + 2.20566i 0.0290560 + 0.174372i
$$161$$ 5.94489 0.468523
$$162$$ 0.707107 0.707107i 0.0555556 0.0555556i
$$163$$ −0.988668 + 0.988668i −0.0774384 + 0.0774384i −0.744765 0.667327i $$-0.767438\pi$$
0.667327 + 0.744765i $$0.267438\pi$$
$$164$$ 5.82553 0.454897
$$165$$ 10.6055 1.76721i 0.825637 0.137577i
$$166$$ 5.05963i 0.392703i
$$167$$ −7.42584 + 7.42584i −0.574629 + 0.574629i −0.933418 0.358790i $$-0.883189\pi$$
0.358790 + 0.933418i $$0.383189\pi$$
$$168$$ 0.728588 0.728588i 0.0562118 0.0562118i
$$169$$ 12.4350i 0.956541i
$$170$$ −6.85591 + 9.59758i −0.525824 + 0.736101i
$$171$$ −3.24961 + 2.90517i −0.248504 + 0.222164i
$$172$$ 3.04079 + 3.04079i 0.231858 + 0.231858i
$$173$$ −11.0462 11.0462i −0.839825 0.839825i 0.149011 0.988836i $$-0.452391\pi$$
−0.988836 + 0.149011i $$0.952391\pi$$
$$174$$ 0.494819 0.0375122
$$175$$ −2.26484 + 4.62737i −0.171206 + 0.349796i
$$176$$ 4.80832 0.362441
$$177$$ 8.57770 + 8.57770i 0.644739 + 0.644739i
$$178$$ 0.768128 0.768128i 0.0575736 0.0575736i
$$179$$ 19.0425 1.42330 0.711652 0.702532i $$-0.247947\pi$$
0.711652 + 0.702532i $$0.247947\pi$$
$$180$$ −1.29975 + 1.81952i −0.0968776 + 0.135619i
$$181$$ 1.78110i 0.132388i −0.997807 0.0661941i $$-0.978914\pi$$
0.997807 0.0661941i $$-0.0210857\pi$$
$$182$$ −0.547637 0.547637i −0.0405936 0.0405936i
$$183$$ −3.76477 3.76477i −0.278300 0.278300i
$$184$$ −5.76961 −0.425341
$$185$$ −2.84749 17.0885i −0.209351 1.25637i
$$186$$ 8.62312i 0.632278i
$$187$$ 17.9343 + 17.9343i 1.31148 + 1.31148i
$$188$$ 0.910451 0.910451i 0.0664014 0.0664014i
$$189$$ 1.03038 0.0749491
$$190$$ 6.09977 7.60215i 0.442524 0.551518i
$$191$$ −14.8650 −1.07559 −0.537797 0.843075i $$-0.680743\pi$$
−0.537797 + 0.843075i $$0.680743\pi$$
$$192$$ −0.707107 + 0.707107i −0.0510310 + 0.0510310i
$$193$$ −5.04632 5.04632i −0.363242 0.363242i 0.501763 0.865005i $$-0.332685\pi$$
−0.865005 + 0.501763i $$0.832685\pi$$
$$194$$ 3.98335i 0.285988i
$$195$$ 1.36763 + 0.976946i 0.0979378 + 0.0699606i
$$196$$ −5.93832 −0.424166
$$197$$ −7.66209 7.66209i −0.545901 0.545901i 0.379351 0.925253i $$-0.376147\pi$$
−0.925253 + 0.379351i $$0.876147\pi$$
$$198$$ 3.39999 + 3.39999i 0.241627 + 0.241627i
$$199$$ 20.9302i 1.48370i 0.670565 + 0.741851i $$0.266052\pi$$
−0.670565 + 0.741851i $$0.733948\pi$$
$$200$$ 2.19807 4.49094i 0.155427 0.317557i
$$201$$ −12.9984 −0.916839
$$202$$ 9.94134 9.94134i 0.699470 0.699470i
$$203$$ 0.360520 + 0.360520i 0.0253035 + 0.0253035i
$$204$$ −5.27479 −0.369309
$$205$$ −10.5997 7.57173i −0.740312 0.528832i
$$206$$ −9.38086 −0.653596
$$207$$ −4.07973 4.07973i −0.283561 0.283561i
$$208$$ 0.531491 + 0.531491i 0.0368523 + 0.0368523i
$$209$$ −13.9690 15.6252i −0.966256 1.08081i
$$210$$ −2.27266 + 0.378698i −0.156829 + 0.0261327i
$$211$$ 27.6388i 1.90273i −0.308062 0.951366i $$-0.599681\pi$$
0.308062 0.951366i $$-0.400319\pi$$
$$212$$ −3.53266 + 3.53266i −0.242624 + 0.242624i
$$213$$ −1.45718 + 1.45718i −0.0998441 + 0.0998441i
$$214$$ 2.18160i 0.149131i
$$215$$ −1.58051 9.48504i −0.107790 0.646875i
$$216$$ −1.00000 −0.0680414
$$217$$ −6.28270 + 6.28270i −0.426498 + 0.426498i
$$218$$ −13.0310 + 13.0310i −0.882569 + 0.882569i
$$219$$ 4.68331 0.316469
$$220$$ −8.74883 6.24961i −0.589846 0.421349i
$$221$$ 3.96475i 0.266698i
$$222$$ 5.47836 5.47836i 0.367684 0.367684i
$$223$$ 8.04571 + 8.04571i 0.538781 + 0.538781i 0.923171 0.384390i $$-0.125588\pi$$
−0.384390 + 0.923171i $$0.625588\pi$$
$$224$$ −1.03038 −0.0688451
$$225$$ 4.72984 1.62130i 0.315323 0.108087i
$$226$$ −7.43754 −0.494738
$$227$$ 1.98330 1.98330i 0.131636 0.131636i −0.638219 0.769855i $$-0.720329\pi$$
0.769855 + 0.638219i $$0.220329\pi$$
$$228$$ 4.35209 + 0.243552i 0.288224 + 0.0161296i
$$229$$ 19.6443i 1.29813i −0.760732 0.649066i $$-0.775160\pi$$
0.760732 0.649066i $$-0.224840\pi$$
$$230$$ 10.4979 + 7.49905i 0.692212 + 0.494473i
$$231$$ 4.95439i 0.325975i
$$232$$ −0.349890 0.349890i −0.0229714 0.0229714i
$$233$$ −4.73992 + 4.73992i −0.310523 + 0.310523i −0.845112 0.534589i $$-0.820466\pi$$
0.534589 + 0.845112i $$0.320466\pi$$
$$234$$ 0.751642i 0.0491364i
$$235$$ −2.83994 + 0.473225i −0.185257 + 0.0308698i
$$236$$ 12.1307i 0.789641i
$$237$$ −1.95921 1.95921i −0.127264 0.127264i
$$238$$ −3.84315 3.84315i −0.249114 0.249114i
$$239$$ 21.1851i 1.37035i −0.728378 0.685176i $$-0.759725\pi$$
0.728378 0.685176i $$-0.240275\pi$$
$$240$$ 2.20566 0.367533i 0.142375 0.0237241i
$$241$$ 16.2784i 1.04859i −0.851538 0.524293i $$-0.824329\pi$$
0.851538 0.524293i $$-0.175671\pi$$
$$242$$ −8.57008 + 8.57008i −0.550905 + 0.550905i
$$243$$ −0.707107 0.707107i −0.0453609 0.0453609i
$$244$$ 5.32419i 0.340846i
$$245$$ 10.8049 + 7.71833i 0.690299 + 0.493106i
$$246$$ 5.82553i 0.371422i
$$247$$ 0.183064 3.27121i 0.0116481 0.208142i
$$248$$ 6.09747 6.09747i 0.387190 0.387190i
$$249$$ −5.05963 −0.320641
$$250$$ −9.83652 + 5.31441i −0.622116 + 0.336113i
$$251$$ 5.24992 0.331372 0.165686 0.986179i $$-0.447016\pi$$
0.165686 + 0.986179i $$0.447016\pi$$
$$252$$ −0.728588 0.728588i −0.0458967 0.0458967i
$$253$$ 19.6166 19.6166i 1.23329 1.23329i
$$254$$ 13.2342i 0.830388i
$$255$$ 9.59758 + 6.85591i 0.601024 + 0.429333i
$$256$$ 1.00000 0.0625000
$$257$$ 16.0320 16.0320i 1.00005 1.00005i 4.94079e−5 1.00000i $$-0.499984\pi$$
1.00000 4.94079e-5i $$-1.57270e-5\pi$$
$$258$$ 3.04079 3.04079i 0.189311 0.189311i
$$259$$ 7.98294 0.496036
$$260$$ −0.276253 1.65786i −0.0171325 0.102816i
$$261$$ 0.494819i 0.0306285i
$$262$$ −8.92844 + 8.92844i −0.551601 + 0.551601i
$$263$$ −5.94999 + 5.94999i −0.366892 + 0.366892i −0.866342 0.499450i $$-0.833535\pi$$
0.499450 + 0.866342i $$0.333535\pi$$
$$264$$ 4.80832i 0.295931i
$$265$$ 11.0193 1.83617i 0.676911 0.112795i
$$266$$ 2.99343 + 3.34833i 0.183539 + 0.205299i
$$267$$ −0.768128 0.768128i −0.0470087 0.0470087i
$$268$$ 9.19128 + 9.19128i 0.561447 + 0.561447i
$$269$$ −26.2880 −1.60281 −0.801404 0.598123i $$-0.795913\pi$$
−0.801404 + 0.598123i $$0.795913\pi$$
$$270$$ 1.81952 + 1.29975i 0.110732 + 0.0791002i
$$271$$ −11.9318 −0.724802 −0.362401 0.932022i $$-0.618043\pi$$
−0.362401 + 0.932022i $$0.618043\pi$$
$$272$$ 3.72984 + 3.72984i 0.226155 + 0.226155i
$$273$$ −0.547637 + 0.547637i −0.0331445 + 0.0331445i
$$274$$ −0.535560 −0.0323544
$$275$$ 7.79573 + 22.7426i 0.470100 + 1.37143i
$$276$$ 5.76961i 0.347290i
$$277$$ −13.1943 13.1943i −0.792771 0.792771i 0.189173 0.981944i $$-0.439419\pi$$
−0.981944 + 0.189173i $$0.939419\pi$$
$$278$$ −16.1179 16.1179i −0.966688 0.966688i
$$279$$ 8.62312 0.516253
$$280$$ 1.87480 + 1.33924i 0.112040 + 0.0800346i
$$281$$ 25.4814i 1.52009i −0.649870 0.760045i $$-0.725177\pi$$
0.649870 0.760045i $$-0.274823\pi$$
$$282$$ −0.910451 0.910451i −0.0542165 0.0542165i
$$283$$ −14.9451 + 14.9451i −0.888392 + 0.888392i −0.994369 0.105977i $$-0.966203\pi$$
0.105977 + 0.994369i $$0.466203\pi$$
$$284$$ 2.06076 0.122284
$$285$$ −7.60215 6.09977i −0.450313 0.361319i
$$286$$ −3.61413 −0.213708
$$287$$ 4.24441 4.24441i 0.250540 0.250540i
$$288$$ 0.707107 + 0.707107i 0.0416667 + 0.0416667i
$$289$$ 10.8234i 0.636671i
$$290$$ 0.181862 + 1.09140i 0.0106793 + 0.0640893i
$$291$$ −3.98335 −0.233508
$$292$$ −3.31160 3.31160i −0.193797 0.193797i
$$293$$ −19.3388 19.3388i −1.12978 1.12978i −0.990212 0.139570i $$-0.955428\pi$$
−0.139570 0.990212i $$-0.544572\pi$$
$$294$$ 5.93832i 0.346330i
$$295$$ −15.7669 + 22.0720i −0.917982 + 1.28508i
$$296$$ −7.74758 −0.450319
$$297$$ 3.39999 3.39999i 0.197288 0.197288i
$$298$$ −11.2289 11.2289i −0.650473 0.650473i
$$299$$ 4.33668 0.250797
$$300$$ −4.49094 2.19807i −0.259284 0.126906i
$$301$$ 4.43097 0.255397
$$302$$ −9.44035 9.44035i −0.543231 0.543231i
$$303$$ −9.94134 9.94134i −0.571115 0.571115i
$$304$$ −2.90517 3.24961i −0.166623 0.186378i
$$305$$ 6.92011 9.68746i 0.396244 0.554702i
$$306$$ 5.27479i 0.301540i
$$307$$ −0.00353863 + 0.00353863i −0.000201960 + 0.000201960i −0.707208 0.707006i $$-0.750045\pi$$
0.707006 + 0.707208i $$0.250045\pi$$
$$308$$ 3.50328 3.50328i 0.199618 0.199618i
$$309$$ 9.38086i 0.533659i
$$310$$ −19.0196 + 3.16928i −1.08024 + 0.180003i
$$311$$ −11.6925 −0.663019 −0.331509 0.943452i $$-0.607558\pi$$
−0.331509 + 0.943452i $$0.607558\pi$$
$$312$$ 0.531491 0.531491i 0.0300898 0.0300898i
$$313$$ −16.6688 + 16.6688i −0.942174 + 0.942174i −0.998417 0.0562432i $$-0.982088\pi$$
0.0562432 + 0.998417i $$0.482088\pi$$
$$314$$ −16.5988 −0.936727
$$315$$ 0.378698 + 2.27266i 0.0213372 + 0.128050i
$$316$$ 2.77074i 0.155866i
$$317$$ 6.96737 6.96737i 0.391327 0.391327i −0.483834 0.875160i $$-0.660756\pi$$
0.875160 + 0.483834i $$0.160756\pi$$
$$318$$ 3.53266 + 3.53266i 0.198102 + 0.198102i
$$319$$ 2.37925 0.133212
$$320$$ −1.81952 1.29975i −0.101714 0.0726582i
$$321$$ −2.18160 −0.121765
$$322$$ −4.20367 + 4.20367i −0.234261 + 0.234261i
$$323$$ 1.28468 22.9564i 0.0714818 1.27733i
$$324$$ 1.00000i 0.0555556i
$$325$$ −1.65216 + 3.37558i −0.0916454 + 0.187243i
$$326$$ 1.39819i 0.0774384i
$$327$$ 13.0310 + 13.0310i 0.720614 + 0.720614i
$$328$$ −4.11927 + 4.11927i −0.227449 + 0.227449i
$$329$$ 1.32669i 0.0731426i
$$330$$ −6.24961 + 8.74883i −0.344030 + 0.481607i
$$331$$ 12.2381i 0.672669i 0.941743 + 0.336335i $$0.109187\pi$$
−0.941743 + 0.336335i $$0.890813\pi$$
$$332$$ 3.57770 + 3.57770i 0.196352 + 0.196352i
$$333$$ −5.47836 5.47836i −0.300212 0.300212i
$$334$$ 10.5017i 0.574629i
$$335$$ −4.77735 28.6701i −0.261015 1.56641i
$$336$$ 1.03038i 0.0562118i
$$337$$ 18.9918 18.9918i 1.03455 1.03455i 0.0351664 0.999381i $$-0.488804\pi$$
0.999381 0.0351664i $$-0.0111961\pi$$
$$338$$ 8.79290 + 8.79290i 0.478271 + 0.478271i
$$339$$ 7.43754i 0.403952i
$$340$$ −1.93866 11.6344i −0.105138 0.630962i
$$341$$ 41.4627i 2.24533i
$$342$$ 0.243552 4.35209i 0.0131698 0.235334i
$$343$$ −9.42671 + 9.42671i −0.508994 + 0.508994i
$$344$$ −4.30033 −0.231858
$$345$$ 7.49905 10.4979i 0.403735 0.565189i
$$346$$ 15.6216 0.839825
$$347$$ 1.51527 + 1.51527i 0.0813438 + 0.0813438i 0.746608 0.665264i $$-0.231681\pi$$
−0.665264 + 0.746608i $$0.731681\pi$$
$$348$$ −0.349890 + 0.349890i −0.0187561 + 0.0187561i
$$349$$ 21.3136i 1.14089i 0.821336 + 0.570444i $$0.193229\pi$$
−0.821336 + 0.570444i $$0.806771\pi$$
$$350$$ −1.67056 4.87353i −0.0892950 0.260501i
$$351$$ 0.751642 0.0401197
$$352$$ −3.39999 + 3.39999i −0.181220 + 0.181220i
$$353$$ 9.37463 9.37463i 0.498961 0.498961i −0.412153 0.911115i $$-0.635223\pi$$
0.911115 + 0.412153i $$0.135223\pi$$
$$354$$ −12.1307 −0.644739
$$355$$ −3.74959 2.67847i −0.199008 0.142158i
$$356$$ 1.08630i 0.0575736i
$$357$$ −3.84315 + 3.84315i −0.203401 + 0.203401i
$$358$$ −13.4651 + 13.4651i −0.711652 + 0.711652i
$$359$$ 30.1209i 1.58972i −0.606792 0.794861i $$-0.707544\pi$$
0.606792 0.794861i $$-0.292456\pi$$
$$360$$ −0.367533 2.20566i −0.0193707 0.116248i
$$361$$ −2.11992 + 18.8814i −0.111575 + 0.993756i
$$362$$ 1.25943 + 1.25943i 0.0661941 + 0.0661941i
$$363$$ 8.57008 + 8.57008i 0.449812 + 0.449812i
$$364$$ 0.774476 0.0405936
$$365$$ 1.72127 + 10.3298i 0.0900954 + 0.540685i
$$366$$ 5.32419 0.278300
$$367$$ −10.0986 10.0986i −0.527140 0.527140i 0.392578 0.919719i $$-0.371583\pi$$
−0.919719 + 0.392578i $$0.871583\pi$$
$$368$$ 4.07973 4.07973i 0.212671 0.212671i
$$369$$ −5.82553 −0.303265
$$370$$ 14.0969 + 10.0699i 0.732861 + 0.523510i
$$371$$ 5.14771i 0.267256i
$$372$$ −6.09747 6.09747i −0.316139 0.316139i
$$373$$ 11.5759 + 11.5759i 0.599377 + 0.599377i 0.940147 0.340770i $$-0.110688\pi$$
−0.340770 + 0.940147i $$0.610688\pi$$
$$374$$ −25.3629 −1.31148
$$375$$ 5.31441 + 9.83652i 0.274435 + 0.507956i
$$376$$ 1.28757i 0.0664014i
$$377$$ 0.262992 + 0.262992i 0.0135448 + 0.0135448i
$$378$$ −0.728588 + 0.728588i −0.0374745 + 0.0374745i
$$379$$ 30.6895 1.57641 0.788206 0.615412i $$-0.211010\pi$$
0.788206 + 0.615412i $$0.211010\pi$$
$$380$$ 1.06234 + 9.68873i 0.0544971 + 0.497021i
$$381$$ −13.2342 −0.678009
$$382$$ 10.5111 10.5111i 0.537797 0.537797i
$$383$$ −6.71232 6.71232i −0.342983 0.342983i 0.514504 0.857488i $$-0.327976\pi$$
−0.857488 + 0.514504i $$0.827976\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ −10.9277 + 1.82090i −0.556926 + 0.0928017i
$$386$$ 7.13657 0.363242
$$387$$ −3.04079 3.04079i −0.154572 0.154572i
$$388$$ 2.81665 + 2.81665i 0.142994 + 0.142994i
$$389$$ 1.69598i 0.0859894i 0.999075 + 0.0429947i $$0.0136899\pi$$
−0.999075 + 0.0429947i $$0.986310\pi$$
$$390$$ −1.65786 + 0.276253i −0.0839492 + 0.0139886i
$$391$$ 30.4335 1.53909
$$392$$ 4.19903 4.19903i 0.212083 0.212083i
$$393$$ 8.92844 + 8.92844i 0.450380 + 0.450380i
$$394$$ 10.8358 0.545901
$$395$$ 3.60127 5.04142i 0.181199 0.253661i
$$396$$ −4.80832 −0.241627
$$397$$ −17.6346 17.6346i −0.885057 0.885057i 0.108986 0.994043i $$-0.465240\pi$$
−0.994043 + 0.108986i $$0.965240\pi$$
$$398$$ −14.7999 14.7999i −0.741851 0.741851i
$$399$$ 3.34833 2.99343i 0.167626 0.149859i
$$400$$ 1.62130 + 4.72984i 0.0810651 + 0.236492i
$$401$$ 1.30146i 0.0649918i −0.999472 0.0324959i $$-0.989654\pi$$
0.999472 0.0324959i $$-0.0103456\pi$$
$$402$$ 9.19128 9.19128i 0.458420 0.458420i
$$403$$ −4.58311 + 4.58311i −0.228301 + 0.228301i
$$404$$ 14.0592i 0.699470i
$$405$$ 1.29975 1.81952i 0.0645851 0.0904126i
$$406$$ −0.509852 −0.0253035
$$407$$ 26.3417 26.3417i 1.30571 1.30571i
$$408$$ 3.72984 3.72984i 0.184655 0.184655i
$$409$$ 18.8682 0.932971 0.466485 0.884529i $$-0.345520\pi$$
0.466485 + 0.884529i $$0.345520\pi$$
$$410$$ 12.8491 2.14107i 0.634572 0.105740i
$$411$$ 0.535560i 0.0264172i
$$412$$ 6.63327 6.63327i 0.326798 0.326798i
$$413$$ −8.83828 8.83828i −0.434903 0.434903i
$$414$$ 5.76961 0.283561
$$415$$ −1.85958 11.1598i −0.0912831 0.547813i
$$416$$ −0.751642 −0.0368523
$$417$$ −16.1179 + 16.1179i −0.789298 + 0.789298i
$$418$$ 20.9262 + 1.17107i 1.02354 + 0.0572791i
$$419$$ 20.1568i 0.984725i 0.870390 + 0.492363i $$0.163867\pi$$
−0.870390 + 0.492363i $$0.836133\pi$$
$$420$$ 1.33924 1.87480i 0.0653480 0.0914806i
$$421$$ 8.85286i 0.431462i 0.976453 + 0.215731i $$0.0692134\pi$$
−0.976453 + 0.215731i $$0.930787\pi$$
$$422$$ 19.5436 + 19.5436i 0.951366 + 0.951366i
$$423$$ −0.910451 + 0.910451i −0.0442676 + 0.0442676i
$$424$$ 4.99593i 0.242624i
$$425$$ −11.5943 + 23.6887i −0.562408 + 1.14907i
$$426$$ 2.06076i 0.0998441i
$$427$$ 3.87914 + 3.87914i 0.187725 + 0.187725i
$$428$$ 1.54262 + 1.54262i 0.0745656 + 0.0745656i
$$429$$ 3.61413i 0.174492i
$$430$$ 7.82453 + 5.58935i 0.377332 + 0.269542i
$$431$$ 25.3047i 1.21889i 0.792830 + 0.609443i $$0.208607\pi$$
−0.792830 + 0.609443i $$0.791393\pi$$
$$432$$ 0.707107 0.707107i 0.0340207 0.0340207i
$$433$$ 6.00560 + 6.00560i 0.288611 + 0.288611i 0.836531 0.547920i $$-0.184580\pi$$
−0.547920 + 0.836531i $$0.684580\pi$$
$$434$$ 8.88509i 0.426498i
$$435$$ 1.09140 0.181862i 0.0523287 0.00871963i
$$436$$ 18.4286i 0.882569i
$$437$$ −25.1099 1.40520i −1.20117 0.0672198i
$$438$$ −3.31160 + 3.31160i −0.158234 + 0.158234i
$$439$$ −38.4260 −1.83397 −0.916986 0.398919i $$-0.869386\pi$$
−0.916986 + 0.398919i $$0.869386\pi$$
$$440$$ 10.6055 1.76721i 0.505597 0.0842486i
$$441$$ 5.93832 0.282777
$$442$$ −2.80350 2.80350i −0.133349 0.133349i
$$443$$ 27.7457 27.7457i 1.31824 1.31824i 0.403066 0.915171i $$-0.367945\pi$$
0.915171 0.403066i $$-0.132055\pi$$
$$444$$ 7.74758i 0.367684i
$$445$$ 1.41191 1.97654i 0.0669311 0.0936969i
$$446$$ −11.3784 −0.538781
$$447$$ −11.2289 + 11.2289i −0.531109 + 0.531109i
$$448$$ 0.728588 0.728588i 0.0344226 0.0344226i
$$449$$ 28.1598 1.32894 0.664472 0.747313i $$-0.268656\pi$$
0.664472 + 0.747313i $$0.268656\pi$$
$$450$$ −2.19807 + 4.49094i −0.103618 + 0.211705i
$$451$$ 28.0110i 1.31899i
$$452$$ 5.25913 5.25913i 0.247369 0.247369i
$$453$$ −9.44035 + 9.44035i −0.443546 + 0.443546i
$$454$$ 2.80480i 0.131636i
$$455$$ −1.40917 1.00663i −0.0660631 0.0471913i
$$456$$ −3.24961 + 2.90517i −0.152177 + 0.136047i
$$457$$ −19.5575 19.5575i −0.914859 0.914859i 0.0817904 0.996650i $$-0.473936\pi$$
−0.996650 + 0.0817904i $$0.973936\pi$$
$$458$$ 13.8906 + 13.8906i 0.649066 + 0.649066i
$$459$$ 5.27479 0.246206
$$460$$ −12.7258 + 2.12052i −0.593342 + 0.0988698i
$$461$$ 9.61570 0.447848 0.223924 0.974607i $$-0.428113\pi$$
0.223924 + 0.974607i $$0.428113\pi$$
$$462$$ −3.50328 3.50328i −0.162988 0.162988i
$$463$$ 16.6735 16.6735i 0.774882 0.774882i −0.204074 0.978956i $$-0.565418\pi$$
0.978956 + 0.204074i $$0.0654182\pi$$
$$464$$ 0.494819 0.0229714
$$465$$ 3.16928 + 19.0196i 0.146972 + 0.882015i
$$466$$ 6.70326i 0.310523i
$$467$$ −17.1190 17.1190i −0.792171 0.792171i 0.189676 0.981847i $$-0.439256\pi$$
−0.981847 + 0.189676i $$0.939256\pi$$
$$468$$ −0.531491 0.531491i −0.0245682 0.0245682i
$$469$$ 13.3933 0.618446
$$470$$ 1.67352 2.34276i 0.0771938 0.108064i
$$471$$ 16.5988i 0.764834i
$$472$$ 8.57770 + 8.57770i 0.394820 + 0.394820i
$$473$$ 14.6211 14.6211i 0.672278 0.672278i
$$474$$ 2.77074 0.127264
$$475$$ 10.6600 19.0096i 0.489113 0.872221i
$$476$$ 5.43503 0.249114
$$477$$ 3.53266 3.53266i 0.161749 0.161749i
$$478$$ 14.9801 + 14.9801i 0.685176 + 0.685176i
$$479$$ 14.2801i 0.652474i 0.945288 + 0.326237i $$0.105781\pi$$
−0.945288 + 0.326237i $$0.894219\pi$$
$$480$$ −1.29975 + 1.81952i −0.0593252 + 0.0830493i
$$481$$ 5.82340 0.265524
$$482$$ 11.5106 + 11.5106i 0.524293 + 0.524293i
$$483$$ 4.20367 + 4.20367i 0.191274 + 0.191274i
$$484$$ 12.1199i 0.550905i
$$485$$ −1.46401 8.78590i −0.0664774 0.398947i
$$486$$ 1.00000 0.0453609
$$487$$ −13.6790 + 13.6790i −0.619856 + 0.619856i −0.945494 0.325639i $$-0.894421\pi$$
0.325639 + 0.945494i $$0.394421\pi$$
$$488$$ −3.76477 3.76477i −0.170423 0.170423i
$$489$$ −1.39819 −0.0632282
$$490$$ −13.0979 + 2.18253i −0.591702 + 0.0985965i
$$491$$ 6.60655 0.298150 0.149075 0.988826i $$-0.452370\pi$$
0.149075 + 0.988826i $$0.452370\pi$$
$$492$$ 4.11927 + 4.11927i 0.185711 + 0.185711i
$$493$$ 1.84560 + 1.84560i 0.0831215 + 0.0831215i
$$494$$ 2.18365 + 2.44254i 0.0982471 + 0.109895i
$$495$$ 8.74883 + 6.24961i 0.393231 + 0.280899i
$$496$$ 8.62312i 0.387190i
$$497$$ 1.50144 1.50144i 0.0673490 0.0673490i
$$498$$ 3.57770 3.57770i 0.160320 0.160320i
$$499$$ 35.7269i 1.59935i 0.600430 + 0.799677i $$0.294996\pi$$
−0.600430 + 0.799677i $$0.705004\pi$$
$$500$$ 3.19762 10.7133i 0.143002 0.479114i
$$501$$ −10.5017 −0.469182
$$502$$ −3.71225 + 3.71225i −0.165686 + 0.165686i
$$503$$ −8.52003 + 8.52003i −0.379889 + 0.379889i −0.871062 0.491173i $$-0.836568\pi$$
0.491173 + 0.871062i $$0.336568\pi$$
$$504$$ 1.03038 0.0458967
$$505$$ 18.2734 25.5809i 0.813156 1.13834i
$$506$$ 27.7421i 1.23329i
$$507$$ 8.79290 8.79290i 0.390506 0.390506i
$$508$$ 9.35800 + 9.35800i 0.415194 + 0.415194i
$$509$$ −13.4408 −0.595753 −0.297877 0.954604i $$-0.596278\pi$$
−0.297877 + 0.954604i $$0.596278\pi$$
$$510$$ −11.6344 + 1.93866i −0.515179 + 0.0858452i
$$511$$ −4.82559 −0.213471
$$512$$ −0.707107 + 0.707107i −0.0312500 + 0.0312500i
$$513$$ −4.35209 0.243552i −0.192149 0.0107531i
$$514$$ 22.6727i 1.00005i
$$515$$ −20.6910 + 3.44777i −0.911752 + 0.151927i
$$516$$ 4.30033i 0.189311i
$$517$$ −4.37774 4.37774i −0.192533 0.192533i
$$518$$ −5.64479 + 5.64479i −0.248018 + 0.248018i
$$519$$ 15.6216i 0.685714i
$$520$$ 1.36763 + 0.976946i 0.0599744 + 0.0428419i
$$521$$ 13.5544i 0.593831i 0.954904 + 0.296916i $$0.0959580\pi$$
−0.954904 + 0.296916i $$0.904042\pi$$
$$522$$ 0.349890 + 0.349890i 0.0153143 + 0.0153143i
$$523$$ 5.40357 + 5.40357i 0.236282 + 0.236282i 0.815308 0.579027i $$-0.196567\pi$$
−0.579027 + 0.815308i $$0.696567\pi$$
$$524$$ 12.6267i 0.551601i
$$525$$ −4.87353 + 1.67056i −0.212698 + 0.0729090i
$$526$$ 8.41456i 0.366892i
$$527$$ −32.1629 + 32.1629i −1.40104 + 1.40104i
$$528$$ 3.39999 + 3.39999i 0.147966 + 0.147966i
$$529$$ 10.2884i 0.447321i
$$530$$ −6.49346 + 9.09020i −0.282058 + 0.394853i
$$531$$ 12.1307i 0.526427i
$$532$$ −4.48430 0.250951i −0.194419 0.0108801i
$$533$$ 3.09622 3.09622i 0.134112 0.134112i
$$534$$ 1.08630 0.0470087
$$535$$ −0.801810 4.81186i −0.0346653 0.208035i
$$536$$ −12.9984 −0.561447
$$537$$ 13.4651 + 13.4651i 0.581062 + 0.581062i
$$538$$ 18.5884 18.5884i 0.801404 0.801404i
$$539$$ 28.5533i 1.22988i
$$540$$ −2.20566 + 0.367533i −0.0949163 + 0.0158161i
$$541$$ 7.68488 0.330399 0.165200 0.986260i $$-0.447173\pi$$
0.165200 + 0.986260i $$0.447173\pi$$
$$542$$ 8.43702 8.43702i 0.362401 0.362401i
$$543$$ 1.25943 1.25943i 0.0540473 0.0540473i
$$544$$ −5.27479 −0.226155
$$545$$ −23.9525 + 33.5312i −1.02601 + 1.43632i
$$546$$ 0.774476i 0.0331445i
$$547$$ −17.8604 + 17.8604i −0.763656 + 0.763656i −0.976981 0.213325i $$-0.931571\pi$$
0.213325 + 0.976981i $$0.431571\pi$$
$$548$$ 0.378698 0.378698i 0.0161772 0.0161772i
$$549$$ 5.32419i 0.227231i
$$550$$ −21.5938 10.5690i −0.920765 0.450664i
$$551$$ −1.43754 1.60797i −0.0612411 0.0685018i
$$552$$ −4.07973 4.07973i −0.173645 0.173645i
$$553$$ 2.01873 + 2.01873i 0.0858451 + 0.0858451i
$$554$$ 18.6596 0.792771
$$555$$ 10.0699 14.0969i 0.427444 0.598379i
$$556$$ 22.7942 0.966688
$$557$$ 12.5198 + 12.5198i 0.530480 + 0.530480i 0.920715 0.390235i $$-0.127606\pi$$
−0.390235 + 0.920715i $$0.627606\pi$$
$$558$$ −6.09747 + 6.09747i −0.258126 + 0.258126i
$$559$$ 3.23231 0.136712
$$560$$ −2.27266 + 0.378698i −0.0960375 + 0.0160029i
$$561$$ 25.3629i 1.07082i
$$562$$ 18.0180 + 18.0180i 0.760045 + 0.760045i
$$563$$ 11.0759 + 11.0759i 0.466791 + 0.466791i 0.900873 0.434082i $$-0.142927\pi$$
−0.434082 + 0.900873i $$0.642927\pi$$
$$564$$ 1.28757 0.0542165
$$565$$ −16.4046 + 2.73354i −0.690149 + 0.115001i
$$566$$ 21.1355i 0.888392i
$$567$$ 0.728588 + 0.728588i 0.0305978 + 0.0305978i
$$568$$ −1.45718 + 1.45718i −0.0611418 + 0.0611418i
$$569$$ −43.4414 −1.82116 −0.910579 0.413336i $$-0.864364\pi$$
−0.910579 + 0.413336i $$0.864364\pi$$
$$570$$ 9.68873 1.06234i 0.405816 0.0444967i
$$571$$ 15.6768 0.656052 0.328026 0.944669i $$-0.393617\pi$$
0.328026 + 0.944669i $$0.393617\pi$$
$$572$$ 2.55558 2.55558i 0.106854 0.106854i
$$573$$ −10.5111 10.5111i −0.439109 0.439109i
$$574$$ 6.00250i 0.250540i
$$575$$ 25.9109 + 12.6820i 1.08056 + 0.528876i
$$576$$ −1.00000 −0.0416667
$$577$$ 6.59569 + 6.59569i 0.274582 + 0.274582i 0.830942 0.556359i $$-0.187802\pi$$
−0.556359 + 0.830942i $$0.687802\pi$$
$$578$$ −7.65330 7.65330i −0.318335 0.318335i
$$579$$ 7.13657i 0.296586i
$$580$$ −0.900333 0.643141i −0.0373843 0.0267050i
$$581$$ 5.21334 0.216286
$$582$$ 2.81665 2.81665i 0.116754 0.116754i
$$583$$ 16.9861 + 16.9861i 0.703494 + 0.703494i
$$584$$ 4.68331 0.193797
$$585$$ 0.276253 + 1.65786i 0.0114217 + 0.0685442i
$$586$$ 27.3491 1.12978
$$587$$ −23.8623 23.8623i −0.984904 0.984904i 0.0149835 0.999888i $$-0.495230\pi$$
−0.999888 + 0.0149835i $$0.995230\pi$$
$$588$$ −4.19903 4.19903i −0.173165 0.173165i
$$589$$ 28.0218 25.0517i 1.15462 1.03224i
$$590$$ −4.45843 26.7561i −0.183551 1.10153i
$$591$$ 10.8358i 0.445727i
$$592$$ 5.47836 5.47836i 0.225159 0.225159i
$$593$$ 22.7988 22.7988i 0.936236 0.936236i −0.0618495 0.998085i $$-0.519700\pi$$
0.998085 + 0.0618495i $$0.0196999\pi$$
$$594$$ 4.80832i 0.197288i
$$595$$ −9.88915 7.06418i −0.405416 0.289603i
$$596$$ 15.8801 0.650473
$$597$$ −14.7999 + 14.7999i −0.605719 + 0.605719i
$$598$$ −3.06650 + 3.06650i −0.125398 + 0.125398i
$$599$$ −11.4248 −0.466805 −0.233402 0.972380i $$-0.574986\pi$$
−0.233402 + 0.972380i $$0.574986\pi$$
$$600$$ 4.72984 1.62130i 0.193095 0.0661894i
$$601$$ 7.14156i 0.291310i −0.989335 0.145655i $$-0.953471\pi$$
0.989335 0.145655i $$-0.0465290\pi$$
$$602$$ −3.13317 + 3.13317i −0.127698 + 0.127698i
$$603$$ −9.19128 9.19128i −0.374298 0.374298i
$$604$$ 13.3507 0.543231
$$605$$ −15.7529 + 22.0524i −0.640445 + 0.896559i
$$606$$ 14.0592 0.571115
$$607$$ 6.44190 6.44190i 0.261469 0.261469i −0.564182 0.825651i $$-0.690808\pi$$
0.825651 + 0.564182i $$0.190808\pi$$
$$608$$ 4.35209 + 0.243552i 0.176501 + 0.00987733i
$$609$$ 0.509852i 0.0206602i
$$610$$ 1.95681 + 11.7433i 0.0792290 + 0.475473i
$$611$$ 0.967793i 0.0391527i
$$612$$ −3.72984 3.72984i −0.150770 0.150770i
$$613$$ −21.1379 + 21.1379i −0.853752 + 0.853752i −0.990593 0.136841i $$-0.956305\pi$$
0.136841 + 0.990593i $$0.456305\pi$$
$$614$$ 0.00500438i 0.000201960i
$$615$$ −2.14107 12.8491i −0.0863363 0.518126i
$$616$$ 4.95439i 0.199618i
$$617$$ −9.52678 9.52678i −0.383534 0.383534i 0.488840 0.872373i $$-0.337420\pi$$
−0.872373 + 0.488840i $$0.837420\pi$$
$$618$$ −6.63327 6.63327i −0.266829 0.266829i
$$619$$ 6.57762i 0.264377i −0.991225 0.132188i $$-0.957800\pi$$
0.991225 0.132188i $$-0.0422004\pi$$
$$620$$ 11.2079 15.6899i 0.450120 0.630123i
$$621$$ 5.76961i 0.231526i
$$622$$ 8.26782 8.26782i 0.331509 0.331509i
$$623$$ 0.791463 + 0.791463i 0.0317093 + 0.0317093i
$$624$$ 0.751642i 0.0300898i
$$625$$ −19.7428 + 15.3370i −0.789710 + 0.613480i
$$626$$ 23.5732i 0.942174i
$$627$$ 1.17107 20.9262i 0.0467682 0.835713i
$$628$$ 11.7372 11.7372i 0.468363 0.468363i
$$629$$ 40.8668 1.62947
$$630$$ −1.87480 1.33924i −0.0746936 0.0533564i
$$631$$ −17.0875 −0.680241 −0.340121 0.940382i $$-0.610468\pi$$
−0.340121 + 0.940382i $$0.610468\pi$$
$$632$$ −1.95921 1.95921i −0.0779332 0.0779332i
$$633$$ 19.5436 19.5436i 0.776787 0.776787i
$$634$$ 9.85335i 0.391327i
$$635$$ −4.86401 29.1901i −0.193022 1.15837i
$$636$$ −4.99593 −0.198102
$$637$$ −3.15616 + 3.15616i −0.125052 + 0.125052i
$$638$$ −1.68238 + 1.68238i −0.0666062 + 0.0666062i
$$639$$ −2.06076 −0.0815224
$$640$$ 2.20566 0.367533i 0.0871862 0.0145280i
$$641$$ 46.7376i 1.84602i 0.384773 + 0.923011i $$0.374280\pi$$
−0.384773 + 0.923011i $$0.625720\pi$$
$$642$$ 1.54262 1.54262i 0.0608825 0.0608825i
$$643$$ −7.16897 + 7.16897i −0.282717 + 0.282717i −0.834191 0.551475i $$-0.814065\pi$$
0.551475 + 0.834191i $$0.314065\pi$$
$$644$$ 5.94489i 0.234261i
$$645$$ 5.58935 7.82453i 0.220080 0.308091i
$$646$$ 15.3242 + 17.1410i 0.602922 + 0.674404i
$$647$$ −6.19558 6.19558i −0.243574 0.243574i 0.574753 0.818327i $$-0.305098\pi$$
−0.818327 + 0.574753i $$0.805098\pi$$
$$648$$ −0.707107 0.707107i −0.0277778 0.0277778i
$$649$$ −58.3282 −2.28958
$$650$$ −1.21864 3.55515i −0.0477989 0.139444i
$$651$$ −8.88509 −0.348234
$$652$$ 0.988668 + 0.988668i 0.0387192 + 0.0387192i
$$653$$ 17.2336 17.2336i 0.674401 0.674401i −0.284326 0.958728i $$-0.591770\pi$$
0.958728 + 0.284326i $$0.0917699\pi$$
$$654$$ −18.4286 −0.720614
$$655$$ −16.4116 + 22.9746i −0.641253 + 0.897690i
$$656$$ 5.82553i 0.227449i
$$657$$ 3.31160 + 3.31160i 0.129198 + 0.129198i
$$658$$ 0.938110 + 0.938110i 0.0365713 + 0.0365713i
$$659$$ −21.6005 −0.841436 −0.420718 0.907191i $$-0.638222\pi$$
−0.420718 + 0.907191i $$0.638222\pi$$
$$660$$ −1.76721 10.6055i −0.0687887 0.412818i
$$661$$ 1.49297i 0.0580696i −0.999578 0.0290348i $$-0.990757\pi$$
0.999578 0.0290348i $$-0.00924337\pi$$
$$662$$ −8.65367 8.65367i −0.336335 0.336335i
$$663$$ −2.80350 + 2.80350i −0.108879 + 0.108879i
$$664$$ −5.05963 −0.196352
$$665$$ 7.83310 + 6.28508i 0.303755 + 0.243725i
$$666$$ 7.74758 0.300212
$$667$$ 2.01873 2.01873i 0.0781655 0.0781655i
$$668$$ 7.42584 + 7.42584i 0.287314 + 0.287314i
$$669$$ 11.3784i 0.439913i
$$670$$ 23.6509 + 16.8947i 0.913714 + 0.652700i
$$671$$ 25.6004 0.988291
$$672$$ −0.728588 0.728588i −0.0281059 0.0281059i
$$673$$ −8.49705 8.49705i −0.327537 0.327537i 0.524112 0.851649i $$-0.324397\pi$$
−0.851649 + 0.524112i $$0.824397\pi$$
$$674$$ 26.8584i 1.03455i
$$675$$ 4.49094 + 2.19807i 0.172856 + 0.0846037i
$$676$$ −12.4350 −0.478271
$$677$$ −5.92660 + 5.92660i −0.227778 + 0.227778i −0.811764 0.583986i $$-0.801492\pi$$
0.583986 + 0.811764i $$0.301492\pi$$
$$678$$ −5.25913 5.25913i −0.201976 0.201976i
$$679$$ 4.10436 0.157511
$$680$$ 9.59758 + 6.85591i 0.368050 + 0.262912i
$$681$$ 2.80480 0.107480
$$682$$ −29.3186 29.3186i −1.12267 1.12267i
$$683$$ 26.3647 + 26.3647i 1.00882 + 1.00882i 0.999961 + 0.00885484i $$0.00281862\pi$$
0.00885484 + 0.999961i $$0.497181\pi$$
$$684$$ 2.90517 + 3.24961i 0.111082 + 0.124252i
$$685$$ −1.18126 + 0.196836i −0.0451337 + 0.00752071i
$$686$$ 13.3314i 0.508994i
$$687$$ 13.8906 13.8906i 0.529960 0.529960i
$$688$$ 3.04079 3.04079i 0.115929 0.115929i
$$689$$ 3.75515i 0.143060i
$$690$$ 2.12052 + 12.7258i 0.0807268 + 0.484462i
$$691$$ 19.3186 0.734913 0.367456 0.930041i $$-0.380229\pi$$
0.367456 + 0.930041i $$0.380229\pi$$
$$692$$ −11.0462 + 11.0462i −0.419912 + 0.419912i
$$693$$ −3.50328 + 3.50328i −0.133079 + 0.133079i
$$694$$ −2.14291 −0.0813438
$$695$$ −41.4744 29.6267i −1.57322 1.12381i
$$696$$ 0.494819i 0.0187561i
$$697$$ 21.7283 21.7283i 0.823017 0.823017i
$$698$$ −15.0710 15.0710i −0.570444 0.570444i
$$699$$ −6.70326 −0.253541
$$700$$ 4.62737 + 2.26484i 0.174898 + 0.0856031i
$$701$$ 8.82340 0.333255 0.166628 0.986020i $$-0.446712\pi$$
0.166628 + 0.986020i $$0.446712\pi$$
$$702$$ −0.531491 + 0.531491i −0.0200598 + 0.0200598i
$$703$$ −33.7181 1.88694i −1.27170 0.0711672i
$$704$$ 4.80832i 0.181220i
$$705$$ −2.34276 1.67352i −0.0882335 0.0630284i
$$706$$ 13.2577i 0.498961i
$$707$$ 10.2434 + 10.2434i 0.385241 + 0.385241i
$$708$$ 8.57770 8.57770i 0.322370 0.322370i
$$709$$ 1.20583i 0.0452859i 0.999744 + 0.0226429i $$0.00720808\pi$$
−0.999744 + 0.0226429i $$0.992792\pi$$
$$710$$ 4.54533 0.757396i 0.170583 0.0284246i
$$711$$ 2.77074i 0.103911i
$$712$$ −0.768128 0.768128i −0.0287868 0.0287868i
$$713$$ 35.1800 + 35.1800i 1.31750 + 1.31750i
$$714$$ 5.43503i 0.203401i
$$715$$ −7.97154 + 1.32831i −0.298119 + 0.0496761i
$$716$$ 19.0425i 0.711652i
$$717$$ 14.9801 14.9801i 0.559443 0.559443i
$$718$$ 21.2987 + 21.2987i 0.794861 + 0.794861i
$$719$$ 9.38938i 0.350165i 0.984554 + 0.175082i $$0.0560192\pi$$
−0.984554 + 0.175082i $$0.943981\pi$$
$$720$$ 1.81952 + 1.29975i 0.0678095 + 0.0484388i
$$721$$ 9.66585i 0.359975i
$$722$$ −11.8521 14.8502i −0.441091 0.552665i
$$723$$ 11.5106 11.5106i 0.428084 0.428084i
$$724$$ −1.78110 −0.0661941
$$725$$ 0.802251 + 2.34042i 0.0297949 + 0.0869209i
$$726$$ −12.1199 −0.449812
$$727$$ −17.4688 17.4688i −0.647884 0.647884i 0.304597 0.952481i $$-0.401478\pi$$
−0.952481 + 0.304597i $$0.901478\pi$$
$$728$$ −0.547637 + 0.547637i −0.0202968 + 0.0202968i
$$729$$ 1.00000i 0.0370370i
$$730$$ −8.52138 6.08713i −0.315390 0.225295i
$$731$$ 22.6833 0.838973
$$732$$ −3.76477 + 3.76477i −0.139150 + 0.139150i
$$733$$ 13.1840 13.1840i 0.486963 0.486963i −0.420383 0.907347i $$-0.638104\pi$$
0.907347 + 0.420383i $$0.138104\pi$$
$$734$$ 14.2815 0.527140
$$735$$ 2.18253 + 13.0979i 0.0805037 + 0.483123i
$$736$$ 5.76961i 0.212671i
$$737$$ 44.1946 44.1946i 1.62793 1.62793i
$$738$$ 4.11927 4.11927i 0.151632 0.151632i
$$739$$ 47.8710i 1.76096i −0.474080 0.880482i $$-0.657219\pi$$
0.474080 0.880482i $$-0.342781\pi$$
$$740$$ −17.0885 + 2.84749i −0.628185 + 0.104676i
$$741$$ 2.44254 2.18365i 0.0897290 0.0802184i
$$742$$ −3.63998 3.63998i −0.133628 0.133628i
$$743$$ 19.4260 + 19.4260i 0.712670 + 0.712670i 0.967093 0.254423i $$-0.0818855\pi$$
−0.254423 + 0.967093i $$0.581886\pi$$
$$744$$ 8.62312 0.316139
$$745$$ −28.8941 20.6401i −1.05860 0.756196i
$$746$$ −16.3708 −0.599377
$$747$$ −3.57770 3.57770i −0.130901 0.130901i
$$748$$ 17.9343 17.9343i 0.655741 0.655741i
$$749$$ 2.24788 0.0821356
$$750$$ −10.7133 3.19762i −0.391195 0.116760i
$$751$$ 23.5009i 0.857559i −0.903409 0.428779i $$-0.858944\pi$$
0.903409 0.428779i $$-0.141056\pi$$
$$752$$ −0.910451 0.910451i −0.0332007 0.0332007i
$$753$$ 3.71225 + 3.71225i 0.135282 + 0.135282i
$$754$$ −0.371927 −0.0135448
$$755$$ −24.2918 17.3525i −0.884069 0.631523i
$$756$$ 1.03038i 0.0374745i
$$757$$ 19.2062 + 19.2062i 0.698060 + 0.698060i 0.963992 0.265932i $$-0.0856796\pi$$
−0.265932 + 0.963992i $$0.585680\pi$$
$$758$$ −21.7007 + 21.7007i −0.788206 + 0.788206i
$$759$$ 27.7421 1.00697
$$760$$ −7.60215 6.09977i −0.275759 0.221262i
$$761$$ −23.7982 −0.862685 −0.431343 0.902188i $$-0.641960\pi$$
−0.431343 + 0.902188i $$0.641960\pi$$
$$762$$ 9.35800 9.35800i 0.339005 0.339005i
$$763$$ −13.4268 13.4268i −0.486084 0.486084i
$$764$$ 14.8650i 0.537797i
$$765$$ 1.93866 + 11.6344i 0.0700923 + 0.420642i
$$766$$ 9.49265 0.342983
$$767$$ −6.44736 6.44736i −0.232801 0.232801i
$$768$$ 0.707107 + 0.707107i 0.0255155 + 0.0255155i
$$769$$ 28.9884i 1.04535i 0.852532 + 0.522675i $$0.175066\pi$$
−0.852532 + 0.522675i $$0.824934\pi$$
$$770$$ 6.43947 9.01461i 0.232062 0.324864i
$$771$$ 22.6727 0.816537
$$772$$ −5.04632 + 5.04632i −0.181621 + 0.181621i
$$773$$ 29.2365 + 29.2365i 1.05156 + 1.05156i 0.998596 + 0.0529667i $$0.0168677\pi$$
0.0529667 + 0.998596i $$0.483132\pi$$
$$774$$ 4.30033 0.154572
$$775$$ −40.7860 + 13.9807i −1.46508 + 0.502201i
$$776$$ −3.98335 −0.142994
$$777$$ 5.64479 + 5.64479i 0.202506 + 0.202506i
$$778$$ −1.19924 1.19924i −0.0429947 0.0429947i