# Properties

 Label 546.2.l.l.211.1 Level $546$ Weight $2$ Character 546.211 Analytic conductor $4.360$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.l (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{17})$$ Defining polynomial: $$x^{4} - x^{3} + 5x^{2} + 4x + 16$$ x^4 - x^3 + 5*x^2 + 4*x + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 211.1 Root $$1.28078 - 2.21837i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.211 Dual form 546.2.l.l.295.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.28078 + 2.21837i) q^{10} +(-0.780776 - 1.35234i) q^{11} -1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(-1.28078 - 2.21837i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.06155 - 7.03482i) q^{17} +1.00000 q^{18} +(-0.780776 + 1.35234i) q^{19} +(1.28078 - 2.21837i) q^{20} -1.00000 q^{21} +(-0.780776 + 1.35234i) q^{22} +(-3.56155 - 6.16879i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.56155 q^{25} +(-2.84233 + 2.21837i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-1.06155 - 1.83866i) q^{29} +(-1.28078 + 2.21837i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(0.780776 - 1.35234i) q^{33} -8.12311 q^{34} +(1.28078 - 2.21837i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.28078 + 5.68247i) q^{37} +1.56155 q^{38} +(2.84233 - 2.21837i) q^{39} -2.56155 q^{40} +(-2.62311 - 4.54335i) q^{41} +(0.500000 + 0.866025i) q^{42} +(4.00000 - 6.92820i) q^{43} +1.56155 q^{44} +(1.28078 - 2.21837i) q^{45} +(-3.56155 + 6.16879i) q^{46} -12.6847 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.780776 - 1.35234i) q^{50} +8.12311 q^{51} +(3.34233 + 1.35234i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(2.00000 + 3.46410i) q^{55} +(-0.500000 + 0.866025i) q^{56} -1.56155 q^{57} +(-1.06155 + 1.83866i) q^{58} +(1.56155 - 2.70469i) q^{59} +2.56155 q^{60} +(-2.62311 + 4.54335i) q^{61} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.28078 + 9.14657i) q^{65} -1.56155 q^{66} +(-0.438447 - 0.759413i) q^{67} +(4.06155 + 7.03482i) q^{68} +(3.56155 - 6.16879i) q^{69} -2.56155 q^{70} +(-6.68466 + 11.5782i) q^{71} +(-0.500000 + 0.866025i) q^{72} -6.56155 q^{73} +(3.28078 - 5.68247i) q^{74} +(0.780776 + 1.35234i) q^{75} +(-0.780776 - 1.35234i) q^{76} +1.56155 q^{77} +(-3.34233 - 1.35234i) q^{78} -2.43845 q^{79} +(1.28078 + 2.21837i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.62311 + 4.54335i) q^{82} +3.12311 q^{83} +(0.500000 - 0.866025i) q^{84} +(-10.4039 + 18.0201i) q^{85} -8.00000 q^{86} +(1.06155 - 1.83866i) q^{87} +(-0.780776 - 1.35234i) q^{88} +(-3.78078 - 6.54850i) q^{89} -2.56155 q^{90} +(3.34233 + 1.35234i) q^{91} +7.12311 q^{92} +(6.34233 + 10.9852i) q^{94} +(2.00000 - 3.46410i) q^{95} -1.00000 q^{96} +(4.56155 - 7.90084i) q^{97} +(-0.500000 + 0.866025i) q^{98} +1.56155 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100})$$ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 + q^19 + q^20 - 4 * q^21 + q^22 - 6 * q^23 + 2 * q^24 - 2 * q^25 + q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - q^30 - 2 * q^32 - q^33 - 16 * q^34 + q^35 - 2 * q^36 + 9 * q^37 - 2 * q^38 - q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 16 * q^43 - 2 * q^44 + q^45 - 6 * q^46 - 26 * q^47 + 2 * q^48 - 2 * q^49 + q^50 + 16 * q^51 + q^52 + 28 * q^53 + 2 * q^54 + 8 * q^55 - 2 * q^56 + 2 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 6 * q^69 - 2 * q^70 - 2 * q^71 - 2 * q^72 - 18 * q^73 + 9 * q^74 - q^75 + q^76 - 2 * q^77 - q^78 - 18 * q^79 + q^80 - 2 * q^81 + 6 * q^82 - 4 * q^83 + 2 * q^84 - 21 * q^85 - 32 * q^86 - 4 * q^87 + q^88 - 11 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 13 * q^94 + 8 * q^95 - 4 * q^96 + 10 * q^97 - 2 * q^98 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −2.56155 −1.14556 −0.572781 0.819709i $$-0.694135\pi$$
−0.572781 + 0.819709i $$0.694135\pi$$
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ −0.500000 + 0.866025i −0.188982 + 0.327327i
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 1.28078 + 2.21837i 0.405017 + 0.701510i
$$11$$ −0.780776 1.35234i −0.235413 0.407747i 0.723980 0.689821i $$-0.242311\pi$$
−0.959393 + 0.282074i $$0.908978\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −0.500000 3.57071i −0.138675 0.990338i
$$14$$ 1.00000 0.267261
$$15$$ −1.28078 2.21837i −0.330695 0.572781i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 4.06155 7.03482i 0.985071 1.70619i 0.343452 0.939170i $$-0.388404\pi$$
0.641619 0.767023i $$-0.278263\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −0.780776 + 1.35234i −0.179122 + 0.310249i −0.941580 0.336789i $$-0.890659\pi$$
0.762458 + 0.647038i $$0.223992\pi$$
$$20$$ 1.28078 2.21837i 0.286390 0.496043i
$$21$$ −1.00000 −0.218218
$$22$$ −0.780776 + 1.35234i −0.166462 + 0.288321i
$$23$$ −3.56155 6.16879i −0.742635 1.28628i −0.951292 0.308293i $$-0.900242\pi$$
0.208656 0.977989i $$-0.433091\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ 1.56155 0.312311
$$26$$ −2.84233 + 2.21837i −0.557427 + 0.435058i
$$27$$ −1.00000 −0.192450
$$28$$ −0.500000 0.866025i −0.0944911 0.163663i
$$29$$ −1.06155 1.83866i −0.197125 0.341431i 0.750470 0.660905i $$-0.229827\pi$$
−0.947595 + 0.319474i $$0.896494\pi$$
$$30$$ −1.28078 + 2.21837i −0.233837 + 0.405017i
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0.780776 1.35234i 0.135916 0.235413i
$$34$$ −8.12311 −1.39310
$$35$$ 1.28078 2.21837i 0.216491 0.374973i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 3.28078 + 5.68247i 0.539356 + 0.934193i 0.998939 + 0.0460575i $$0.0146657\pi$$
−0.459582 + 0.888135i $$0.652001\pi$$
$$38$$ 1.56155 0.253317
$$39$$ 2.84233 2.21837i 0.455137 0.355223i
$$40$$ −2.56155 −0.405017
$$41$$ −2.62311 4.54335i −0.409660 0.709552i 0.585191 0.810895i $$-0.301019\pi$$
−0.994852 + 0.101343i $$0.967686\pi$$
$$42$$ 0.500000 + 0.866025i 0.0771517 + 0.133631i
$$43$$ 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i $$-0.624505\pi$$
0.991241 0.132068i $$-0.0421616\pi$$
$$44$$ 1.56155 0.235413
$$45$$ 1.28078 2.21837i 0.190927 0.330695i
$$46$$ −3.56155 + 6.16879i −0.525122 + 0.909539i
$$47$$ −12.6847 −1.85025 −0.925124 0.379666i $$-0.876039\pi$$
−0.925124 + 0.379666i $$0.876039\pi$$
$$48$$ 0.500000 0.866025i 0.0721688 0.125000i
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ −0.780776 1.35234i −0.110418 0.191250i
$$51$$ 8.12311 1.13746
$$52$$ 3.34233 + 1.35234i 0.463498 + 0.187536i
$$53$$ 7.00000 0.961524 0.480762 0.876851i $$-0.340360\pi$$
0.480762 + 0.876851i $$0.340360\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 2.00000 + 3.46410i 0.269680 + 0.467099i
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ −1.56155 −0.206833
$$58$$ −1.06155 + 1.83866i −0.139389 + 0.241428i
$$59$$ 1.56155 2.70469i 0.203297 0.352120i −0.746292 0.665619i $$-0.768168\pi$$
0.949589 + 0.313498i $$0.101501\pi$$
$$60$$ 2.56155 0.330695
$$61$$ −2.62311 + 4.54335i −0.335854 + 0.581717i −0.983649 0.180099i $$-0.942358\pi$$
0.647794 + 0.761815i $$0.275692\pi$$
$$62$$ 0 0
$$63$$ −0.500000 0.866025i −0.0629941 0.109109i
$$64$$ 1.00000 0.125000
$$65$$ 1.28078 + 9.14657i 0.158861 + 1.13449i
$$66$$ −1.56155 −0.192214
$$67$$ −0.438447 0.759413i −0.0535648 0.0927770i 0.838000 0.545671i $$-0.183725\pi$$
−0.891565 + 0.452894i $$0.850392\pi$$
$$68$$ 4.06155 + 7.03482i 0.492536 + 0.853097i
$$69$$ 3.56155 6.16879i 0.428761 0.742635i
$$70$$ −2.56155 −0.306164
$$71$$ −6.68466 + 11.5782i −0.793323 + 1.37408i 0.130576 + 0.991438i $$0.458317\pi$$
−0.923899 + 0.382637i $$0.875016\pi$$
$$72$$ −0.500000 + 0.866025i −0.0589256 + 0.102062i
$$73$$ −6.56155 −0.767972 −0.383986 0.923339i $$-0.625449\pi$$
−0.383986 + 0.923339i $$0.625449\pi$$
$$74$$ 3.28078 5.68247i 0.381383 0.660574i
$$75$$ 0.780776 + 1.35234i 0.0901563 + 0.156155i
$$76$$ −0.780776 1.35234i −0.0895612 0.155125i
$$77$$ 1.56155 0.177955
$$78$$ −3.34233 1.35234i −0.378444 0.153123i
$$79$$ −2.43845 −0.274347 −0.137173 0.990547i $$-0.543802\pi$$
−0.137173 + 0.990547i $$0.543802\pi$$
$$80$$ 1.28078 + 2.21837i 0.143195 + 0.248021i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −2.62311 + 4.54335i −0.289674 + 0.501729i
$$83$$ 3.12311 0.342805 0.171403 0.985201i $$-0.445170\pi$$
0.171403 + 0.985201i $$0.445170\pi$$
$$84$$ 0.500000 0.866025i 0.0545545 0.0944911i
$$85$$ −10.4039 + 18.0201i −1.12846 + 1.95455i
$$86$$ −8.00000 −0.862662
$$87$$ 1.06155 1.83866i 0.113810 0.197125i
$$88$$ −0.780776 1.35234i −0.0832310 0.144160i
$$89$$ −3.78078 6.54850i −0.400761 0.694139i 0.593056 0.805161i $$-0.297921\pi$$
−0.993818 + 0.111022i $$0.964588\pi$$
$$90$$ −2.56155 −0.270011
$$91$$ 3.34233 + 1.35234i 0.350371 + 0.141764i
$$92$$ 7.12311 0.742635
$$93$$ 0 0
$$94$$ 6.34233 + 10.9852i 0.654161 + 1.13304i
$$95$$ 2.00000 3.46410i 0.205196 0.355409i
$$96$$ −1.00000 −0.102062
$$97$$ 4.56155 7.90084i 0.463156 0.802209i −0.535961 0.844243i $$-0.680050\pi$$
0.999116 + 0.0420341i $$0.0133838\pi$$
$$98$$ −0.500000 + 0.866025i −0.0505076 + 0.0874818i
$$99$$ 1.56155 0.156942
$$100$$ −0.780776 + 1.35234i −0.0780776 + 0.135234i
$$101$$ −7.40388 12.8239i −0.736714 1.27603i −0.953967 0.299911i $$-0.903043\pi$$
0.217254 0.976115i $$-0.430290\pi$$
$$102$$ −4.06155 7.03482i −0.402154 0.696551i
$$103$$ −10.2462 −1.00959 −0.504795 0.863239i $$-0.668432\pi$$
−0.504795 + 0.863239i $$0.668432\pi$$
$$104$$ −0.500000 3.57071i −0.0490290 0.350137i
$$105$$ 2.56155 0.249982
$$106$$ −3.50000 6.06218i −0.339950 0.588811i
$$107$$ 7.46543 + 12.9305i 0.721711 + 1.25004i 0.960314 + 0.278923i $$0.0899773\pi$$
−0.238603 + 0.971117i $$0.576689\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 4.24621 0.406713 0.203357 0.979105i $$-0.434815\pi$$
0.203357 + 0.979105i $$0.434815\pi$$
$$110$$ 2.00000 3.46410i 0.190693 0.330289i
$$111$$ −3.28078 + 5.68247i −0.311398 + 0.539356i
$$112$$ 1.00000 0.0944911
$$113$$ 1.28078 2.21837i 0.120485 0.208687i −0.799474 0.600701i $$-0.794888\pi$$
0.919959 + 0.392014i $$0.128222\pi$$
$$114$$ 0.780776 + 1.35234i 0.0731264 + 0.126659i
$$115$$ 9.12311 + 15.8017i 0.850734 + 1.47351i
$$116$$ 2.12311 0.197125
$$117$$ 3.34233 + 1.35234i 0.308998 + 0.125024i
$$118$$ −3.12311 −0.287505
$$119$$ 4.06155 + 7.03482i 0.372322 + 0.644881i
$$120$$ −1.28078 2.21837i −0.116918 0.202509i
$$121$$ 4.28078 7.41452i 0.389161 0.674047i
$$122$$ 5.24621 0.474970
$$123$$ 2.62311 4.54335i 0.236517 0.409660i
$$124$$ 0 0
$$125$$ 8.80776 0.787790
$$126$$ −0.500000 + 0.866025i −0.0445435 + 0.0771517i
$$127$$ 10.2462 + 17.7470i 0.909204 + 1.57479i 0.815172 + 0.579219i $$0.196642\pi$$
0.0940321 + 0.995569i $$0.470024\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 8.00000 0.704361
$$130$$ 7.28078 5.68247i 0.638566 0.498386i
$$131$$ −2.24621 −0.196252 −0.0981262 0.995174i $$-0.531285\pi$$
−0.0981262 + 0.995174i $$0.531285\pi$$
$$132$$ 0.780776 + 1.35234i 0.0679579 + 0.117706i
$$133$$ −0.780776 1.35234i −0.0677019 0.117263i
$$134$$ −0.438447 + 0.759413i −0.0378761 + 0.0656033i
$$135$$ 2.56155 0.220463
$$136$$ 4.06155 7.03482i 0.348275 0.603230i
$$137$$ −8.28078 + 14.3427i −0.707474 + 1.22538i 0.258317 + 0.966060i $$0.416832\pi$$
−0.965791 + 0.259321i $$0.916501\pi$$
$$138$$ −7.12311 −0.606359
$$139$$ 4.78078 8.28055i 0.405500 0.702347i −0.588879 0.808221i $$-0.700431\pi$$
0.994380 + 0.105874i $$0.0337640\pi$$
$$140$$ 1.28078 + 2.21837i 0.108245 + 0.187486i
$$141$$ −6.34233 10.9852i −0.534120 0.925124i
$$142$$ 13.3693 1.12193
$$143$$ −4.43845 + 3.46410i −0.371162 + 0.289683i
$$144$$ 1.00000 0.0833333
$$145$$ 2.71922 + 4.70983i 0.225819 + 0.391130i
$$146$$ 3.28078 + 5.68247i 0.271519 + 0.470285i
$$147$$ 0.500000 0.866025i 0.0412393 0.0714286i
$$148$$ −6.56155 −0.539356
$$149$$ 5.71922 9.90599i 0.468537 0.811530i −0.530816 0.847487i $$-0.678115\pi$$
0.999353 + 0.0359569i $$0.0114479\pi$$
$$150$$ 0.780776 1.35234i 0.0637501 0.110418i
$$151$$ 6.93087 0.564026 0.282013 0.959411i $$-0.408998\pi$$
0.282013 + 0.959411i $$0.408998\pi$$
$$152$$ −0.780776 + 1.35234i −0.0633293 + 0.109690i
$$153$$ 4.06155 + 7.03482i 0.328357 + 0.568731i
$$154$$ −0.780776 1.35234i −0.0629168 0.108975i
$$155$$ 0 0
$$156$$ 0.500000 + 3.57071i 0.0400320 + 0.285886i
$$157$$ −13.6847 −1.09215 −0.546077 0.837735i $$-0.683880\pi$$
−0.546077 + 0.837735i $$0.683880\pi$$
$$158$$ 1.21922 + 2.11176i 0.0969962 + 0.168002i
$$159$$ 3.50000 + 6.06218i 0.277568 + 0.480762i
$$160$$ 1.28078 2.21837i 0.101254 0.175378i
$$161$$ 7.12311 0.561379
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ 4.24621 7.35465i 0.332589 0.576061i −0.650430 0.759566i $$-0.725411\pi$$
0.983019 + 0.183505i $$0.0587445\pi$$
$$164$$ 5.24621 0.409660
$$165$$ −2.00000 + 3.46410i −0.155700 + 0.269680i
$$166$$ −1.56155 2.70469i −0.121200 0.209925i
$$167$$ 10.2462 + 17.7470i 0.792876 + 1.37330i 0.924179 + 0.381959i $$0.124750\pi$$
−0.131304 + 0.991342i $$0.541916\pi$$
$$168$$ −1.00000 −0.0771517
$$169$$ −12.5000 + 3.57071i −0.961538 + 0.274670i
$$170$$ 20.8078 1.59588
$$171$$ −0.780776 1.35234i −0.0597075 0.103416i
$$172$$ 4.00000 + 6.92820i 0.304997 + 0.528271i
$$173$$ 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i $$-0.593460\pi$$
0.973670 0.227964i $$-0.0732068\pi$$
$$174$$ −2.12311 −0.160952
$$175$$ −0.780776 + 1.35234i −0.0590211 + 0.102228i
$$176$$ −0.780776 + 1.35234i −0.0588532 + 0.101937i
$$177$$ 3.12311 0.234747
$$178$$ −3.78078 + 6.54850i −0.283381 + 0.490831i
$$179$$ 9.12311 + 15.8017i 0.681893 + 1.18107i 0.974402 + 0.224811i $$0.0721763\pi$$
−0.292510 + 0.956263i $$0.594490\pi$$
$$180$$ 1.28078 + 2.21837i 0.0954634 + 0.165348i
$$181$$ −3.24621 −0.241289 −0.120644 0.992696i $$-0.538496\pi$$
−0.120644 + 0.992696i $$0.538496\pi$$
$$182$$ −0.500000 3.57071i −0.0370625 0.264679i
$$183$$ −5.24621 −0.387811
$$184$$ −3.56155 6.16879i −0.262561 0.454769i
$$185$$ −8.40388 14.5560i −0.617866 1.07017i
$$186$$ 0 0
$$187$$ −12.6847 −0.927594
$$188$$ 6.34233 10.9852i 0.462562 0.801181i
$$189$$ 0.500000 0.866025i 0.0363696 0.0629941i
$$190$$ −4.00000 −0.290191
$$191$$ −1.56155 + 2.70469i −0.112990 + 0.195704i −0.916974 0.398946i $$-0.869376\pi$$
0.803984 + 0.594650i $$0.202709\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ 4.06155 + 7.03482i 0.292357 + 0.506377i 0.974367 0.224966i $$-0.0722271\pi$$
−0.682010 + 0.731343i $$0.738894\pi$$
$$194$$ −9.12311 −0.655001
$$195$$ −7.28078 + 5.68247i −0.521387 + 0.406930i
$$196$$ 1.00000 0.0714286
$$197$$ −4.21922 7.30791i −0.300607 0.520667i 0.675666 0.737208i $$-0.263856\pi$$
−0.976274 + 0.216541i $$0.930523\pi$$
$$198$$ −0.780776 1.35234i −0.0554874 0.0961069i
$$199$$ 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i $$-0.641397\pi$$
0.996850 0.0793045i $$-0.0252700\pi$$
$$200$$ 1.56155 0.110418
$$201$$ 0.438447 0.759413i 0.0309257 0.0535648i
$$202$$ −7.40388 + 12.8239i −0.520935 + 0.902286i
$$203$$ 2.12311 0.149013
$$204$$ −4.06155 + 7.03482i −0.284366 + 0.492536i
$$205$$ 6.71922 + 11.6380i 0.469291 + 0.812836i
$$206$$ 5.12311 + 8.87348i 0.356944 + 0.618245i
$$207$$ 7.12311 0.495090
$$208$$ −2.84233 + 2.21837i −0.197080 + 0.153816i
$$209$$ 2.43845 0.168671
$$210$$ −1.28078 2.21837i −0.0883820 0.153082i
$$211$$ 1.56155 + 2.70469i 0.107502 + 0.186198i 0.914758 0.404003i $$-0.132382\pi$$
−0.807256 + 0.590202i $$0.799048\pi$$
$$212$$ −3.50000 + 6.06218i −0.240381 + 0.416352i
$$213$$ −13.3693 −0.916050
$$214$$ 7.46543 12.9305i 0.510327 0.883912i
$$215$$ −10.2462 + 17.7470i −0.698786 + 1.21033i
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ −2.12311 3.67733i −0.143795 0.249060i
$$219$$ −3.28078 5.68247i −0.221694 0.383986i
$$220$$ −4.00000 −0.269680
$$221$$ −27.1501 10.9852i −1.82631 0.738947i
$$222$$ 6.56155 0.440383
$$223$$ −13.1231 22.7299i −0.878788 1.52211i −0.852672 0.522447i $$-0.825019\pi$$
−0.0261163 0.999659i $$-0.508314\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ −0.780776 + 1.35234i −0.0520518 + 0.0901563i
$$226$$ −2.56155 −0.170392
$$227$$ 9.56155 16.5611i 0.634623 1.09920i −0.351972 0.936010i $$-0.614489\pi$$
0.986595 0.163188i $$-0.0521778\pi$$
$$228$$ 0.780776 1.35234i 0.0517082 0.0895612i
$$229$$ −20.0540 −1.32520 −0.662602 0.748972i $$-0.730548\pi$$
−0.662602 + 0.748972i $$0.730548\pi$$
$$230$$ 9.12311 15.8017i 0.601560 1.04193i
$$231$$ 0.780776 + 1.35234i 0.0513713 + 0.0889777i
$$232$$ −1.06155 1.83866i −0.0696944 0.120714i
$$233$$ −23.3693 −1.53097 −0.765487 0.643451i $$-0.777502\pi$$
−0.765487 + 0.643451i $$0.777502\pi$$
$$234$$ −0.500000 3.57071i −0.0326860 0.233425i
$$235$$ 32.4924 2.11957
$$236$$ 1.56155 + 2.70469i 0.101648 + 0.176060i
$$237$$ −1.21922 2.11176i −0.0791971 0.137173i
$$238$$ 4.06155 7.03482i 0.263271 0.455999i
$$239$$ −5.36932 −0.347312 −0.173656 0.984806i $$-0.555558\pi$$
−0.173656 + 0.984806i $$0.555558\pi$$
$$240$$ −1.28078 + 2.21837i −0.0826738 + 0.143195i
$$241$$ 10.4039 18.0201i 0.670173 1.16077i −0.307682 0.951489i $$-0.599553\pi$$
0.977855 0.209284i $$-0.0671134\pi$$
$$242$$ −8.56155 −0.550357
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ −2.62311 4.54335i −0.167927 0.290858i
$$245$$ 1.28078 + 2.21837i 0.0818258 + 0.141726i
$$246$$ −5.24621 −0.334486
$$247$$ 5.21922 + 2.11176i 0.332091 + 0.134368i
$$248$$ 0 0
$$249$$ 1.56155 + 2.70469i 0.0989594 + 0.171403i
$$250$$ −4.40388 7.62775i −0.278526 0.482421i
$$251$$ −13.8078 + 23.9157i −0.871538 + 1.50955i −0.0111332 + 0.999938i $$0.503544\pi$$
−0.860405 + 0.509611i $$0.829789\pi$$
$$252$$ 1.00000 0.0629941
$$253$$ −5.56155 + 9.63289i −0.349652 + 0.605615i
$$254$$ 10.2462 17.7470i 0.642904 1.11354i
$$255$$ −20.8078 −1.30303
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −0.184658 0.319838i −0.0115187 0.0199509i 0.860209 0.509942i $$-0.170333\pi$$
−0.871727 + 0.489991i $$0.837000\pi$$
$$258$$ −4.00000 6.92820i −0.249029 0.431331i
$$259$$ −6.56155 −0.407715
$$260$$ −8.56155 3.46410i −0.530965 0.214834i
$$261$$ 2.12311 0.131417
$$262$$ 1.12311 + 1.94528i 0.0693857 + 0.120180i
$$263$$ 1.56155 + 2.70469i 0.0962895 + 0.166778i 0.910146 0.414288i $$-0.135969\pi$$
−0.813857 + 0.581066i $$0.802636\pi$$
$$264$$ 0.780776 1.35234i 0.0480535 0.0832310i
$$265$$ −17.9309 −1.10148
$$266$$ −0.780776 + 1.35234i −0.0478725 + 0.0829176i
$$267$$ 3.78078 6.54850i 0.231380 0.400761i
$$268$$ 0.876894 0.0535648
$$269$$ −9.43845 + 16.3479i −0.575472 + 0.996747i 0.420518 + 0.907284i $$0.361848\pi$$
−0.995990 + 0.0894630i $$0.971485\pi$$
$$270$$ −1.28078 2.21837i −0.0779456 0.135006i
$$271$$ −13.3693 23.1563i −0.812128 1.40665i −0.911372 0.411584i $$-0.864976\pi$$
0.0992436 0.995063i $$-0.468358\pi$$
$$272$$ −8.12311 −0.492536
$$273$$ 0.500000 + 3.57071i 0.0302614 + 0.216109i
$$274$$ 16.5616 1.00052
$$275$$ −1.21922 2.11176i −0.0735219 0.127344i
$$276$$ 3.56155 + 6.16879i 0.214380 + 0.371318i
$$277$$ 7.71922 13.3701i 0.463803 0.803331i −0.535343 0.844634i $$-0.679818\pi$$
0.999147 + 0.0413038i $$0.0131511\pi$$
$$278$$ −9.56155 −0.573464
$$279$$ 0 0
$$280$$ 1.28078 2.21837i 0.0765410 0.132573i
$$281$$ −15.9309 −0.950356 −0.475178 0.879890i $$-0.657616\pi$$
−0.475178 + 0.879890i $$0.657616\pi$$
$$282$$ −6.34233 + 10.9852i −0.377680 + 0.654161i
$$283$$ 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i $$0.0359589\pi$$
−0.399188 + 0.916869i $$0.630708\pi$$
$$284$$ −6.68466 11.5782i −0.396662 0.687038i
$$285$$ 4.00000 0.236940
$$286$$ 5.21922 + 2.11176i 0.308619 + 0.124871i
$$287$$ 5.24621 0.309674
$$288$$ −0.500000 0.866025i −0.0294628 0.0510310i
$$289$$ −24.4924 42.4221i −1.44073 2.49542i
$$290$$ 2.71922 4.70983i 0.159678 0.276571i
$$291$$ 9.12311 0.534806
$$292$$ 3.28078 5.68247i 0.191993 0.332541i
$$293$$ −10.9654 + 18.9927i −0.640608 + 1.10956i 0.344690 + 0.938717i $$0.387984\pi$$
−0.985297 + 0.170848i $$0.945349\pi$$
$$294$$ −1.00000 −0.0583212
$$295$$ −4.00000 + 6.92820i −0.232889 + 0.403376i
$$296$$ 3.28078 + 5.68247i 0.190691 + 0.330287i
$$297$$ 0.780776 + 1.35234i 0.0453052 + 0.0784710i
$$298$$ −11.4384 −0.662611
$$299$$ −20.2462 + 15.8017i −1.17087 + 0.913835i
$$300$$ −1.56155 −0.0901563
$$301$$ 4.00000 + 6.92820i 0.230556 + 0.399335i
$$302$$ −3.46543 6.00231i −0.199413 0.345394i
$$303$$ 7.40388 12.8239i 0.425342 0.736714i
$$304$$ 1.56155 0.0895612
$$305$$ 6.71922 11.6380i 0.384742 0.666392i
$$306$$ 4.06155 7.03482i 0.232184 0.402154i
$$307$$ 18.9309 1.08044 0.540221 0.841523i $$-0.318341\pi$$
0.540221 + 0.841523i $$0.318341\pi$$
$$308$$ −0.780776 + 1.35234i −0.0444889 + 0.0770570i
$$309$$ −5.12311 8.87348i −0.291443 0.504795i
$$310$$ 0 0
$$311$$ −6.93087 −0.393014 −0.196507 0.980502i $$-0.562960\pi$$
−0.196507 + 0.980502i $$0.562960\pi$$
$$312$$ 2.84233 2.21837i 0.160915 0.125590i
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 6.84233 + 11.8513i 0.386135 + 0.668805i
$$315$$ 1.28078 + 2.21837i 0.0721636 + 0.124991i
$$316$$ 1.21922 2.11176i 0.0685867 0.118796i
$$317$$ 16.5616 0.930189 0.465095 0.885261i $$-0.346020\pi$$
0.465095 + 0.885261i $$0.346020\pi$$
$$318$$ 3.50000 6.06218i 0.196270 0.339950i
$$319$$ −1.65767 + 2.87117i −0.0928117 + 0.160755i
$$320$$ −2.56155 −0.143195
$$321$$ −7.46543 + 12.9305i −0.416680 + 0.721711i
$$322$$ −3.56155 6.16879i −0.198478 0.343773i
$$323$$ 6.34233 + 10.9852i 0.352897 + 0.611235i
$$324$$ 1.00000 0.0555556
$$325$$ −0.780776 5.57586i −0.0433097 0.309293i
$$326$$ −8.49242 −0.470352
$$327$$ 2.12311 + 3.67733i 0.117408 + 0.203357i
$$328$$ −2.62311 4.54335i −0.144837 0.250865i
$$329$$ 6.34233 10.9852i 0.349664 0.605636i
$$330$$ 4.00000 0.220193
$$331$$ 2.68466 4.64996i 0.147562 0.255585i −0.782764 0.622319i $$-0.786191\pi$$
0.930326 + 0.366734i $$0.119524\pi$$
$$332$$ −1.56155 + 2.70469i −0.0857013 + 0.148439i
$$333$$ −6.56155 −0.359571
$$334$$ 10.2462 17.7470i 0.560648 0.971070i
$$335$$ 1.12311 + 1.94528i 0.0613618 + 0.106282i
$$336$$ 0.500000 + 0.866025i 0.0272772 + 0.0472456i
$$337$$ 19.4924 1.06182 0.530910 0.847428i $$-0.321850\pi$$
0.530910 + 0.847428i $$0.321850\pi$$
$$338$$ 9.34233 + 9.03996i 0.508156 + 0.491709i
$$339$$ 2.56155 0.139124
$$340$$ −10.4039 18.0201i −0.564230 0.977275i
$$341$$ 0 0
$$342$$ −0.780776 + 1.35234i −0.0422196 + 0.0731264i
$$343$$ 1.00000 0.0539949
$$344$$ 4.00000 6.92820i 0.215666 0.373544i
$$345$$ −9.12311 + 15.8017i −0.491171 + 0.850734i
$$346$$ −18.0000 −0.967686
$$347$$ 11.0270 19.0993i 0.591960 1.02530i −0.402009 0.915636i $$-0.631688\pi$$
0.993968 0.109668i $$-0.0349789\pi$$
$$348$$ 1.06155 + 1.83866i 0.0569052 + 0.0985627i
$$349$$ 9.00000 + 15.5885i 0.481759 + 0.834431i 0.999781 0.0209364i $$-0.00666475\pi$$
−0.518022 + 0.855367i $$0.673331\pi$$
$$350$$ 1.56155 0.0834685
$$351$$ 0.500000 + 3.57071i 0.0266880 + 0.190591i
$$352$$ 1.56155 0.0832310
$$353$$ 6.59612 + 11.4248i 0.351076 + 0.608081i 0.986438 0.164133i $$-0.0524826\pi$$
−0.635362 + 0.772214i $$0.719149\pi$$
$$354$$ −1.56155 2.70469i −0.0829956 0.143753i
$$355$$ 17.1231 29.6581i 0.908800 1.57409i
$$356$$ 7.56155 0.400761
$$357$$ −4.06155 + 7.03482i −0.214960 + 0.372322i
$$358$$ 9.12311 15.8017i 0.482171 0.835145i
$$359$$ −18.2462 −0.962998 −0.481499 0.876447i $$-0.659908\pi$$
−0.481499 + 0.876447i $$0.659908\pi$$
$$360$$ 1.28078 2.21837i 0.0675028 0.116918i
$$361$$ 8.28078 + 14.3427i 0.435830 + 0.754880i
$$362$$ 1.62311 + 2.81130i 0.0853085 + 0.147759i
$$363$$ 8.56155 0.449365
$$364$$ −2.84233 + 2.21837i −0.148979 + 0.116274i
$$365$$ 16.8078 0.879759
$$366$$ 2.62311 + 4.54335i 0.137112 + 0.237485i
$$367$$ 13.8078 + 23.9157i 0.720759 + 1.24839i 0.960696 + 0.277603i $$0.0895401\pi$$
−0.239936 + 0.970789i $$0.577127\pi$$
$$368$$ −3.56155 + 6.16879i −0.185659 + 0.321570i
$$369$$ 5.24621 0.273107
$$370$$ −8.40388 + 14.5560i −0.436897 + 0.756728i
$$371$$ −3.50000 + 6.06218i −0.181711 + 0.314733i
$$372$$ 0 0
$$373$$ 15.9654 27.6529i 0.826659 1.43182i −0.0739860 0.997259i $$-0.523572\pi$$
0.900645 0.434556i $$-0.143095\pi$$
$$374$$ 6.34233 + 10.9852i 0.327954 + 0.568033i
$$375$$ 4.40388 + 7.62775i 0.227415 + 0.393895i
$$376$$ −12.6847 −0.654161
$$377$$ −6.03457 + 4.70983i −0.310796 + 0.242569i
$$378$$ −1.00000 −0.0514344
$$379$$ 1.80776 + 3.13114i 0.0928586 + 0.160836i 0.908713 0.417422i $$-0.137066\pi$$
−0.815854 + 0.578258i $$0.803733\pi$$
$$380$$ 2.00000 + 3.46410i 0.102598 + 0.177705i
$$381$$ −10.2462 + 17.7470i −0.524929 + 0.909204i
$$382$$ 3.12311 0.159792
$$383$$ −3.90388 + 6.76172i −0.199479 + 0.345508i −0.948360 0.317197i $$-0.897258\pi$$
0.748881 + 0.662705i $$0.230592\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ −4.00000 −0.203859
$$386$$ 4.06155 7.03482i 0.206728 0.358063i
$$387$$ 4.00000 + 6.92820i 0.203331 + 0.352180i
$$388$$ 4.56155 + 7.90084i 0.231578 + 0.401104i
$$389$$ −17.6847 −0.896648 −0.448324 0.893871i $$-0.647979\pi$$
−0.448324 + 0.893871i $$0.647979\pi$$
$$390$$ 8.56155 + 3.46410i 0.433531 + 0.175412i
$$391$$ −57.8617 −2.92619
$$392$$ −0.500000 0.866025i −0.0252538 0.0437409i
$$393$$ −1.12311 1.94528i −0.0566532 0.0981262i
$$394$$ −4.21922 + 7.30791i −0.212561 + 0.368167i
$$395$$ 6.24621 0.314281
$$396$$ −0.780776 + 1.35234i −0.0392355 + 0.0679579i
$$397$$ 0.465435 0.806157i 0.0233595 0.0404598i −0.854109 0.520093i $$-0.825897\pi$$
0.877469 + 0.479634i $$0.159230\pi$$
$$398$$ −16.0000 −0.802008
$$399$$ 0.780776 1.35234i 0.0390877 0.0677019i
$$400$$ −0.780776 1.35234i −0.0390388 0.0676172i
$$401$$ −9.40388 16.2880i −0.469607 0.813384i 0.529789 0.848130i $$-0.322271\pi$$
−0.999396 + 0.0347457i $$0.988938\pi$$
$$402$$ −0.876894 −0.0437355
$$403$$ 0 0
$$404$$ 14.8078 0.736714
$$405$$ 1.28078 + 2.21837i 0.0636423 + 0.110232i
$$406$$ −1.06155 1.83866i −0.0526840 0.0912513i
$$407$$ 5.12311 8.87348i 0.253943 0.439842i
$$408$$ 8.12311 0.402154
$$409$$ 3.71922 6.44188i 0.183904 0.318531i −0.759303 0.650737i $$-0.774460\pi$$
0.943207 + 0.332207i $$0.107793\pi$$
$$410$$ 6.71922 11.6380i 0.331839 0.574762i
$$411$$ −16.5616 −0.816921
$$412$$ 5.12311 8.87348i 0.252397 0.437165i
$$413$$ 1.56155 + 2.70469i 0.0768390 + 0.133089i
$$414$$ −3.56155 6.16879i −0.175041 0.303180i
$$415$$ −8.00000 −0.392705
$$416$$ 3.34233 + 1.35234i 0.163871 + 0.0663041i
$$417$$ 9.56155 0.468231
$$418$$ −1.21922 2.11176i −0.0596342 0.103289i
$$419$$ 0.684658 + 1.18586i 0.0334478 + 0.0579332i 0.882265 0.470754i $$-0.156018\pi$$
−0.848817 + 0.528687i $$0.822685\pi$$
$$420$$ −1.28078 + 2.21837i −0.0624955 + 0.108245i
$$421$$ 31.3002 1.52548 0.762739 0.646707i $$-0.223854\pi$$
0.762739 + 0.646707i $$0.223854\pi$$
$$422$$ 1.56155 2.70469i 0.0760152 0.131662i
$$423$$ 6.34233 10.9852i 0.308375 0.534120i
$$424$$ 7.00000 0.339950
$$425$$ 6.34233 10.9852i 0.307648 0.532862i
$$426$$ 6.68466 + 11.5782i 0.323873 + 0.560964i
$$427$$ −2.62311 4.54335i −0.126941 0.219868i
$$428$$ −14.9309 −0.721711
$$429$$ −5.21922 2.11176i −0.251986 0.101957i
$$430$$ 20.4924 0.988232
$$431$$ 2.68466 + 4.64996i 0.129315 + 0.223981i 0.923412 0.383811i $$-0.125389\pi$$
−0.794096 + 0.607792i $$0.792055\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 16.8423 29.1718i 0.809391 1.40191i −0.103896 0.994588i $$-0.533131\pi$$
0.913287 0.407318i $$-0.133536\pi$$
$$434$$ 0 0
$$435$$ −2.71922 + 4.70983i −0.130377 + 0.225819i
$$436$$ −2.12311 + 3.67733i −0.101678 + 0.176112i
$$437$$ 11.1231 0.532090
$$438$$ −3.28078 + 5.68247i −0.156762 + 0.271519i
$$439$$ 4.87689 + 8.44703i 0.232761 + 0.403155i 0.958620 0.284690i $$-0.0918905\pi$$
−0.725858 + 0.687844i $$0.758557\pi$$
$$440$$ 2.00000 + 3.46410i 0.0953463 + 0.165145i
$$441$$ 1.00000 0.0476190
$$442$$ 4.06155 + 29.0053i 0.193188 + 1.37964i
$$443$$ 10.0540 0.477679 0.238839 0.971059i $$-0.423233\pi$$
0.238839 + 0.971059i $$0.423233\pi$$
$$444$$ −3.28078 5.68247i −0.155699 0.269678i
$$445$$ 9.68466 + 16.7743i 0.459097 + 0.795179i
$$446$$ −13.1231 + 22.7299i −0.621397 + 1.07629i
$$447$$ 11.4384 0.541020
$$448$$ −0.500000 + 0.866025i −0.0236228 + 0.0409159i
$$449$$ 15.6847 27.1666i 0.740205 1.28207i −0.212197 0.977227i $$-0.568062\pi$$
0.952402 0.304845i $$-0.0986048\pi$$
$$450$$ 1.56155 0.0736123
$$451$$ −4.09612 + 7.09468i −0.192879 + 0.334076i
$$452$$ 1.28078 + 2.21837i 0.0602427 + 0.104343i
$$453$$ 3.46543 + 6.00231i 0.162820 + 0.282013i
$$454$$ −19.1231 −0.897492
$$455$$ −8.56155 3.46410i −0.401372 0.162400i
$$456$$ −1.56155 −0.0731264
$$457$$ −0.0345652 0.0598686i −0.00161689 0.00280054i 0.865216 0.501400i $$-0.167181\pi$$
−0.866833 + 0.498599i $$0.833848\pi$$
$$458$$ 10.0270 + 17.3673i 0.468530 + 0.811518i
$$459$$ −4.06155 + 7.03482i −0.189577 + 0.328357i
$$460$$ −18.2462 −0.850734
$$461$$ 15.5270 26.8935i 0.723164 1.25256i −0.236561 0.971617i $$-0.576020\pi$$
0.959725 0.280940i $$-0.0906462\pi$$
$$462$$ 0.780776 1.35234i 0.0363250 0.0629168i
$$463$$ 24.6847 1.14719 0.573597 0.819138i $$-0.305548\pi$$
0.573597 + 0.819138i $$0.305548\pi$$
$$464$$ −1.06155 + 1.83866i −0.0492814 + 0.0853578i
$$465$$ 0 0
$$466$$ 11.6847 + 20.2384i 0.541281 + 0.937527i
$$467$$ 28.9848 1.34126 0.670629 0.741793i $$-0.266024\pi$$
0.670629 + 0.741793i $$0.266024\pi$$
$$468$$ −2.84233 + 2.21837i −0.131387 + 0.102544i
$$469$$ 0.876894 0.0404912
$$470$$ −16.2462 28.1393i −0.749382 1.29797i
$$471$$ −6.84233 11.8513i −0.315278 0.546077i
$$472$$ 1.56155 2.70469i 0.0718763 0.124493i
$$473$$ −12.4924 −0.574402
$$474$$ −1.21922 + 2.11176i −0.0560008 + 0.0969962i
$$475$$ −1.21922 + 2.11176i −0.0559418 + 0.0968941i
$$476$$ −8.12311 −0.372322
$$477$$ −3.50000 + 6.06218i −0.160254 + 0.277568i
$$478$$ 2.68466 + 4.64996i 0.122793 + 0.212684i
$$479$$ −13.4654 23.3228i −0.615251 1.06565i −0.990340 0.138658i $$-0.955721\pi$$
0.375089 0.926989i $$-0.377612\pi$$
$$480$$ 2.56155 0.116918
$$481$$ 18.6501 14.5560i 0.850371 0.663694i
$$482$$ −20.8078 −0.947768
$$483$$ 3.56155 + 6.16879i 0.162056 + 0.280690i
$$484$$ 4.28078 + 7.41452i 0.194581 + 0.337024i
$$485$$ −11.6847 + 20.2384i −0.530573 + 0.918979i
$$486$$ −1.00000 −0.0453609
$$487$$ −5.65767 + 9.79937i −0.256374 + 0.444052i −0.965268 0.261263i $$-0.915861\pi$$
0.708894 + 0.705315i $$0.249194\pi$$
$$488$$ −2.62311 + 4.54335i −0.118742 + 0.205668i
$$489$$ 8.49242 0.384041
$$490$$ 1.28078 2.21837i 0.0578596 0.100216i
$$491$$ −8.24621 14.2829i −0.372146 0.644576i 0.617749 0.786375i $$-0.288045\pi$$
−0.989895 + 0.141799i $$0.954711\pi$$
$$492$$ 2.62311 + 4.54335i 0.118259 + 0.204830i
$$493$$ −17.2462 −0.776730
$$494$$ −0.780776 5.57586i −0.0351288 0.250870i
$$495$$ −4.00000 −0.179787
$$496$$ 0 0
$$497$$ −6.68466 11.5782i −0.299848 0.519352i
$$498$$ 1.56155 2.70469i 0.0699749 0.121200i
$$499$$ 13.7538 0.615704 0.307852 0.951434i $$-0.400390\pi$$
0.307852 + 0.951434i $$0.400390\pi$$
$$500$$ −4.40388 + 7.62775i −0.196948 + 0.341123i
$$501$$ −10.2462 + 17.7470i −0.457767 + 0.792876i
$$502$$ 27.6155 1.23254
$$503$$ −2.24621 + 3.89055i −0.100154 + 0.173471i −0.911748 0.410750i $$-0.865267\pi$$
0.811594 + 0.584222i $$0.198600\pi$$
$$504$$ −0.500000 0.866025i −0.0222718 0.0385758i
$$505$$ 18.9654 + 32.8491i 0.843951 + 1.46177i
$$506$$ 11.1231 0.494482
$$507$$ −9.34233 9.03996i −0.414907 0.401479i
$$508$$ −20.4924 −0.909204
$$509$$ 10.5961 + 18.3530i 0.469665 + 0.813483i 0.999398 0.0346809i $$-0.0110415\pi$$
−0.529734 + 0.848164i $$0.677708\pi$$
$$510$$ 10.4039 + 18.0201i 0.460692 + 0.797941i
$$511$$ 3.28078 5.68247i 0.145133 0.251378i
$$512$$ 1.00000 0.0441942
$$513$$ 0.780776 1.35234i 0.0344721 0.0597075i
$$514$$ −0.184658 + 0.319838i −0.00814493 + 0.0141074i
$$515$$ 26.2462 1.15655
$$516$$ −4.00000 + 6.92820i −0.176090 + 0.304997i
$$517$$ 9.90388 + 17.1540i 0.435572 + 0.754433i
$$518$$ 3.28078 + 5.68247i 0.144149 + 0.249673i
$$519$$ 18.0000 0.790112
$$520$$ 1.28078 + 9.14657i 0.0561658 + 0.401104i
$$521$$ 34.1231 1.49496 0.747480 0.664284i $$-0.231263\pi$$
0.747480 + 0.664284i $$0.231263\pi$$
$$522$$ −1.06155 1.83866i −0.0464629 0.0804761i
$$523$$ −1.90388 3.29762i −0.0832509 0.144195i 0.821394 0.570362i $$-0.193197\pi$$
−0.904645 + 0.426167i $$0.859864\pi$$
$$524$$ 1.12311 1.94528i 0.0490631 0.0849798i
$$525$$ −1.56155 −0.0681518
$$526$$ 1.56155 2.70469i 0.0680869 0.117930i
$$527$$ 0 0
$$528$$ −1.56155 −0.0679579
$$529$$ −13.8693 + 24.0224i −0.603014 + 1.04445i
$$530$$ 8.96543 + 15.5286i 0.389434 + 0.674519i
$$531$$ 1.56155 + 2.70469i 0.0677656 + 0.117373i
$$532$$ 1.56155 0.0677019
$$533$$ −14.9115 + 11.6380i −0.645887 + 0.504099i
$$534$$ −7.56155 −0.327220
$$535$$ −19.1231 33.1222i −0.826764 1.43200i
$$536$$ −0.438447 0.759413i −0.0189380 0.0328016i
$$537$$ −9.12311 + 15.8017i −0.393691 + 0.681893i
$$538$$ 18.8769 0.813841
$$539$$ −0.780776 + 1.35234i −0.0336304 + 0.0582496i
$$540$$ −1.28078 + 2.21837i −0.0551158 + 0.0954634i
$$541$$ −26.1771 −1.12544 −0.562720 0.826647i $$-0.690245\pi$$
−0.562720 + 0.826647i $$0.690245\pi$$
$$542$$ −13.3693 + 23.1563i −0.574261 + 0.994650i
$$543$$ −1.62311 2.81130i −0.0696541 0.120644i
$$544$$ 4.06155 + 7.03482i 0.174138 + 0.301615i
$$545$$ −10.8769 −0.465915
$$546$$ 2.84233 2.21837i 0.121640 0.0949375i
$$547$$ 7.61553 0.325616 0.162808 0.986658i $$-0.447945\pi$$
0.162808 + 0.986658i $$0.447945\pi$$
$$548$$ −8.28078 14.3427i −0.353737 0.612691i
$$549$$ −2.62311 4.54335i −0.111951 0.193906i
$$550$$ −1.21922 + 2.11176i −0.0519879 + 0.0900456i
$$551$$ 3.31534 0.141238
$$552$$ 3.56155 6.16879i 0.151590 0.262561i
$$553$$ 1.21922 2.11176i 0.0518467 0.0898011i
$$554$$ −15.4384 −0.655917
$$555$$ 8.40388 14.5560i 0.356725 0.617866i
$$556$$ 4.78078 + 8.28055i 0.202750 + 0.351173i
$$557$$ −1.93845 3.35749i −0.0821346 0.142261i 0.822032 0.569441i $$-0.192840\pi$$
−0.904167 + 0.427180i $$0.859507\pi$$
$$558$$ 0 0
$$559$$ −26.7386 10.8188i −1.13092 0.457585i
$$560$$ −2.56155 −0.108245
$$561$$ −6.34233 10.9852i −0.267773 0.463797i
$$562$$ 7.96543 + 13.7965i 0.336002 + 0.581972i
$$563$$ 11.1231 19.2658i 0.468783 0.811956i −0.530580 0.847635i $$-0.678026\pi$$
0.999363 + 0.0356787i $$0.0113593\pi$$
$$564$$ 12.6847 0.534120
$$565$$ −3.28078 + 5.68247i −0.138023 + 0.239063i
$$566$$ 10.0000 17.3205i 0.420331 0.728035i
$$567$$ 1.00000 0.0419961
$$568$$ −6.68466 + 11.5782i −0.280482 + 0.485809i
$$569$$ 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i $$-0.0141058\pi$$
−0.537874 + 0.843025i $$0.680772\pi$$
$$570$$ −2.00000 3.46410i −0.0837708 0.145095i
$$571$$ −12.8769 −0.538881 −0.269441 0.963017i $$-0.586839\pi$$
−0.269441 + 0.963017i $$0.586839\pi$$
$$572$$ −0.780776 5.57586i −0.0326459 0.233138i
$$573$$ −3.12311 −0.130470
$$574$$ −2.62311 4.54335i −0.109486 0.189636i
$$575$$ −5.56155 9.63289i −0.231933 0.401719i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ −31.4384 −1.30880 −0.654400 0.756149i $$-0.727079\pi$$
−0.654400 + 0.756149i $$0.727079\pi$$
$$578$$ −24.4924 + 42.4221i −1.01875 + 1.76453i
$$579$$ −4.06155 + 7.03482i −0.168792 + 0.292357i
$$580$$ −5.43845 −0.225819
$$581$$ −1.56155 + 2.70469i −0.0647841 + 0.112209i
$$582$$ −4.56155 7.90084i −0.189082 0.327500i
$$583$$ −5.46543 9.46641i −0.226355 0.392059i
$$584$$ −6.56155 −0.271519
$$585$$ −8.56155 3.46410i −0.353977 0.143223i
$$586$$ 21.9309 0.905956
$$587$$ 7.12311 + 12.3376i 0.294002 + 0.509226i 0.974752 0.223289i $$-0.0716794\pi$$
−0.680750 + 0.732516i $$0.738346\pi$$
$$588$$ 0.500000 + 0.866025i 0.0206197 + 0.0357143i
$$589$$ 0 0
$$590$$ 8.00000 0.329355
$$591$$ 4.21922 7.30791i 0.173556 0.300607i
$$592$$ 3.28078 5.68247i 0.134839 0.233548i
$$593$$ 31.9848 1.31346 0.656730 0.754126i $$-0.271939\pi$$
0.656730 + 0.754126i $$0.271939\pi$$
$$594$$ 0.780776 1.35234i 0.0320356 0.0554874i
$$595$$ −10.4039 18.0201i −0.426518 0.738750i
$$596$$ 5.71922 + 9.90599i 0.234269 + 0.405765i
$$597$$ 16.0000 0.654836
$$598$$ 23.8078 + 9.63289i 0.973572 + 0.393918i
$$599$$ −33.8617 −1.38355 −0.691777 0.722112i $$-0.743172\pi$$
−0.691777 + 0.722112i $$0.743172\pi$$
$$600$$ 0.780776 + 1.35234i 0.0318751 + 0.0552092i
$$601$$ 12.6501 + 21.9106i 0.516008 + 0.893752i 0.999827 + 0.0185842i $$0.00591589\pi$$
−0.483819 + 0.875168i $$0.660751\pi$$
$$602$$ 4.00000 6.92820i 0.163028 0.282372i
$$603$$ 0.876894 0.0357099
$$604$$ −3.46543 + 6.00231i −0.141007 + 0.244230i
$$605$$ −10.9654 + 18.9927i −0.445808 + 0.772163i
$$606$$ −14.8078 −0.601524
$$607$$ −8.49242 + 14.7093i −0.344697 + 0.597032i −0.985299 0.170841i $$-0.945352\pi$$
0.640602 + 0.767873i $$0.278685\pi$$
$$608$$ −0.780776 1.35234i −0.0316647 0.0548448i
$$609$$ 1.06155 + 1.83866i 0.0430163 + 0.0745064i
$$610$$ −13.4384 −0.544107
$$611$$ 6.34233 + 45.2933i 0.256583 + 1.83237i
$$612$$ −8.12311 −0.328357
$$613$$ −8.71922 15.1021i −0.352166 0.609970i 0.634463 0.772954i $$-0.281221\pi$$
−0.986629 + 0.162984i $$0.947888\pi$$
$$614$$ −9.46543 16.3946i −0.381994 0.661633i
$$615$$ −6.71922 + 11.6380i −0.270945 + 0.469291i
$$616$$ 1.56155 0.0629168
$$617$$ 11.0885 19.2059i 0.446408 0.773201i −0.551741 0.834015i $$-0.686036\pi$$
0.998149 + 0.0608143i $$0.0193697\pi$$
$$618$$ −5.12311 + 8.87348i −0.206082 + 0.356944i
$$619$$ 30.9309 1.24322 0.621608 0.783328i $$-0.286480\pi$$
0.621608 + 0.783328i $$0.286480\pi$$
$$620$$ 0 0
$$621$$ 3.56155 + 6.16879i 0.142920 + 0.247545i
$$622$$ 3.46543 + 6.00231i 0.138951 + 0.240671i
$$623$$ 7.56155 0.302947
$$624$$ −3.34233 1.35234i −0.133800 0.0541371i
$$625$$ −30.3693 −1.21477
$$626$$ 3.00000 + 5.19615i 0.119904 + 0.207680i
$$627$$ 1.21922 + 2.11176i 0.0486911 + 0.0843355i
$$628$$ 6.84233 11.8513i 0.273039 0.472917i
$$629$$ 53.3002 2.12522
$$630$$ 1.28078 2.21837i 0.0510274 0.0883820i
$$631$$ 19.4654 33.7151i 0.774907 1.34218i −0.159940 0.987127i $$-0.551130\pi$$
0.934847 0.355051i $$-0.115537\pi$$
$$632$$ −2.43845 −0.0969962
$$633$$ −1.56155 + 2.70469i −0.0620662 + 0.107502i
$$634$$ −8.28078 14.3427i −0.328872 0.569622i
$$635$$ −26.2462 45.4598i −1.04155 1.80402i
$$636$$ −7.00000 −0.277568
$$637$$ −2.84233 + 2.21837i −0.112617 + 0.0878950i
$$638$$ 3.31534 0.131256
$$639$$ −6.68466 11.5782i −0.264441 0.458025i
$$640$$ 1.28078 + 2.21837i 0.0506271 + 0.0876888i
$$641$$ −6.28078 + 10.8786i −0.248076 + 0.429680i −0.962992 0.269530i $$-0.913132\pi$$
0.714916 + 0.699210i $$0.246465\pi$$
$$642$$ 14.9309 0.589274
$$643$$ −17.6577 + 30.5840i −0.696351 + 1.20611i 0.273373 + 0.961908i $$0.411861\pi$$
−0.969723 + 0.244206i $$0.921473\pi$$
$$644$$ −3.56155 + 6.16879i −0.140345 + 0.243084i
$$645$$ −20.4924 −0.806888
$$646$$ 6.34233 10.9852i 0.249536 0.432208i
$$647$$ 23.0270 + 39.8839i 0.905284 + 1.56800i 0.820535 + 0.571596i $$0.193676\pi$$
0.0847492 + 0.996402i $$0.472991\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ −4.87689 −0.191435
$$650$$ −4.43845 + 3.46410i −0.174090 + 0.135873i
$$651$$ 0 0
$$652$$ 4.24621 + 7.35465i 0.166294 + 0.288030i
$$653$$ −8.21922 14.2361i −0.321643 0.557102i 0.659184 0.751982i $$-0.270902\pi$$
−0.980827 + 0.194879i $$0.937568\pi$$
$$654$$ 2.12311 3.67733i 0.0830200 0.143795i
$$655$$ 5.75379 0.224819
$$656$$ −2.62311 + 4.54335i −0.102415 + 0.177388i
$$657$$ 3.28078 5.68247i 0.127995 0.221694i
$$658$$ −12.6847 −0.494499
$$659$$ −15.4654 + 26.7869i −0.602448 + 1.04347i 0.390001 + 0.920814i $$0.372475\pi$$
−0.992449 + 0.122656i $$0.960859\pi$$
$$660$$ −2.00000 3.46410i −0.0778499 0.134840i
$$661$$ −8.52699 14.7692i −0.331661 0.574454i 0.651176 0.758926i $$-0.274276\pi$$
−0.982838 + 0.184472i $$0.940942\pi$$
$$662$$ −5.36932 −0.208684
$$663$$ −4.06155 29.0053i −0.157738 1.12647i
$$664$$ 3.12311 0.121200
$$665$$ 2.00000 + 3.46410i 0.0775567 + 0.134332i
$$666$$ 3.28078 + 5.68247i 0.127128 + 0.220191i
$$667$$ −7.56155 + 13.0970i −0.292784 + 0.507118i
$$668$$ −20.4924 −0.792876
$$669$$ 13.1231 22.7299i 0.507369 0.878788i
$$670$$ 1.12311 1.94528i 0.0433894 0.0751526i
$$671$$ 8.19224 0.316258
$$672$$ 0.500000 0.866025i 0.0192879 0.0334077i
$$673$$ 9.62311 + 16.6677i 0.370943 + 0.642493i 0.989711 0.143081i $$-0.0457010\pi$$
−0.618767 + 0.785574i $$0.712368\pi$$
$$674$$ −9.74621 16.8809i −0.375410 0.650229i
$$675$$ −1.56155 −0.0601042
$$676$$ 3.15767 12.6107i 0.121449 0.485026i
$$677$$ 24.7386 0.950783 0.475391 0.879774i $$-0.342306\pi$$
0.475391 + 0.879774i $$0.342306\pi$$
$$678$$ −1.28078 2.21837i −0.0491879 0.0851960i
$$679$$ 4.56155 + 7.90084i 0.175056 + 0.303206i
$$680$$ −10.4039 + 18.0201i −0.398971 + 0.691037i
$$681$$ 19.1231 0.732799
$$682$$ 0 0
$$683$$ −3.75379 + 6.50175i −0.143635 + 0.248783i −0.928863 0.370424i $$-0.879212\pi$$
0.785228 + 0.619207i $$0.212546\pi$$
$$684$$ 1.56155 0.0597075
$$685$$ 21.2116 36.7396i 0.810455 1.40375i
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ −10.0270 17.3673i −0.382553 0.662602i
$$688$$ −8.00000 −0.304997
$$689$$ −3.50000 24.9950i −0.133339 0.952234i
$$690$$ 18.2462 0.694621
$$691$$ −16.4924 28.5657i −0.627401 1.08669i −0.988071 0.153997i $$-0.950785\pi$$
0.360670 0.932694i $$-0.382548\pi$$
$$692$$ 9.00000 + 15.5885i 0.342129 + 0.592584i
$$693$$ −0.780776 + 1.35234i −0.0296592 + 0.0513713i
$$694$$ −22.0540 −0.837157
$$695$$ −12.2462 + 21.2111i −0.464525 + 0.804581i
$$696$$ 1.06155 1.83866i 0.0402381 0.0696944i
$$697$$ −42.6155 −1.61418
$$698$$ 9.00000 15.5885i 0.340655 0.590032i
$$699$$ −11.6847 20.2384i −0.441954 0.765487i
$$700$$ −0.780776 1.35234i −0.0295106 0.0511138i
$$701$$ 14.3002 0.540111 0.270055 0.962845i $$-0.412958\pi$$
0.270055 + 0.962845i $$0.412958\pi$$
$$702$$ 2.84233 2.21837i 0.107277 0.0837270i
$$703$$ −10.2462 −0.386443
$$704$$ −0.780776 1.35234i −0.0294266 0.0509684i
$$705$$ 16.2462 + 28.1393i 0.611868 + 1.05979i
$$706$$ 6.59612 11.4248i 0.248248 0.429978i
$$707$$ 14.8078 0.556903
$$708$$ −1.56155 + 2.70469i −0.0586867 + 0.101648i
$$709$$ −7.65009 + 13.2504i −0.287305 + 0.497627i −0.973166 0.230106i $$-0.926093\pi$$
0.685860 + 0.727733i $$0.259426\pi$$
$$710$$ −34.2462 −1.28524
$$711$$ 1.21922 2.11176i 0.0457245 0.0791971i
$$712$$ −3.78078 6.54850i −0.141691 0.245415i
$$713$$ 0 0
$$714$$ 8.12311 0.304000
$$715$$ 11.3693 8.87348i 0.425188 0.331849i
$$716$$ −18.2462 −0.681893
$$717$$ −2.68466 4.64996i −0.100260 0.173656i
$$718$$ 9.12311 + 15.8017i 0.340471 + 0.589714i
$$719$$ 9.90388 17.1540i 0.369352 0.639737i −0.620112 0.784513i $$-0.712913\pi$$
0.989464 + 0.144776i $$0.0462462\pi$$
$$720$$ −2.56155 −0.0954634
$$721$$ 5.12311 8.87348i 0.190794 0.330466i
$$722$$ 8.28078 14.3427i 0.308179 0.533781i
$$723$$ 20.8078 0.773849
$$724$$ 1.62311 2.81130i 0.0603222 0.104481i
$$725$$ −1.65767 2.87117i −0.0615643 0.106633i
$$726$$ −4.28078 7.41452i −0.158875 0.275179i
$$727$$ 40.0000 1.48352 0.741759 0.670667i $$-0.233992\pi$$
0.741759 + 0.670667i $$0.233992\pi$$
$$728$$ 3.34233 + 1.35234i 0.123875 + 0.0501212i
$$729$$ 1.00000 0.0370370
$$730$$ −8.40388 14.5560i −0.311042 0.538740i
$$731$$ −32.4924 56.2785i −1.20178 2.08154i
$$732$$ 2.62311 4.54335i 0.0969528 0.167927i
$$733$$ 28.8617 1.06603 0.533016 0.846105i $$-0.321058\pi$$
0.533016 + 0.846105i $$0.321058\pi$$
$$734$$ 13.8078 23.9157i 0.509654 0.882746i
$$735$$ −1.28078 + 2.21837i −0.0472421 + 0.0818258i
$$736$$ 7.12311 0.262561
$$737$$ −0.684658 + 1.18586i −0.0252197 + 0.0436818i
$$738$$ −2.62311 4.54335i −0.0965579 0.167243i
$$739$$ 4.68466 + 8.11407i 0.172328 + 0.298481i 0.939233 0.343279i $$-0.111538\pi$$
−0.766905 + 0.641760i $$0.778204\pi$$
$$740$$ 16.8078 0.617866
$$741$$ 0.780776 + 5.57586i 0.0286825 + 0.204834i
$$742$$ 7.00000 0.256978
$$743$$ −14.2462 24.6752i −0.522643 0.905244i −0.999653 0.0263461i $$-0.991613\pi$$
0.477010 0.878898i $$-0.341721\pi$$
$$744$$ 0 0
$$745$$ −14.6501 + 25.3747i −0.536738 + 0.929657i
$$746$$ −31.9309 −1.16907
$$747$$ −1.56155 + 2.70469i −0.0571342 + 0.0989594i
$$748$$ 6.34233 10.9852i 0.231899 0.401660i
$$749$$ −14.9309 −0.545562
$$750$$ 4.40388 7.62775i 0.160807 0.278526i
$$751$$ 10.0961 + 17.4870i 0.368413 + 0.638109i 0.989318 0.145777i $$-0.0465681\pi$$
−0.620905 + 0.783886i $$0.713235\pi$$
$$752$$ 6.34233 + 10.9852i 0.231281 + 0.400590i
$$753$$ −27.6155 −1.00637
$$754$$ 7.09612 + 2.87117i 0.258425 + 0.104562i
$$755$$ −17.7538 −0.646127
$$756$$ 0.500000 + 0.866025i 0.0181848 + 0.0314970i
$$757$$ −1.63068 2.82443i −0.0592682 0.102656i 0.834869 0.550449i $$-0.185543\pi$$
−0.894137 + 0.447793i $$0.852210\pi$$
$$758$$ 1.80776 3.13114i 0.0656609 0.113728i
$$759$$ −11.1231 −0.403743
$$760$$ 2.00000 3.46410i 0.0725476 0.125656i
$$761$$ 7.49242 12.9773i 0.271600 0.470425i −0.697672 0.716418i $$-0.745781\pi$$
0.969272 + 0.245993i $$0.0791139\pi$$
$$762$$ 20.4924 0.742362
$$763$$ −2.12311 + 3.67733i −0.0768616 + 0.133128i
$$764$$ −1.56155 2.70469i −0.0564950 0.0978522i
$$765$$ −10.4039 18.0201i −0.376153 0.651516i
$$766$$ 7.80776 0.282106
$$767$$ −10.4384 4.22351i −0.376910 0.152502i
$$768$$ −1.00000 −0.0360844
$$769$$ −6.56155 11.3649i −0.236616 0.409830i 0.723125 0.690717i $$-0.242705\pi$$
−0.959741 + 0.280887i $$0.909372\pi$$
$$770$$ 2.00000 + 3.46410i 0.0720750 + 0.124838i
$$771$$ 0.184658 0.319838i 0.00665031 0.0115187i
$$772$$ −8.12311 −0.292357
$$773$$ 14.3693 24.8884i 0.516828 0.895173i −0.482981 0.875631i $$-0.660446\pi$$
0.999809 0.0195420i $$-0.00622081\pi$$
$$774$$ 4.00000 6.92820i 0.143777 0.249029i
$$775$$ 0 0
$$776$$ 4.56155 7.90084i 0.163750 0.283624i
$$777$$ −3.28078 5.68247i