# Properties

 Label 78.3.l.b.19.1 Level $78$ Weight $3$ Character 78.19 Analytic conductor $2.125$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$78 = 2 \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 78.l (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.12534606201$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 19.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 78.19 Dual form 78.3.l.b.37.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.366025 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.633975 - 0.633975i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(3.26795 - 12.1962i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.09808 - 0.633975i) q^{10} +(-17.6603 + 4.73205i) q^{11} +3.46410i q^{12} +(11.2583 + 6.50000i) q^{13} -17.8564 q^{14} +(-0.401924 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(15.1865 - 8.76795i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(16.1962 + 4.33975i) q^{19} +(-0.464102 + 1.73205i) q^{20} +(-15.4641 - 15.4641i) q^{21} +(12.9282 + 22.3923i) q^{22} +(18.5885 + 10.7321i) q^{23} +(4.73205 - 1.26795i) q^{24} +24.1962i q^{25} +(4.75833 - 17.7583i) q^{26} -5.19615 q^{27} +(6.53590 + 24.3923i) q^{28} +(-19.3301 + 33.4808i) q^{29} +(-1.90192 + 1.09808i) q^{30} +(25.4641 - 25.4641i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-8.19615 + 30.5885i) q^{33} +(-17.5359 - 17.5359i) q^{34} +(-5.66025 - 9.80385i) q^{35} +(5.19615 + 3.00000i) q^{36} +(2.96410 - 0.794229i) q^{37} -23.7128i q^{38} +(19.5000 - 11.2583i) q^{39} +2.53590 q^{40} +(7.91858 + 29.5526i) q^{41} +(-15.4641 + 26.7846i) q^{42} +(-15.3731 + 8.87564i) q^{43} +(25.8564 - 25.8564i) q^{44} +(-2.59808 - 0.696152i) q^{45} +(7.85641 - 29.3205i) q^{46} +(-30.0000 - 30.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-95.6314 - 55.2128i) q^{49} +(33.0526 - 8.85641i) q^{50} -30.3731i q^{51} -26.0000 q^{52} -23.1051 q^{53} +(1.90192 + 7.09808i) q^{54} +(-8.19615 + 14.1962i) q^{55} +(30.9282 - 17.8564i) q^{56} +(20.5359 - 20.5359i) q^{57} +(52.8109 + 14.1506i) q^{58} +(5.50258 - 20.5359i) q^{59} +(2.19615 + 2.19615i) q^{60} +(21.1077 + 36.5596i) q^{61} +(-44.1051 - 25.4641i) q^{62} +(-36.5885 + 9.80385i) q^{63} +8.00000i q^{64} +(11.2583 - 3.01666i) q^{65} +44.7846 q^{66} +(-8.48334 - 31.6603i) q^{67} +(-17.5359 + 30.3731i) q^{68} +(32.1962 - 18.5885i) q^{69} +(-11.3205 + 11.3205i) q^{70} +(33.1244 + 8.87564i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-15.9212 - 15.9212i) q^{73} +(-2.16987 - 3.75833i) q^{74} +(36.2942 + 20.9545i) q^{75} +(-32.3923 + 8.67949i) q^{76} +230.851i q^{77} +(-22.5167 - 22.5167i) q^{78} -89.5692 q^{79} +(-0.928203 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(37.4711 - 21.6340i) q^{82} +(97.4256 - 97.4256i) q^{83} +(42.2487 + 11.3205i) q^{84} +(4.06922 - 15.1865i) q^{85} +(17.7513 + 17.7513i) q^{86} +(33.4808 + 57.9904i) q^{87} +(-44.7846 - 25.8564i) q^{88} +(1.22243 - 0.327550i) q^{89} +3.80385i q^{90} +(116.067 - 116.067i) q^{91} -42.9282 q^{92} +(-16.1436 - 60.2487i) q^{93} +(-30.0000 + 51.9615i) q^{94} +(13.0192 - 7.51666i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-49.3660 - 13.2276i) q^{97} +(-40.4186 + 150.844i) q^{98} +(38.7846 + 38.7846i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10})$$ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 $$4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9} + 6 q^{10} - 36 q^{11} - 16 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} - 12 q^{18} + 44 q^{19} + 12 q^{20} - 48 q^{21} + 24 q^{22} + 12 q^{23} + 12 q^{24} - 26 q^{26} + 40 q^{28} - 60 q^{29} - 18 q^{30} + 88 q^{31} - 8 q^{32} - 12 q^{33} - 84 q^{34} + 12 q^{35} - 2 q^{37} + 78 q^{39} + 24 q^{40} - 48 q^{41} - 48 q^{42} + 84 q^{43} + 48 q^{44} - 24 q^{46} - 120 q^{47} - 192 q^{49} + 56 q^{50} - 104 q^{52} + 60 q^{53} + 18 q^{54} - 12 q^{55} + 96 q^{56} + 96 q^{57} + 90 q^{58} + 216 q^{59} - 12 q^{60} + 126 q^{61} - 24 q^{62} - 84 q^{63} + 96 q^{66} - 124 q^{67} - 84 q^{68} + 108 q^{69} + 24 q^{70} + 84 q^{71} - 12 q^{72} - 178 q^{73} - 26 q^{74} + 114 q^{75} - 88 q^{76} - 192 q^{79} + 24 q^{80} - 18 q^{81} - 6 q^{82} + 168 q^{83} + 72 q^{84} - 150 q^{85} + 168 q^{86} + 30 q^{87} - 96 q^{88} - 54 q^{89} + 104 q^{91} - 144 q^{92} - 120 q^{93} - 120 q^{94} + 156 q^{95} - 194 q^{97} - 82 q^{98} + 72 q^{99}+O(q^{100})$$ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 + 6 * q^10 - 36 * q^11 - 16 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 - 12 * q^18 + 44 * q^19 + 12 * q^20 - 48 * q^21 + 24 * q^22 + 12 * q^23 + 12 * q^24 - 26 * q^26 + 40 * q^28 - 60 * q^29 - 18 * q^30 + 88 * q^31 - 8 * q^32 - 12 * q^33 - 84 * q^34 + 12 * q^35 - 2 * q^37 + 78 * q^39 + 24 * q^40 - 48 * q^41 - 48 * q^42 + 84 * q^43 + 48 * q^44 - 24 * q^46 - 120 * q^47 - 192 * q^49 + 56 * q^50 - 104 * q^52 + 60 * q^53 + 18 * q^54 - 12 * q^55 + 96 * q^56 + 96 * q^57 + 90 * q^58 + 216 * q^59 - 12 * q^60 + 126 * q^61 - 24 * q^62 - 84 * q^63 + 96 * q^66 - 124 * q^67 - 84 * q^68 + 108 * q^69 + 24 * q^70 + 84 * q^71 - 12 * q^72 - 178 * q^73 - 26 * q^74 + 114 * q^75 - 88 * q^76 - 192 * q^79 + 24 * q^80 - 18 * q^81 - 6 * q^82 + 168 * q^83 + 72 * q^84 - 150 * q^85 + 168 * q^86 + 30 * q^87 - 96 * q^88 - 54 * q^89 + 104 * q^91 - 144 * q^92 - 120 * q^93 - 120 * q^94 + 156 * q^95 - 194 * q^97 - 82 * q^98 + 72 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$$.

 $$n$$ $$53$$ $$67$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.366025 1.36603i −0.183013 0.683013i
$$3$$ 0.866025 1.50000i 0.288675 0.500000i
$$4$$ −1.73205 + 1.00000i −0.433013 + 0.250000i
$$5$$ 0.633975 0.633975i 0.126795 0.126795i −0.640862 0.767656i $$-0.721423\pi$$
0.767656 + 0.640862i $$0.221423\pi$$
$$6$$ −2.36603 0.633975i −0.394338 0.105662i
$$7$$ 3.26795 12.1962i 0.466850 1.74231i −0.183833 0.982958i $$-0.558850\pi$$
0.650682 0.759350i $$-0.274483\pi$$
$$8$$ 2.00000 + 2.00000i 0.250000 + 0.250000i
$$9$$ −1.50000 2.59808i −0.166667 0.288675i
$$10$$ −1.09808 0.633975i −0.109808 0.0633975i
$$11$$ −17.6603 + 4.73205i −1.60548 + 0.430186i −0.946691 0.322143i $$-0.895597\pi$$
−0.658787 + 0.752330i $$0.728930\pi$$
$$12$$ 3.46410i 0.288675i
$$13$$ 11.2583 + 6.50000i 0.866025 + 0.500000i
$$14$$ −17.8564 −1.27546
$$15$$ −0.401924 1.50000i −0.0267949 0.100000i
$$16$$ 2.00000 3.46410i 0.125000 0.216506i
$$17$$ 15.1865 8.76795i 0.893325 0.515762i 0.0182967 0.999833i $$-0.494176\pi$$
0.875029 + 0.484071i $$0.160842\pi$$
$$18$$ −3.00000 + 3.00000i −0.166667 + 0.166667i
$$19$$ 16.1962 + 4.33975i 0.852429 + 0.228408i 0.658475 0.752603i $$-0.271202\pi$$
0.193954 + 0.981011i $$0.437869\pi$$
$$20$$ −0.464102 + 1.73205i −0.0232051 + 0.0866025i
$$21$$ −15.4641 15.4641i −0.736386 0.736386i
$$22$$ 12.9282 + 22.3923i 0.587646 + 1.01783i
$$23$$ 18.5885 + 10.7321i 0.808194 + 0.466611i 0.846328 0.532662i $$-0.178808\pi$$
−0.0381345 + 0.999273i $$0.512142\pi$$
$$24$$ 4.73205 1.26795i 0.197169 0.0528312i
$$25$$ 24.1962i 0.967846i
$$26$$ 4.75833 17.7583i 0.183013 0.683013i
$$27$$ −5.19615 −0.192450
$$28$$ 6.53590 + 24.3923i 0.233425 + 0.871154i
$$29$$ −19.3301 + 33.4808i −0.666556 + 1.15451i 0.312305 + 0.949982i $$0.398899\pi$$
−0.978861 + 0.204527i $$0.934434\pi$$
$$30$$ −1.90192 + 1.09808i −0.0633975 + 0.0366025i
$$31$$ 25.4641 25.4641i 0.821423 0.821423i −0.164889 0.986312i $$-0.552727\pi$$
0.986312 + 0.164889i $$0.0527267\pi$$
$$32$$ −5.46410 1.46410i −0.170753 0.0457532i
$$33$$ −8.19615 + 30.5885i −0.248368 + 0.926923i
$$34$$ −17.5359 17.5359i −0.515762 0.515762i
$$35$$ −5.66025 9.80385i −0.161722 0.280110i
$$36$$ 5.19615 + 3.00000i 0.144338 + 0.0833333i
$$37$$ 2.96410 0.794229i 0.0801109 0.0214656i −0.218541 0.975828i $$-0.570130\pi$$
0.298652 + 0.954362i $$0.403463\pi$$
$$38$$ 23.7128i 0.624021i
$$39$$ 19.5000 11.2583i 0.500000 0.288675i
$$40$$ 2.53590 0.0633975
$$41$$ 7.91858 + 29.5526i 0.193136 + 0.720794i 0.992741 + 0.120268i $$0.0383754\pi$$
−0.799605 + 0.600526i $$0.794958\pi$$
$$42$$ −15.4641 + 26.7846i −0.368193 + 0.637729i
$$43$$ −15.3731 + 8.87564i −0.357513 + 0.206410i −0.667989 0.744171i $$-0.732845\pi$$
0.310476 + 0.950581i $$0.399512\pi$$
$$44$$ 25.8564 25.8564i 0.587646 0.587646i
$$45$$ −2.59808 0.696152i −0.0577350 0.0154701i
$$46$$ 7.85641 29.3205i 0.170791 0.637402i
$$47$$ −30.0000 30.0000i −0.638298 0.638298i 0.311838 0.950135i $$-0.399056\pi$$
−0.950135 + 0.311838i $$0.899056\pi$$
$$48$$ −3.46410 6.00000i −0.0721688 0.125000i
$$49$$ −95.6314 55.2128i −1.95166 1.12679i
$$50$$ 33.0526 8.85641i 0.661051 0.177128i
$$51$$ 30.3731i 0.595550i
$$52$$ −26.0000 −0.500000
$$53$$ −23.1051 −0.435946 −0.217973 0.975955i $$-0.569944\pi$$
−0.217973 + 0.975955i $$0.569944\pi$$
$$54$$ 1.90192 + 7.09808i 0.0352208 + 0.131446i
$$55$$ −8.19615 + 14.1962i −0.149021 + 0.258112i
$$56$$ 30.9282 17.8564i 0.552289 0.318864i
$$57$$ 20.5359 20.5359i 0.360279 0.360279i
$$58$$ 52.8109 + 14.1506i 0.910533 + 0.243976i
$$59$$ 5.50258 20.5359i 0.0932640 0.348066i −0.903487 0.428617i $$-0.859001\pi$$
0.996751 + 0.0805505i $$0.0256678\pi$$
$$60$$ 2.19615 + 2.19615i 0.0366025 + 0.0366025i
$$61$$ 21.1077 + 36.5596i 0.346028 + 0.599338i 0.985540 0.169443i $$-0.0541970\pi$$
−0.639512 + 0.768781i $$0.720864\pi$$
$$62$$ −44.1051 25.4641i −0.711373 0.410711i
$$63$$ −36.5885 + 9.80385i −0.580769 + 0.155617i
$$64$$ 8.00000i 0.125000i
$$65$$ 11.2583 3.01666i 0.173205 0.0464102i
$$66$$ 44.7846 0.678555
$$67$$ −8.48334 31.6603i −0.126617 0.472541i 0.873275 0.487227i $$-0.161992\pi$$
−0.999892 + 0.0146863i $$0.995325\pi$$
$$68$$ −17.5359 + 30.3731i −0.257881 + 0.446663i
$$69$$ 32.1962 18.5885i 0.466611 0.269398i
$$70$$ −11.3205 + 11.3205i −0.161722 + 0.161722i
$$71$$ 33.1244 + 8.87564i 0.466540 + 0.125009i 0.484428 0.874831i $$-0.339028\pi$$
−0.0178882 + 0.999840i $$0.505694\pi$$
$$72$$ 2.19615 8.19615i 0.0305021 0.113835i
$$73$$ −15.9212 15.9212i −0.218098 0.218098i 0.589598 0.807697i $$-0.299286\pi$$
−0.807697 + 0.589598i $$0.799286\pi$$
$$74$$ −2.16987 3.75833i −0.0293226 0.0507882i
$$75$$ 36.2942 + 20.9545i 0.483923 + 0.279393i
$$76$$ −32.3923 + 8.67949i −0.426215 + 0.114204i
$$77$$ 230.851i 2.99807i
$$78$$ −22.5167 22.5167i −0.288675 0.288675i
$$79$$ −89.5692 −1.13379 −0.566894 0.823791i $$-0.691855\pi$$
−0.566894 + 0.823791i $$0.691855\pi$$
$$80$$ −0.928203 3.46410i −0.0116025 0.0433013i
$$81$$ −4.50000 + 7.79423i −0.0555556 + 0.0962250i
$$82$$ 37.4711 21.6340i 0.456965 0.263829i
$$83$$ 97.4256 97.4256i 1.17380 1.17380i 0.192507 0.981296i $$-0.438338\pi$$
0.981296 0.192507i $$-0.0616619\pi$$
$$84$$ 42.2487 + 11.3205i 0.502961 + 0.134768i
$$85$$ 4.06922 15.1865i 0.0478732 0.178665i
$$86$$ 17.7513 + 17.7513i 0.206410 + 0.206410i
$$87$$ 33.4808 + 57.9904i 0.384836 + 0.666556i
$$88$$ −44.7846 25.8564i −0.508916 0.293823i
$$89$$ 1.22243 0.327550i 0.0137352 0.00368033i −0.251945 0.967742i $$-0.581070\pi$$
0.265680 + 0.964061i $$0.414404\pi$$
$$90$$ 3.80385i 0.0422650i
$$91$$ 116.067 116.067i 1.27546 1.27546i
$$92$$ −42.9282 −0.466611
$$93$$ −16.1436 60.2487i −0.173587 0.647836i
$$94$$ −30.0000 + 51.9615i −0.319149 + 0.552782i
$$95$$ 13.0192 7.51666i 0.137045 0.0791227i
$$96$$ −6.92820 + 6.92820i −0.0721688 + 0.0721688i
$$97$$ −49.3660 13.2276i −0.508928 0.136367i −0.00478762 0.999989i $$-0.501524\pi$$
−0.504140 + 0.863622i $$0.668191\pi$$
$$98$$ −40.4186 + 150.844i −0.412435 + 1.53923i
$$99$$ 38.7846 + 38.7846i 0.391764 + 0.391764i
$$100$$ −24.1962 41.9090i −0.241962 0.419090i
$$101$$ 30.0500 + 17.3494i 0.297525 + 0.171776i 0.641330 0.767265i $$-0.278383\pi$$
−0.343806 + 0.939041i $$0.611716\pi$$
$$102$$ −41.4904 + 11.1173i −0.406768 + 0.108993i
$$103$$ 196.890i 1.91155i 0.294098 + 0.955775i $$0.404981\pi$$
−0.294098 + 0.955775i $$0.595019\pi$$
$$104$$ 9.51666 + 35.5167i 0.0915064 + 0.341506i
$$105$$ −19.6077 −0.186740
$$106$$ 8.45706 + 31.5622i 0.0797836 + 0.297756i
$$107$$ −18.0910 + 31.3346i −0.169075 + 0.292847i −0.938095 0.346378i $$-0.887411\pi$$
0.769020 + 0.639225i $$0.220745\pi$$
$$108$$ 9.00000 5.19615i 0.0833333 0.0481125i
$$109$$ −127.497 + 127.497i −1.16970 + 1.16970i −0.187422 + 0.982280i $$0.560013\pi$$
−0.982280 + 0.187422i $$0.939987\pi$$
$$110$$ 22.3923 + 6.00000i 0.203566 + 0.0545455i
$$111$$ 1.37564 5.13397i 0.0123932 0.0462520i
$$112$$ −35.7128 35.7128i −0.318864 0.318864i
$$113$$ −39.5596 68.5192i −0.350085 0.606365i 0.636179 0.771541i $$-0.280514\pi$$
−0.986264 + 0.165177i $$0.947181\pi$$
$$114$$ −35.5692 20.5359i −0.312011 0.180139i
$$115$$ 18.5885 4.98076i 0.161639 0.0433110i
$$116$$ 77.3205i 0.666556i
$$117$$ 39.0000i 0.333333i
$$118$$ −30.0666 −0.254802
$$119$$ −57.3064 213.870i −0.481567 1.79723i
$$120$$ 2.19615 3.80385i 0.0183013 0.0316987i
$$121$$ 184.703 106.638i 1.52647 0.881309i
$$122$$ 42.2154 42.2154i 0.346028 0.346028i
$$123$$ 51.1865 + 13.7154i 0.416151 + 0.111507i
$$124$$ −18.6410 + 69.5692i −0.150331 + 0.561042i
$$125$$ 31.1891 + 31.1891i 0.249513 + 0.249513i
$$126$$ 26.7846 + 46.3923i 0.212576 + 0.368193i
$$127$$ 71.3205 + 41.1769i 0.561579 + 0.324228i 0.753779 0.657128i $$-0.228229\pi$$
−0.192200 + 0.981356i $$0.561562\pi$$
$$128$$ 10.9282 2.92820i 0.0853766 0.0228766i
$$129$$ 30.7461i 0.238342i
$$130$$ −8.24167 14.2750i −0.0633975 0.109808i
$$131$$ 5.93336 0.0452928 0.0226464 0.999744i $$-0.492791\pi$$
0.0226464 + 0.999744i $$0.492791\pi$$
$$132$$ −16.3923 61.1769i −0.124184 0.463461i
$$133$$ 105.856 183.349i 0.795913 1.37856i
$$134$$ −40.1436 + 23.1769i −0.299579 + 0.172962i
$$135$$ −3.29423 + 3.29423i −0.0244017 + 0.0244017i
$$136$$ 47.9090 + 12.8372i 0.352272 + 0.0943909i
$$137$$ 44.5859 166.397i 0.325444 1.21457i −0.588420 0.808555i $$-0.700250\pi$$
0.913864 0.406020i $$-0.133084\pi$$
$$138$$ −37.1769 37.1769i −0.269398 0.269398i
$$139$$ −6.35383 11.0052i −0.0457110 0.0791738i 0.842265 0.539064i $$-0.181222\pi$$
−0.887976 + 0.459890i $$0.847889\pi$$
$$140$$ 19.6077 + 11.3205i 0.140055 + 0.0808608i
$$141$$ −70.9808 + 19.0192i −0.503410 + 0.134888i
$$142$$ 48.4974i 0.341531i
$$143$$ −229.583 61.5167i −1.60548 0.430186i
$$144$$ −12.0000 −0.0833333
$$145$$ 8.97114 + 33.4808i 0.0618700 + 0.230902i
$$146$$ −15.9212 + 27.5763i −0.109049 + 0.188878i
$$147$$ −165.638 + 95.6314i −1.12679 + 0.650554i
$$148$$ −4.33975 + 4.33975i −0.0293226 + 0.0293226i
$$149$$ 111.945 + 29.9955i 0.751308 + 0.201312i 0.614098 0.789230i $$-0.289520\pi$$
0.137210 + 0.990542i $$0.456187\pi$$
$$150$$ 15.3397 57.2487i 0.102265 0.381658i
$$151$$ −118.603 118.603i −0.785447 0.785447i 0.195297 0.980744i $$-0.437433\pi$$
−0.980744 + 0.195297i $$0.937433\pi$$
$$152$$ 23.7128 + 41.0718i 0.156005 + 0.270209i
$$153$$ −45.5596 26.3038i −0.297775 0.171921i
$$154$$ 315.349 84.4974i 2.04772 0.548685i
$$155$$ 32.2872i 0.208304i
$$156$$ −22.5167 + 39.0000i −0.144338 + 0.250000i
$$157$$ −16.2961 −0.103797 −0.0518985 0.998652i $$-0.516527\pi$$
−0.0518985 + 0.998652i $$0.516527\pi$$
$$158$$ 32.7846 + 122.354i 0.207498 + 0.774391i
$$159$$ −20.0096 + 34.6577i −0.125847 + 0.217973i
$$160$$ −4.39230 + 2.53590i −0.0274519 + 0.0158494i
$$161$$ 191.636 191.636i 1.19028 1.19028i
$$162$$ 12.2942 + 3.29423i 0.0758903 + 0.0203347i
$$163$$ −74.8616 + 279.387i −0.459273 + 1.71403i 0.215938 + 0.976407i $$0.430719\pi$$
−0.675211 + 0.737624i $$0.735948\pi$$
$$164$$ −43.2679 43.2679i −0.263829 0.263829i
$$165$$ 14.1962 + 24.5885i 0.0860373 + 0.149021i
$$166$$ −168.746 97.4256i −1.01654 0.586901i
$$167$$ −262.277 + 70.2769i −1.57052 + 0.420820i −0.935975 0.352066i $$-0.885479\pi$$
−0.634545 + 0.772886i $$0.718813\pi$$
$$168$$ 61.8564i 0.368193i
$$169$$ 84.5000 + 146.358i 0.500000 + 0.866025i
$$170$$ −22.2346 −0.130792
$$171$$ −13.0192 48.5885i −0.0761359 0.284143i
$$172$$ 17.7513 30.7461i 0.103205 0.178757i
$$173$$ −93.1000 + 53.7513i −0.538150 + 0.310701i −0.744329 0.667813i $$-0.767230\pi$$
0.206179 + 0.978514i $$0.433897\pi$$
$$174$$ 66.9615 66.9615i 0.384836 0.384836i
$$175$$ 295.100 + 79.0718i 1.68629 + 0.451839i
$$176$$ −18.9282 + 70.6410i −0.107547 + 0.401369i
$$177$$ −26.0385 26.0385i −0.147110 0.147110i
$$178$$ −0.894882 1.54998i −0.00502743 0.00870776i
$$179$$ −105.804 61.0859i −0.591083 0.341262i 0.174443 0.984667i $$-0.444188\pi$$
−0.765526 + 0.643405i $$0.777521\pi$$
$$180$$ 5.19615 1.39230i 0.0288675 0.00773503i
$$181$$ 65.2872i 0.360703i 0.983602 + 0.180351i $$0.0577235\pi$$
−0.983602 + 0.180351i $$0.942277\pi$$
$$182$$ −201.033 116.067i −1.10458 0.637729i
$$183$$ 73.1192 0.399558
$$184$$ 15.7128 + 58.6410i 0.0853957 + 0.318701i
$$185$$ 1.37564 2.38269i 0.00743592 0.0128794i
$$186$$ −76.3923 + 44.1051i −0.410711 + 0.237124i
$$187$$ −226.708 + 226.708i −1.21234 + 1.21234i
$$188$$ 81.9615 + 21.9615i 0.435966 + 0.116817i
$$189$$ −16.9808 + 63.3731i −0.0898453 + 0.335307i
$$190$$ −15.0333 15.0333i −0.0791227 0.0791227i
$$191$$ 15.2820 + 26.4693i 0.0800106 + 0.138582i 0.903254 0.429106i $$-0.141171\pi$$
−0.823244 + 0.567688i $$0.807838\pi$$
$$192$$ 12.0000 + 6.92820i 0.0625000 + 0.0360844i
$$193$$ −45.8468 + 12.2846i −0.237548 + 0.0636508i −0.375629 0.926770i $$-0.622573\pi$$
0.138081 + 0.990421i $$0.455907\pi$$
$$194$$ 72.2769i 0.372561i
$$195$$ 5.22501 19.5000i 0.0267949 0.100000i
$$196$$ 220.851 1.12679
$$197$$ 58.1314 + 216.949i 0.295083 + 1.10127i 0.941151 + 0.337986i $$0.109746\pi$$
−0.646068 + 0.763280i $$0.723588\pi$$
$$198$$ 38.7846 67.1769i 0.195882 0.339277i
$$199$$ 139.583 80.5885i 0.701424 0.404967i −0.106454 0.994318i $$-0.533950\pi$$
0.807877 + 0.589351i $$0.200616\pi$$
$$200$$ −48.3923 + 48.3923i −0.241962 + 0.241962i
$$201$$ −54.8372 14.6936i −0.272822 0.0731024i
$$202$$ 12.7006 47.3993i 0.0628743 0.234650i
$$203$$ 345.167 + 345.167i 1.70033 + 1.70033i
$$204$$ 30.3731 + 52.6077i 0.148888 + 0.257881i
$$205$$ 23.7558 + 13.7154i 0.115882 + 0.0669043i
$$206$$ 268.956 72.0666i 1.30561 0.349838i
$$207$$ 64.3923i 0.311074i
$$208$$ 45.0333 26.0000i 0.216506 0.125000i
$$209$$ −306.564 −1.46681
$$210$$ 7.17691 + 26.7846i 0.0341758 + 0.127546i
$$211$$ 77.0718 133.492i 0.365269 0.632665i −0.623550 0.781783i $$-0.714310\pi$$
0.988819 + 0.149119i $$0.0476436\pi$$
$$212$$ 40.0192 23.1051i 0.188770 0.108986i
$$213$$ 42.0000 42.0000i 0.197183 0.197183i
$$214$$ 49.4256 + 13.2436i 0.230961 + 0.0618858i
$$215$$ −4.11920 + 15.3731i −0.0191591 + 0.0715026i
$$216$$ −10.3923 10.3923i −0.0481125 0.0481125i
$$217$$ −227.349 393.779i −1.04769 1.81465i
$$218$$ 220.832 + 127.497i 1.01299 + 0.584851i
$$219$$ −37.6699 + 10.0936i −0.172009 + 0.0460896i
$$220$$ 32.7846i 0.149021i
$$221$$ 227.967 1.03152
$$222$$ −7.51666 −0.0338588
$$223$$ 37.7513 + 140.890i 0.169288 + 0.631792i 0.997454 + 0.0713095i $$0.0227178\pi$$
−0.828166 + 0.560483i $$0.810616\pi$$
$$224$$ −35.7128 + 61.8564i −0.159432 + 0.276145i
$$225$$ 62.8634 36.2942i 0.279393 0.161308i
$$226$$ −79.1192 + 79.1192i −0.350085 + 0.350085i
$$227$$ −349.401 93.6218i −1.53921 0.412431i −0.613201 0.789927i $$-0.710119\pi$$
−0.926011 + 0.377496i $$0.876785\pi$$
$$228$$ −15.0333 + 56.1051i −0.0659356 + 0.246075i
$$229$$ 52.5692 + 52.5692i 0.229560 + 0.229560i 0.812509 0.582949i $$-0.198101\pi$$
−0.582949 + 0.812509i $$0.698101\pi$$
$$230$$ −13.6077 23.5692i −0.0591639 0.102475i
$$231$$ 346.277 + 199.923i 1.49903 + 0.865468i
$$232$$ −105.622 + 28.3013i −0.455266 + 0.121988i
$$233$$ 235.923i 1.01255i −0.862373 0.506273i $$-0.831023\pi$$
0.862373 0.506273i $$-0.168977\pi$$
$$234$$ −53.2750 + 14.2750i −0.227671 + 0.0610042i
$$235$$ −38.0385 −0.161866
$$236$$ 11.0052 + 41.0718i 0.0466320 + 0.174033i
$$237$$ −77.5692 + 134.354i −0.327296 + 0.566894i
$$238$$ −271.177 + 156.564i −1.13940 + 0.657832i
$$239$$ −155.569 + 155.569i −0.650917 + 0.650917i −0.953214 0.302297i $$-0.902247\pi$$
0.302297 + 0.953214i $$0.402247\pi$$
$$240$$ −6.00000 1.60770i −0.0250000 0.00669873i
$$241$$ 98.8820 369.033i 0.410299 1.53126i −0.383771 0.923428i $$-0.625375\pi$$
0.794069 0.607827i $$-0.207959\pi$$
$$242$$ −213.277 213.277i −0.881309 0.881309i
$$243$$ 7.79423 + 13.5000i 0.0320750 + 0.0555556i
$$244$$ −73.1192 42.2154i −0.299669 0.173014i
$$245$$ −95.6314 + 25.6244i −0.390332 + 0.104589i
$$246$$ 74.9423i 0.304643i
$$247$$ 154.133 + 154.133i 0.624021 + 0.624021i
$$248$$ 101.856 0.410711
$$249$$ −61.7654 230.512i −0.248054 0.925749i
$$250$$ 31.1891 54.0211i 0.124756 0.216084i
$$251$$ −63.6462 + 36.7461i −0.253570 + 0.146399i −0.621398 0.783495i $$-0.713435\pi$$
0.367828 + 0.929894i $$0.380102\pi$$
$$252$$ 53.5692 53.5692i 0.212576 0.212576i
$$253$$ −379.061 101.569i −1.49827 0.401459i
$$254$$ 30.1436 112.497i 0.118676 0.442903i
$$255$$ −19.2558 19.2558i −0.0755128 0.0755128i
$$256$$ −8.00000 13.8564i −0.0312500 0.0541266i
$$257$$ 400.658 + 231.320i 1.55898 + 0.900077i 0.997355 + 0.0726847i $$0.0231567\pi$$
0.561624 + 0.827392i $$0.310177\pi$$
$$258$$ 42.0000 11.2539i 0.162791 0.0436196i
$$259$$ 38.7461i 0.149599i
$$260$$ −16.4833 + 16.4833i −0.0633975 + 0.0633975i
$$261$$ 115.981 0.444371
$$262$$ −2.17176 8.10512i −0.00828916 0.0309356i
$$263$$ 250.617 434.081i 0.952915 1.65050i 0.213846 0.976867i $$-0.431401\pi$$
0.739069 0.673630i $$-0.235266\pi$$
$$264$$ −77.5692 + 44.7846i −0.293823 + 0.169639i
$$265$$ −14.6481 + 14.6481i −0.0552757 + 0.0552757i
$$266$$ −289.205 77.4923i −1.08724 0.291324i
$$267$$ 0.567333 2.11731i 0.00212484 0.00793002i
$$268$$ 46.3538 + 46.3538i 0.172962 + 0.172962i
$$269$$ 19.2436 + 33.3308i 0.0715374 + 0.123906i 0.899575 0.436766i $$-0.143876\pi$$
−0.828038 + 0.560672i $$0.810543\pi$$
$$270$$ 5.70577 + 3.29423i 0.0211325 + 0.0122008i
$$271$$ −192.028 + 51.4538i −0.708591 + 0.189866i −0.595075 0.803670i $$-0.702878\pi$$
−0.113516 + 0.993536i $$0.536211\pi$$
$$272$$ 70.1436i 0.257881i
$$273$$ −73.5833 274.617i −0.269536 1.00592i
$$274$$ −243.622 −0.889131
$$275$$ −114.497 427.310i −0.416354 1.55386i
$$276$$ −37.1769 + 64.3923i −0.134699 + 0.233305i
$$277$$ −46.7154 + 26.9711i −0.168648 + 0.0973687i −0.581948 0.813226i $$-0.697709\pi$$
0.413300 + 0.910595i $$0.364376\pi$$
$$278$$ −12.7077 + 12.7077i −0.0457110 + 0.0457110i
$$279$$ −104.354 27.9615i −0.374028 0.100221i
$$280$$ 8.28719 30.9282i 0.0295971 0.110458i
$$281$$ 172.165 + 172.165i 0.612686 + 0.612686i 0.943645 0.330959i $$-0.107372\pi$$
−0.330959 + 0.943645i $$0.607372\pi$$
$$282$$ 51.9615 + 90.0000i 0.184261 + 0.319149i
$$283$$ −433.086 250.042i −1.53034 0.883542i −0.999346 0.0361653i $$-0.988486\pi$$
−0.530993 0.847376i $$-0.678181\pi$$
$$284$$ −66.2487 + 17.7513i −0.233270 + 0.0625045i
$$285$$ 26.0385i 0.0913631i
$$286$$ 336.133i 1.17529i
$$287$$ 386.305 1.34601
$$288$$ 4.39230 + 16.3923i 0.0152511 + 0.0569177i
$$289$$ 9.25387 16.0282i 0.0320203 0.0554608i
$$290$$ 42.4519 24.5096i 0.146386 0.0845159i
$$291$$ −62.5936 + 62.5936i −0.215098 + 0.215098i
$$292$$ 43.4974 + 11.6551i 0.148964 + 0.0399147i
$$293$$ 35.0673 130.873i 0.119684 0.446666i −0.879911 0.475139i $$-0.842398\pi$$
0.999595 + 0.0284731i $$0.00906449\pi$$
$$294$$ 191.263 + 191.263i 0.650554 + 0.650554i
$$295$$ −9.53074 16.5077i −0.0323076 0.0559584i
$$296$$ 7.51666 + 4.33975i 0.0253941 + 0.0146613i
$$297$$ 91.7654 24.5885i 0.308974 0.0827894i
$$298$$ 163.899i 0.549995i
$$299$$ 139.517 + 241.650i 0.466611 + 0.808194i
$$300$$ −83.8179 −0.279393
$$301$$ 58.0103 + 216.497i 0.192725 + 0.719261i
$$302$$ −118.603 + 205.426i −0.392724 + 0.680217i
$$303$$ 52.0481 30.0500i 0.171776 0.0991749i
$$304$$ 47.4256 47.4256i 0.156005 0.156005i
$$305$$ 36.5596 + 9.79612i 0.119868 + 0.0321184i
$$306$$ −19.2558 + 71.8634i −0.0629273 + 0.234848i
$$307$$ 83.6743 + 83.6743i 0.272555 + 0.272555i 0.830128 0.557573i $$-0.188267\pi$$
−0.557573 + 0.830128i $$0.688267\pi$$
$$308$$ −230.851 399.846i −0.749517 1.29820i
$$309$$ 295.335 + 170.512i 0.955775 + 0.551817i
$$310$$ −44.1051 + 11.8179i −0.142275 + 0.0381224i
$$311$$ 178.823i 0.574994i 0.957782 + 0.287497i $$0.0928231\pi$$
−0.957782 + 0.287497i $$0.907177\pi$$
$$312$$ 61.5167 + 16.4833i 0.197169 + 0.0528312i
$$313$$ 230.123 0.735217 0.367609 0.929981i $$-0.380177\pi$$
0.367609 + 0.929981i $$0.380177\pi$$
$$314$$ 5.96479 + 22.2609i 0.0189962 + 0.0708946i
$$315$$ −16.9808 + 29.4115i −0.0539072 + 0.0933700i
$$316$$ 155.138 89.5692i 0.490944 0.283447i
$$317$$ 211.886 211.886i 0.668412 0.668412i −0.288937 0.957348i $$-0.593302\pi$$
0.957348 + 0.288937i $$0.0933017\pi$$
$$318$$ 54.6673 + 14.6481i 0.171910 + 0.0460631i
$$319$$ 182.942 682.750i 0.573487 2.14028i
$$320$$ 5.07180 + 5.07180i 0.0158494 + 0.0158494i
$$321$$ 31.3346 + 54.2731i 0.0976155 + 0.169075i
$$322$$ −331.923 191.636i −1.03082 0.595142i
$$323$$ 284.014 76.1013i 0.879301 0.235608i
$$324$$ 18.0000i 0.0555556i
$$325$$ −157.275 + 272.408i −0.483923 + 0.838179i
$$326$$ 409.051 1.25476
$$327$$ 80.8301 + 301.662i 0.247187 + 0.922514i
$$328$$ −43.2679 + 74.9423i −0.131914 + 0.228483i
$$329$$ −463.923 + 267.846i −1.41010 + 0.814122i
$$330$$ 28.3923 28.3923i 0.0860373 0.0860373i
$$331$$ −95.6743 25.6359i −0.289046 0.0774497i 0.111382 0.993778i $$-0.464472\pi$$
−0.400429 + 0.916328i $$0.631139\pi$$
$$332$$ −71.3205 + 266.172i −0.214821 + 0.801722i
$$333$$ −6.50962 6.50962i −0.0195484 0.0195484i
$$334$$ 192.000 + 332.554i 0.574850 + 0.995670i
$$335$$ −25.4500 14.6936i −0.0759702 0.0438614i
$$336$$ −84.4974 + 22.6410i −0.251480 + 0.0673840i
$$337$$ 53.0770i 0.157498i −0.996894 0.0787492i $$-0.974907\pi$$
0.996894 0.0787492i $$-0.0250926\pi$$
$$338$$ 169.000 169.000i 0.500000 0.500000i
$$339$$ −137.038 −0.404243
$$340$$ 8.13844 + 30.3731i 0.0239366 + 0.0893325i
$$341$$ −329.205 + 570.200i −0.965411 + 1.67214i
$$342$$ −61.6077 + 35.5692i −0.180139 + 0.104004i
$$343$$ −548.420 + 548.420i −1.59889 + 1.59889i
$$344$$ −48.4974 12.9948i −0.140981 0.0377757i
$$345$$ 8.62693 32.1962i 0.0250056 0.0933222i
$$346$$ 107.503 + 107.503i 0.310701 + 0.310701i
$$347$$ 337.583 + 584.711i 0.972863 + 1.68505i 0.686816 + 0.726832i $$0.259008\pi$$
0.286047 + 0.958216i $$0.407659\pi$$
$$348$$ −115.981 66.9615i −0.333278 0.192418i
$$349$$ 572.154 153.308i 1.63941 0.439279i 0.682790 0.730615i $$-0.260766\pi$$
0.956621 + 0.291336i $$0.0940997\pi$$
$$350$$ 432.056i 1.23445i
$$351$$ −58.5000 33.7750i −0.166667 0.0962250i
$$352$$ 103.426 0.293823
$$353$$ 30.8628 + 115.181i 0.0874299 + 0.326293i 0.995763 0.0919541i $$-0.0293113\pi$$
−0.908333 + 0.418247i $$0.862645\pi$$
$$354$$ −26.0385 + 45.1000i −0.0735550 + 0.127401i
$$355$$ 26.6269 15.3731i 0.0750054 0.0433044i
$$356$$ −1.78976 + 1.78976i −0.00502743 + 0.00502743i
$$357$$ −370.435 99.2576i −1.03763 0.278033i
$$358$$ −44.7180 + 166.890i −0.124911 + 0.466172i
$$359$$ −375.415 375.415i −1.04573 1.04573i −0.998903 0.0468219i $$-0.985091\pi$$
−0.0468219 0.998903i $$-0.514909\pi$$
$$360$$ −3.80385 6.58846i −0.0105662 0.0183013i
$$361$$ −69.1532 39.9256i −0.191560 0.110597i
$$362$$ 89.1840 23.8968i 0.246365 0.0660132i
$$363$$ 369.406i 1.01765i
$$364$$ −84.9667 + 317.100i −0.233425 + 0.871154i
$$365$$ −20.1872 −0.0553075
$$366$$ −26.7635 99.8827i −0.0731243 0.272904i
$$367$$ 105.842 183.324i 0.288399 0.499521i −0.685029 0.728516i $$-0.740210\pi$$
0.973428 + 0.228995i $$0.0735438\pi$$
$$368$$ 74.3538 42.9282i 0.202048 0.116653i
$$369$$ 64.9019 64.9019i 0.175886 0.175886i
$$370$$ −3.75833 1.00704i −0.0101576 0.00272173i
$$371$$ −75.5064 + 281.794i −0.203521 + 0.759551i
$$372$$ 88.2102 + 88.2102i 0.237124 + 0.237124i
$$373$$ 33.2199 + 57.5385i 0.0890613 + 0.154259i 0.907115 0.420884i $$-0.138280\pi$$
−0.818053 + 0.575142i $$0.804947\pi$$
$$374$$ 392.669 + 226.708i 1.04992 + 0.606170i
$$375$$ 73.7942 19.7731i 0.196785 0.0527283i
$$376$$ 120.000i 0.319149i
$$377$$ −435.250 + 251.292i −1.15451 + 0.666556i
$$378$$ 92.7846 0.245462
$$379$$ 40.0488 + 149.464i 0.105670 + 0.394364i 0.998420 0.0561867i $$-0.0178942\pi$$
−0.892751 + 0.450551i $$0.851228\pi$$
$$380$$ −15.0333 + 26.0385i −0.0395614 + 0.0685223i
$$381$$ 123.531 71.3205i 0.324228 0.187193i
$$382$$ 30.5641 30.5641i 0.0800106 0.0800106i
$$383$$ −378.382 101.387i −0.987943 0.264718i −0.271556 0.962423i $$-0.587538\pi$$
−0.716386 + 0.697704i $$0.754205\pi$$
$$384$$ 5.07180 18.9282i 0.0132078 0.0492922i
$$385$$ 146.354 + 146.354i 0.380140 + 0.380140i
$$386$$ 33.5622 + 58.1314i 0.0869486 + 0.150599i
$$387$$ 46.1192 + 26.6269i 0.119171 + 0.0688034i
$$388$$ 98.7321 26.4552i 0.254464 0.0681834i
$$389$$ 599.802i 1.54191i −0.636890 0.770954i $$-0.719780\pi$$
0.636890 0.770954i $$-0.280220\pi$$
$$390$$ −28.5500 −0.0732051
$$391$$ 376.392 0.962640
$$392$$ −80.8372 301.688i −0.206217 0.769613i
$$393$$ 5.13844 8.90004i 0.0130749 0.0226464i
$$394$$ 275.081 158.818i 0.698174 0.403091i
$$395$$ −56.7846 + 56.7846i −0.143759 + 0.143759i
$$396$$ −105.962 28.3923i −0.267580 0.0716977i
$$397$$ −138.615 + 517.317i −0.349156 + 1.30307i 0.538526 + 0.842609i $$0.318981\pi$$
−0.887682 + 0.460457i $$0.847685\pi$$
$$398$$ −161.177 161.177i −0.404967 0.404967i
$$399$$ −183.349 317.569i −0.459520 0.795913i
$$400$$ 83.8179 + 48.3923i 0.209545 + 0.120981i
$$401$$ −419.935 + 112.521i −1.04722 + 0.280601i −0.741102 0.671393i $$-0.765696\pi$$
−0.306117 + 0.951994i $$0.599030\pi$$
$$402$$ 80.2872i 0.199719i
$$403$$ 452.200 121.167i 1.12208 0.300662i
$$404$$ −69.3975 −0.171776
$$405$$ 2.08846 + 7.79423i 0.00515668 + 0.0192450i
$$406$$ 345.167 597.846i 0.850164 1.47253i
$$407$$ −48.5885 + 28.0526i −0.119382 + 0.0689252i
$$408$$ 60.7461 60.7461i 0.148888 0.148888i
$$409$$ −665.224 178.246i −1.62646 0.435810i −0.673572 0.739121i $$-0.735241\pi$$
−0.952891 + 0.303312i $$0.901908\pi$$
$$410$$ 10.0404 37.4711i 0.0244887 0.0913930i
$$411$$ −210.983 210.983i −0.513340 0.513340i
$$412$$ −196.890 341.023i −0.477888 0.827726i
$$413$$ −232.477 134.221i −0.562898 0.324989i
$$414$$ −87.9615 + 23.5692i −0.212467 + 0.0569305i
$$415$$ 123.531i 0.297664i
$$416$$ −52.0000 52.0000i −0.125000 0.125000i
$$417$$ −22.0103 −0.0527825
$$418$$ 112.210 + 418.774i 0.268446 + 1.00185i
$$419$$ 144.000 249.415i 0.343675 0.595263i −0.641437 0.767176i $$-0.721661\pi$$
0.985112 + 0.171913i $$0.0549947\pi$$
$$420$$ 33.9615 19.6077i 0.0808608 0.0466850i
$$421$$ 87.8930 87.8930i 0.208772 0.208772i −0.594973 0.803745i $$-0.702837\pi$$
0.803745 + 0.594973i $$0.202837\pi$$
$$422$$ −210.564 56.4205i −0.498967 0.133698i
$$423$$ −32.9423 + 122.942i −0.0778777 + 0.290644i
$$424$$ −46.2102 46.2102i −0.108986 0.108986i
$$425$$ 212.151 + 367.456i 0.499178 + 0.864602i
$$426$$ −72.7461 42.0000i −0.170766 0.0985915i
$$427$$ 514.865 137.958i 1.20577 0.323086i
$$428$$ 72.3641i 0.169075i
$$429$$ −291.100 + 291.100i −0.678555 + 0.678555i
$$430$$ 22.5077 0.0523436
$$431$$ −4.18584 15.6218i −0.00971193 0.0362454i 0.960900 0.276896i $$-0.0893058\pi$$
−0.970612 + 0.240651i $$0.922639\pi$$
$$432$$ −10.3923 + 18.0000i −0.0240563 + 0.0416667i
$$433$$ 307.782 177.698i 0.710813 0.410388i −0.100549 0.994932i $$-0.532060\pi$$
0.811362 + 0.584544i $$0.198727\pi$$
$$434$$ −454.697 + 454.697i −1.04769 + 1.04769i
$$435$$ 57.9904 + 15.5385i 0.133311 + 0.0357206i
$$436$$ 93.3346 348.329i 0.214070 0.798921i
$$437$$ 254.487 + 254.487i 0.582350 + 0.582350i
$$438$$ 27.5763 + 47.7635i 0.0629595 + 0.109049i
$$439$$ 179.412 + 103.583i 0.408682 + 0.235953i 0.690223 0.723596i $$-0.257512\pi$$
−0.281541 + 0.959549i $$0.590846\pi$$
$$440$$ −44.7846 + 12.0000i −0.101783 + 0.0272727i
$$441$$ 331.277i 0.751195i
$$442$$ −83.4416 311.408i −0.188782 0.704544i
$$443$$ 394.641 0.890838 0.445419 0.895322i $$-0.353055\pi$$
0.445419 + 0.895322i $$0.353055\pi$$
$$444$$ 2.75129 + 10.2679i 0.00619660 + 0.0231260i
$$445$$ 0.567333 0.982649i 0.00127490 0.00220820i
$$446$$ 178.641 103.138i 0.400540 0.231252i
$$447$$ 141.940 141.940i 0.317540 0.317540i
$$448$$ 97.5692 + 26.1436i 0.217788 + 0.0583562i
$$449$$ 136.878 510.834i 0.304850 1.13771i −0.628225 0.778032i $$-0.716218\pi$$
0.933075 0.359683i $$-0.117115\pi$$
$$450$$ −72.5885 72.5885i −0.161308 0.161308i
$$451$$ −279.688 484.435i −0.620152 1.07413i
$$452$$ 137.038 + 79.1192i 0.303182 + 0.175042i
$$453$$ −280.617 + 75.1910i −0.619463 + 0.165985i
$$454$$ 511.559i 1.12678i
$$455$$ 147.167i 0.323443i
$$456$$ 82.1436 0.180139
$$457$$ 22.9571 + 85.6769i 0.0502343 + 0.187477i 0.986484 0.163859i $$-0.0523942\pi$$
−0.936250 + 0.351336i $$0.885728\pi$$
$$458$$ 52.5692 91.0526i 0.114780 0.198805i
$$459$$ −78.9115 + 45.5596i −0.171921 + 0.0992584i
$$460$$ −27.2154 + 27.2154i −0.0591639 + 0.0591639i
$$461$$ 75.7961 + 20.3095i 0.164417 + 0.0440553i 0.340088 0.940393i $$-0.389543\pi$$
−0.175672 + 0.984449i $$0.556210\pi$$
$$462$$ 146.354 546.200i 0.316783 1.18225i
$$463$$ −264.908 264.908i −0.572155 0.572155i 0.360575 0.932730i $$-0.382580\pi$$
−0.932730 + 0.360575i $$0.882580\pi$$
$$464$$ 77.3205 + 133.923i 0.166639 + 0.288627i
$$465$$ −48.4308 27.9615i −0.104152 0.0601323i
$$466$$ −322.277 + 86.3538i −0.691581 + 0.185309i
$$467$$ 332.603i 0.712211i −0.934446 0.356106i $$-0.884104\pi$$
0.934446 0.356106i $$-0.115896\pi$$
$$468$$ 39.0000 + 67.5500i 0.0833333 + 0.144338i
$$469$$ −413.856 −0.882423
$$470$$ 13.9230 + 51.9615i 0.0296235 + 0.110556i
$$471$$ −14.1128 + 24.4442i −0.0299636 + 0.0518985i
$$472$$ 52.0770 30.0666i 0.110333 0.0637005i
$$473$$ 229.492 229.492i 0.485184 0.485184i
$$474$$ 211.923 + 56.7846i 0.447095 + 0.119799i
$$475$$ −105.005 + 391.885i −0.221063 + 0.825020i
$$476$$ 313.128 + 313.128i 0.657832 + 0.657832i
$$477$$ 34.6577 + 60.0289i 0.0726576 + 0.125847i
$$478$$ 269.454 + 155.569i 0.563711 + 0.325459i
$$479$$ −655.559 + 175.656i −1.36860 + 0.366715i −0.866967 0.498366i $$-0.833934\pi$$
−0.501632 + 0.865081i $$0.667267\pi$$
$$480$$ 8.78461i 0.0183013i
$$481$$ 38.5333 + 10.3250i 0.0801109 + 0.0214656i
$$482$$ −540.301 −1.12096
$$483$$ −121.492 453.415i −0.251537 0.938748i
$$484$$ −213.277 + 369.406i −0.440655 + 0.763236i
$$485$$ −39.6828 + 22.9109i −0.0818201 + 0.0472389i
$$486$$ 15.5885 15.5885i 0.0320750 0.0320750i
$$487$$ 535.822 + 143.573i 1.10025 + 0.294811i 0.762866 0.646556i $$-0.223791\pi$$
0.337384 + 0.941367i $$0.390458\pi$$
$$488$$ −30.9038 + 115.335i −0.0633275 + 0.236341i
$$489$$ 354.249 + 354.249i 0.724435 + 0.724435i
$$490$$ 70.0070 + 121.256i 0.142872 + 0.247461i
$$491$$ −501.373 289.468i −1.02113 0.589548i −0.106696 0.994292i $$-0.534027\pi$$
−0.914430 + 0.404744i $$0.867361\pi$$
$$492$$ −102.373 + 27.4308i −0.208075 + 0.0557536i
$$493$$ 677.942i 1.37514i
$$494$$ 154.133 266.967i 0.312011 0.540418i
$$495$$ 49.1769 0.0993473
$$496$$ −37.2820 139.138i −0.0751654 0.280521i
$$497$$ 216.497 374.985i 0.435608 0.754496i
$$498$$ −292.277 + 168.746i −0.586901 + 0.338848i
$$499$$ 40.3154 40.3154i 0.0807923 0.0807923i −0.665556 0.746348i $$-0.731805\pi$$
0.746348 + 0.665556i $$0.231805\pi$$
$$500$$ −85.2102 22.8320i −0.170420 0.0456640i
$$501$$ −121.723 + 454.277i −0.242960 + 0.906740i
$$502$$ 73.4923 + 73.4923i 0.146399 + 0.146399i
$$503$$ 182.894 + 316.781i 0.363605 + 0.629783i 0.988551 0.150885i $$-0.0482123\pi$$
−0.624946 + 0.780668i $$0.714879\pi$$
$$504$$ −92.7846 53.5692i −0.184096 0.106288i
$$505$$ 30.0500 8.05187i 0.0595049 0.0159443i
$$506$$ 554.985i 1.09681i
$$507$$ 292.717 0.577350
$$508$$ −164.708 −0.324228
$$509$$ −179.747 670.824i −0.353137 1.31793i −0.882813 0.469725i $$-0.844353\pi$$
0.529675 0.848200i $$-0.322314\pi$$
$$510$$ −19.2558 + 33.3519i −0.0377564 + 0.0653960i
$$511$$ −246.206 + 142.147i −0.481813 + 0.278175i
$$512$$ −16.0000 + 16.0000i −0.0312500 + 0.0312500i
$$513$$ −84.1577 22.5500i −0.164050 0.0439571i
$$514$$ 169.338 631.977i 0.329451 1.22953i
$$515$$ 124.823 + 124.823i 0.242375 + 0.242375i
$$516$$ −30.7461 53.2539i −0.0595855 0.103205i
$$517$$ 671.769 + 387.846i 1.29936 + 0.750186i
$$518$$ −52.9282 + 14.1821i −0.102178 + 0.0273785i
$$519$$ 186.200i 0.358767i
$$520$$ 28.5500 + 16.4833i 0.0549038 + 0.0316987i
$$521$$ 49.0526 0.0941508 0.0470754 0.998891i $$-0.485010\pi$$
0.0470754 + 0.998891i $$0.485010\pi$$
$$522$$ −42.4519 158.433i −0.0813255 0.303511i
$$523$$ −30.6654 + 53.1140i −0.0586337 + 0.101556i −0.893852 0.448362i $$-0.852008\pi$$
0.835219 + 0.549918i $$0.185341\pi$$
$$524$$ −10.2769 + 5.93336i −0.0196124 + 0.0113232i
$$525$$ 374.172 374.172i 0.712708 0.712708i
$$526$$ −684.697 183.464i −1.30171 0.348791i
$$527$$ 163.443 609.979i 0.310139 1.15746i
$$528$$ 89.5692 + 89.5692i 0.169639 + 0.169639i
$$529$$ −34.1462 59.1429i −0.0645485 0.111801i
$$530$$ 25.3712 + 14.6481i 0.0478702 + 0.0276378i
$$531$$ −61.6077 + 16.5077i −0.116022 + 0.0310880i
$$532$$ 423.426i 0.795913i
$$533$$ −102.942 + 384.183i −0.193136 + 0.720794i
$$534$$ −3.09996 −0.00580517
$$535$$ 8.39608 + 31.3346i 0.0156936 + 0.0585693i
$$536$$ 46.3538 80.2872i 0.0864810 0.149790i
$$537$$ −183.258 + 105.804i −0.341262 + 0.197028i
$$538$$ 38.4871 38.4871i 0.0715374 0.0715374i
$$539$$ 1950.14 + 522.540i 3.61808 + 0.969461i
$$540$$ 2.41154 9.00000i 0.00446582 0.0166667i
$$541$$ −334.410 334.410i −0.618132 0.618132i 0.326920 0.945052i $$-0.393989\pi$$
−0.945052 + 0.326920i $$0.893989\pi$$
$$542$$ 140.574 + 243.482i 0.259362 + 0.449229i
$$543$$ 97.9308 + 56.5404i 0.180351 + 0.104126i
$$544$$ −95.8179 + 25.6743i −0.176136 + 0.0471955i
$$545$$ 161.660i 0.296624i
$$546$$ −348.200 + 201.033i −0.637729 + 0.368193i
$$547$$ −567.854 −1.03812 −0.519062 0.854737i $$-0.673719\pi$$
−0.519062 + 0.854737i $$0.673719\pi$$
$$548$$ 89.1718 + 332.794i 0.162722 + 0.607287i
$$549$$ 63.3231 109.679i 0.115343 0.199779i
$$550$$ −541.808 + 312.813i −0.985105 + 0.568751i
$$551$$ −458.372 + 458.372i −0.831891 + 0.831891i
$$552$$ 101.569 + 27.2154i 0.184002 + 0.0493032i
$$553$$ −292.708 + 1092.40i −0.529309 + 1.97541i
$$554$$ 53.9423 + 53.9423i 0.0973687 + 0.0973687i
$$555$$ −2.38269 4.12693i −0.00429313 0.00743592i
$$556$$ 22.0103 + 12.7077i 0.0395869 + 0.0228555i
$$557$$ 395.583 105.996i 0.710202 0.190298i 0.114406 0.993434i $$-0.463503\pi$$
0.595796 + 0.803136i $$0.296837\pi$$
$$558$$ 152.785i 0.273808i
$$559$$ −230.767 −0.412821
$$560$$ −45.2820 −0.0808608
$$561$$ 143.727 + 536.396i 0.256198 + 0.956143i
$$562$$ 172.165 298.198i 0.306343 0.530601i
$$563$$ 30.0000 17.3205i 0.0532860 0.0307647i −0.473120 0.880998i $$-0.656872\pi$$
0.526406 + 0.850233i $$0.323539\pi$$
$$564$$ 103.923 103.923i 0.184261 0.184261i
$$565$$ −68.5192 18.3597i −0.121273 0.0324950i
$$566$$ −183.044 + 683.128i −0.323399 + 1.20694i
$$567$$ 80.3538 + 80.3538i 0.141718 + 0.141718i
$$568$$ 48.4974 + 84.0000i 0.0853828 + 0.147887i
$$569$$ −243.300 140.469i −0.427592 0.246870i 0.270728 0.962656i $$-0.412736\pi$$
−0.698320 + 0.715785i $$0.746069\pi$$
$$570$$ −35.5692 + 9.53074i −0.0624021 + 0.0167206i
$$571$$ 978.823i 1.71423i −0.515128 0.857113i $$-0.672256\pi$$
0.515128 0.857113i $$-0.327744\pi$$
$$572$$ 459.167 123.033i 0.802739 0.215093i
$$573$$ 52.9385 0.0923883
$$574$$ −141.397 527.703i −0.246337 0.919342i
$$575$$ −259.674 + 449.769i −0.451608 + 0.782207i
$$576$$ 20.7846 12.0000i 0.0360844 0.0208333i
$$577$$ 317.289 317.289i 0.549894 0.549894i −0.376516 0.926410i $$-0.622878\pi$$
0.926410 + 0.376516i $$0.122878\pi$$
$$578$$ −25.2820 6.77430i −0.0437405 0.0117202i
$$579$$ −21.2776 + 79.4090i −0.0367488 + 0.137148i
$$580$$ −49.0192 49.0192i −0.0845159 0.0845159i
$$581$$ −869.836 1506.60i −1.49714 2.59311i
$$582$$ 108.415 + 62.5936i 0.186281 + 0.107549i
$$583$$ 408.042 109.335i 0.699901 0.187538i
$$584$$ 63.6846i 0.109049i
$$585$$ −24.7250 24.7250i −0.0422650 0.0422650i
$$586$$ −191.611 −0.326982
$$587$$ 152.900 + 570.631i 0.260477 + 0.972114i 0.964961 + 0.262394i $$0.0845119\pi$$
−0.704484 + 0.709720i $$0.748821\pi$$
$$588$$ 191.263 331.277i 0.325277 0.563396i
$$589$$ 522.928 301.913i 0.887824 0.512585i
$$590$$ −19.0615 + 19.0615i −0.0323076 + 0.0323076i
$$591$$ 375.767 + 100.687i 0.635816 + 0.170366i
$$592$$ 3.17691 11.8564i 0.00536641 0.0200277i
$$593$$ −460.853 460.853i −0.777155 0.777155i 0.202191 0.979346i $$-0.435194\pi$$
−0.979346 + 0.202191i $$0.935194\pi$$
$$594$$ −67.1769 116.354i −0.113092 0.195882i
$$595$$ −171.919 99.2576i −0.288940 0.166820i
$$596$$ −223.890 + 59.9911i −0.375654 + 0.100656i
$$597$$ 279.167i 0.467616i
$$598$$ 279.033 279.033i 0.466611 0.466611i
$$599$$ 967.923 1.61590 0.807949 0.589252i $$-0.200578\pi$$
0.807949 + 0.589252i $$0.200578\pi$$
$$600$$ 30.6795 + 114.497i 0.0511325 + 0.190829i
$$601$$ −230.225 + 398.761i −0.383070 + 0.663497i −0.991499 0.130111i $$-0.958466\pi$$
0.608429 + 0.793608i $$0.291800\pi$$
$$602$$ 274.508 158.487i 0.455993 0.263268i
$$603$$ −69.5307 + 69.5307i −0.115308 + 0.115308i
$$604$$ 324.028 + 86.8231i 0.536470 + 0.143747i
$$605$$ 49.4911 184.703i 0.0818034 0.305295i
$$606$$ −60.1000 60.1000i −0.0991749 0.0991749i
$$607$$ 19.9615 + 34.5744i 0.0328855 + 0.0569594i 0.882000 0.471250i $$-0.156197\pi$$
−0.849114 + 0.528209i $$0.822864\pi$$
$$608$$ −82.1436 47.4256i −0.135105 0.0780027i
$$609$$ 816.673 218.827i 1.34101 0.359322i
$$610$$ 53.5270i 0.0877491i
$$611$$ −142.750 532.750i −0.233633 0.871931i
$$612$$ 105.215 0.171921
$$613$$ 122.949 + 458.851i 0.200569 + 0.748533i 0.990755 + 0.135666i $$0.0433173\pi$$
−0.790186 + 0.612867i $$0.790016\pi$$
$$614$$ 83.6743 144.928i 0.136277 0.236039i
$$615$$ 41.1462 23.7558i 0.0669043 0.0386272i
$$616$$ −461.703 + 461.703i −0.749517 + 0.749517i
$$617$$ 593.322 + 158.980i 0.961624 + 0.257666i 0.705287 0.708921i $$-0.250818\pi$$
0.256336 + 0.966588i $$0.417485\pi$$
$$618$$ 124.823 465.846i 0.201979 0.753796i
$$619$$ −417.520 417.520i −0.674508 0.674508i 0.284244 0.958752i $$-0.408257\pi$$
−0.958752 + 0.284244i $$0.908257\pi$$
$$620$$ 32.2872 + 55.9230i 0.0520761 + 0.0901985i
$$621$$ −96.5885 55.7654i −0.155537 0.0897993i
$$622$$ 244.277 65.4538i 0.392728 0.105231i
$$623$$ 15.9794i 0.0256491i
$$624$$ 90.0666i 0.144338i
$$625$$ −565.358 −0.904572
$$626$$ −84.2309 314.354i −0.134554 0.502163i
$$627$$ −265.492 + 459.846i −0.423433 + 0.733407i
$$628$$ 28.2257 16.2961i 0.0449454 0.0259492i
$$629$$ 38.0507 38.0507i 0.0604939 0.0604939i
$$630$$ 46.3923 + 12.4308i 0.0736386 + 0.0197314i
$$631$$ −44.7255 + 166.918i −0.0708804 + 0.264529i −0.992268 0.124117i $$-0.960390\pi$$
0.921387 + 0.388646i $$0.127057\pi$$
$$632$$ −179.138 179.138i −0.283447 0.283447i
$$633$$ −133.492 231.215i −0.210888 0.365269i
$$634$$ −366.998 211.886i −0.578861 0.334206i
$$635$$ 71.3205 19.1103i 0.112316 0.0300949i
$$636$$ 80.0385i 0.125847i
$$637$$ −717.767 1243.21i −1.12679 1.95166i
$$638$$ −999.615 −1.56680
$$639$$ −26.6269 99.3731i −0.0416697 0.155513i
$$640$$ 5.07180 8.78461i 0.00792468 0.0137260i
$$641$$ −359.425 + 207.514i −0.560725 + 0.323735i −0.753437 0.657521i $$-0.771605\pi$$
0.192711 + 0.981256i $$0.438272\pi$$
$$642$$ 62.6692 62.6692i 0.0976155 0.0976155i
$$643$$ −345.023 92.4486i −0.536583 0.143777i −0.0196567 0.999807i $$-0.506257\pi$$
−0.516927 + 0.856030i $$0.672924\pi$$
$$644$$ −140.287 + 523.559i −0.217837 + 0.812980i
$$645$$ 19.4923 + 19.4923i 0.0302206 + 0.0302206i
$$646$$ −207.913 360.115i −0.321846 0.557454i
$$647$$ −504.862 291.482i −0.780312 0.450513i 0.0562291 0.998418i $$-0.482092\pi$$
−0.836541 + 0.547905i $$0.815426\pi$$
$$648$$ −24.5885 + 6.58846i −0.0379452 + 0.0101674i
$$649$$ 388.708i 0.598933i
$$650$$ 429.683 + 115.133i 0.661051 + 0.177128i
$$651$$ −787.559 −1.20977
$$652$$ −149.723 558.774i −0.229637 0.857016i
$$653$$ −182.172 + 315.531i −0.278977 + 0.483202i −0.971131 0.238548i $$-0.923329\pi$$
0.692154 + 0.721750i $$0.256662\pi$$
$$654$$ 382.492 220.832i 0.584851 0.337664i
$$655$$ 3.76160 3.76160i 0.00574290 0.00574290i
$$656$$ 118.210 + 31.6743i 0.180199 + 0.0482841i
$$657$$ −17.4826 + 65.2461i −0.0266098 + 0.0993092i
$$658$$ 535.692 + 535.692i 0.814122 + 0.814122i
$$659$$ 580.592 + 1005.62i 0.881020 + 1.52597i 0.850208 + 0.526446i $$0.176476\pi$$
0.0308117 + 0.999525i $$0.490191\pi$$
$$660$$ −49.1769 28.3923i −0.0745105 0.0430186i
$$661$$ 274.738 73.6159i 0.415641 0.111371i −0.0449374 0.998990i $$-0.514309\pi$$
0.460578 + 0.887619i $$0.347642\pi$$
$$662$$ 140.077i 0.211597i
$$663$$ 197.425 341.950i 0.297775 0.515762i
$$664$$ 389.703 0.586901
$$665$$ −49.1281 183.349i −0.0738769 0.275712i
$$666$$ −6.50962 + 11.2750i −0.00977420 + 0.0169294i
$$667$$ −718.634 + 414.904i −1.07741 + 0.622045i
$$668$$ 384.000 384.000i 0.574850 0.574850i
$$669$$ 244.028 + 65.3872i 0.364766 + 0.0977386i
$$670$$ −10.7564 + 40.1436i −0.0160544 + 0.0599158i
$$671$$ −545.769 545.769i −0.813367 0.813367i
$$672$$ 61.8564 + 107.138i 0.0920482 + 0.159432i
$$673$$ −791.667 457.069i −1.17633 0.679152i −0.221164 0.975237i $$-0.570986\pi$$
−0.955162 + 0.296085i $$0.904319\pi$$
$$674$$ −72.5045 + 19.4275i −0.107573 + 0.0288242i
$$675$$ 125.727i 0.186262i
$$676$$ −292.717 169.000i −0.433013 0.250000i
$$677$$ −148.677 −0.219611 −0.109806 0.993953i $$-0.535023\pi$$
−0.109806 + 0.993953i $$0.535023\pi$$
$$678$$ 50.1596 + 187.198i 0.0739817 + 0.276103i
$$679$$ −322.651 + 558.848i −0.475186 + 0.823046i
$$680$$ 38.5115 22.2346i 0.0566346 0.0326980i
$$681$$ −443.023 + 443.023i −0.650548 + 0.650548i
$$682$$ 899.405 + 240.995i 1.31878 + 0.353365i
$$683$$ −210.382 + 785.156i −0.308026 + 1.14957i 0.622282 + 0.782793i $$0.286206\pi$$
−0.930309 + 0.366777i $$0.880461\pi$$
$$684$$ 71.1384 + 71.1384i 0.104004 + 0.104004i
$$685$$ −77.2250 133.758i −0.112737 0.195267i
$$686$$ 949.892 + 548.420i 1.38468 + 0.799447i
$$687$$ 124.380 33.3275i 0.181048 0.0485117i
$$688$$ 71.0052i 0.103205i
$$689$$ −260.125 150.183i −0.377540 0.217973i
$$690$$ −47.1384 −0.0683166
$$691$$ −66.6654 248.799i −0.0964767 0.360056i 0.900762 0.434312i $$-0.143008\pi$$
−0.997239 + 0.0742560i $$0.976342\pi$$
$$692$$ 107.503 186.200i 0.155351 0.269075i
$$693$$ 599.769 346.277i 0.865468 0.499678i
$$694$$ 675.167 675.167i 0.972863 0.972863i
$$695$$ −11.0052 2.94882i −0.0158348 0.00424291i
$$696$$ −49.0192 + 182.942i −0.0704299 + 0.262848i
$$697$$ 379.371 + 379.371i 0.544292 + 0.544292i
$$698$$ −418.846 725.463i −0.600066 1.03934i
$$699$$ −353.885 204.315i −0.506273 0.292297i
$$700$$ −590.200 + 158.144i −0.843143 + 0.225919i
$$701$$ 1174.97i 1.67614i 0.545563 + 0.838070i $$0.316316\pi$$
−0.545563 + 0.838070i $$0.683684\pi$$
$$702$$ −24.7250 + 92.2750i −0.0352208 + 0.131446i
$$703$$ 51.4538 0.0731917
$$704$$ −37.8564 141.282i −0.0537733 0.200685i
$$705$$ −32.9423 + 57.0577i −0.0467266 + 0.0809329i
$$706$$ 146.044 84.3186i 0.206861 0.119431i
$$707$$ 309.797 309.797i 0.438186 0.438186i
$$708$$ 71.1384 + 19.0615i 0.100478 + 0.0269230i
$$709$$ 181.920 678.936i 0.256587 0.957597i −0.710613 0.703583i $$-0.751582\pi$$
0.967200 0.254014i $$-0.0817510\pi$$
$$710$$ −30.7461 30.7461i −0.0433044 0.0433044i
$$711$$ 134.354 + 232.708i 0.188965 + 0.327296i
$$712$$ 3.09996 + 1.78976i 0.00435388 + 0.00251371i
$$713$$ 746.620 200.056i 1.04715 0.280584i
$$714$$ 542.354i 0.759599i
$$715$$ −184.550 + 106.550i −0.258112 + 0.149021i
$$716$$ 244.344 0.341262
$$717$$ 98.6269 + 368.081i 0.137555 + 0.513362i
$$718$$ −375.415 + 650.238i −0.522863 + 0.905625i
$$719$$ −607.146 + 350.536i −0.844431 + 0.487533i −0.858768 0.512365i $$-0.828770\pi$$
0.0143368 + 0.999897i $$0.495436\pi$$
$$720$$ −7.60770 + 7.60770i −0.0105662 + 0.0105662i
$$721$$ 2401.30 + 643.426i 3.33051 + 0.892407i
$$722$$ −29.2276 + 109.079i −0.0404814 + 0.151079i
$$723$$ −467.915 467.915i −0.647185 0.647185i
$$724$$ −65.2872 113.081i −0.0901757 0.156189i
$$725$$ −810.106 467.715i −1.11739 0.645124i
$$726$$ −504.619 + 135.212i −0.695067 + 0.186243i
$$727$$ 284.715i 0.391630i 0.980641 + 0.195815i $$0.0627353\pi$$
−0.980641 + 0.195815i $$0.937265\pi$$
$$728$$ 464.267 0.637729
$$729$$ 27.0000 0.0370370
$$730$$ 7.38904 + 27.5763i 0.0101220 + 0.0377757i
$$731$$ −155.642 + 269.581i −0.212917 + 0.368783i
$$732$$ −126.646 + 73.1192i −0.173014 + 0.0998896i
$$733$$ 815.307 815.307i 1.11229 1.11229i 0.119447 0.992841i $$-0.461888\pi$$
0.992841 0.119447i $$-0.0381122\pi$$
$$734$$ −289.167 77.4820i −0.393960 0.105561i
$$735$$ −44.3827 + 165.638i −0.0603846 + 0.225358i
$$736$$ −85.8564 85.8564i −0.116653 0.116653i
$$737$$ 299.636 + 518.985i 0.406562 + 0.704185i
$$738$$ −112.413 64.9019i −0.152322 0.0879430i
$$739$$ −1119.41 + 299.944i −1.51476 + 0.405878i −0.918012 0.396553i $$-0.870206\pi$$
−0.596745 + 0.802431i $$0.703540\pi$$
$$740$$ 5.50258i 0.00743592i
$$741$$ 364.683 97.7166i 0.492150 0.131871i
$$742$$ 412.574 0.556030
$$743$$ −1.15906 4.32566i −0.00155997 0.00582189i 0.965141 0.261729i $$-0.0842926\pi$$
−0.966701 + 0.255907i $$0.917626\pi$$
$$744$$ 88.2102 152.785i 0.118562 0.205356i
$$745$$ 89.9866 51.9538i 0.120787 0.0697366i
$$746$$ 66.4397 66.4397i 0.0890613 0.0890613i
$$747$$ −399.258 106.981i −0.534481 0.143214i
$$748$$ 165.962 619.377i 0.221874 0.828044i
$$749$$ 323.041 + 323.041i 0.431296 + 0.431296i
$$750$$ −54.0211 93.5673i −0.0720282 0.124756i
$$751$$ 647.611 + 373.899i 0.862332 + 0.497868i 0.864793 0.502129i $$-0.167450\pi$$
−0.00246040 + 0.999997i $$0.500783\pi$$
$$752$$ −163.923 + 43.9230i −0.217983 + 0.0584083i
$$753$$ 127.292i 0.169047i
$$754$$ 502.583 + 502.583i 0.666556 + 0.666556i
$$755$$ −150.382 −0.199181
$$756$$ −33.9615 126.746i −0.0449227 0.167654i
$$757$$ 478.128 828.142i 0.631609 1.09398i −0.355614 0.934633i $$-0.615728\pi$$
0.987223 0.159346i $$-0.0509386\pi$$
$$758$$ 189.513 109.415i 0.250017 0.144347i
$$759$$ −480.631 + 480.631i −0.633242 + 0.633242i
$$760$$ 41.0718 + 11.0052i 0.0540418 + 0.0144805i
$$761$$ 165.015 615.843i 0.216839 0.809255i −0.768672 0.639643i $$-0.779082\pi$$
0.985511 0.169611i $$-0.0542513\pi$$
$$762$$ −142.641 142.641i −0.187193 0.187193i
$$763$$ 1138.32 + 1971.63i 1.49190 + 2.58405i
$$764$$ −52.9385 30.5641i −0.0692912 0.0400053i
$$765$$ −45.5596 + 12.2077i −0.0595550 + 0.0159577i
$$766$$ 553.990i 0.723224i
$$767$$ 195.433 195.433i 0.254802 0.254802i
$$768$$ −27.7128 −0.0360844
$$769$$ 198.506 + 740.834i 0.258135 +