# Properties

 Label 625.2.d.b.251.1 Level $625$ Weight $2$ Character 625.251 Analytic conductor $4.991$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$625 = 5^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 625.d (of order $$5$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.99065012633$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 25) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 251.1 Root $$0.809017 + 0.587785i$$ of defining polynomial Character $$\chi$$ $$=$$ 625.251 Dual form 625.2.d.b.376.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034 q^{7} +(-0.690983 - 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})$$ $$q+(-1.30902 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034 q^{7} +(-0.690983 - 2.12663i) q^{8} +(1.61803 + 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(0.500000 + 0.363271i) q^{12} +(1.50000 + 1.08981i) q^{13} +(0.809017 - 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(1.61803 + 4.97980i) q^{17} -3.23607 q^{18} +(0.263932 + 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(-2.61803 + 8.05748i) q^{22} +(3.04508 - 2.21238i) q^{23} +2.23607 q^{24} -3.00000 q^{26} +(-4.04508 + 2.93893i) q^{27} +(-0.118034 + 0.363271i) q^{28} +(-1.11803 + 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} -3.38197 q^{32} +(1.61803 + 4.97980i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(-0.190983 - 0.138757i) q^{37} +(-1.11803 - 0.812299i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(0.309017 + 0.951057i) q^{42} +4.85410 q^{43} +(-1.00000 - 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(-0.190983 + 0.587785i) q^{47} +(-3.92705 + 2.85317i) q^{48} -6.61803 q^{49} -5.23607 q^{51} +(0.927051 - 0.673542i) q^{52} +(1.07295 - 3.30220i) q^{53} +(2.50000 - 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} -0.854102 q^{57} +(-1.80902 - 5.56758i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(3.92705 + 2.85317i) q^{62} +(-1.00000 - 0.726543i) q^{63} +(-3.42705 + 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(-1.47214 - 4.53077i) q^{67} +3.23607 q^{68} +(1.16312 + 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(1.38197 - 4.25325i) q^{72} +(-7.28115 + 5.29007i) q^{73} +0.381966 q^{74} +0.527864 q^{76} +(-2.61803 + 1.90211i) q^{77} +(0.927051 - 2.85317i) q^{78} +(-2.50000 + 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} -1.23607 q^{82} +(1.92705 + 5.93085i) q^{83} +(-0.309017 - 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(-2.92705 - 2.12663i) q^{87} +(-9.47214 - 6.88191i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(-0.718847 - 2.21238i) q^{92} +3.00000 q^{93} +(-0.309017 - 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(1.19098 - 3.66547i) q^{97} +(8.66312 - 6.29412i) q^{98} +10.4721 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{6} + 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10})$$ 4 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^6 + 2 * q^7 - 5 * q^8 + 2 * q^9 $$4 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{6} + 2 q^{7} - 5 q^{8} + 2 q^{9} + 8 q^{11} + 2 q^{12} + 6 q^{13} + q^{14} + 9 q^{16} + 2 q^{17} - 4 q^{18} + 10 q^{19} + 3 q^{21} - 6 q^{22} + q^{23} - 12 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{31} - 18 q^{32} + 2 q^{33} - 14 q^{34} + 4 q^{36} - 3 q^{37} - 6 q^{39} - 2 q^{41} - q^{42} + 6 q^{43} - 4 q^{44} - 12 q^{46} - 3 q^{47} - 9 q^{48} - 22 q^{49} - 12 q^{51} - 3 q^{52} + 11 q^{53} + 10 q^{54} - 5 q^{56} + 10 q^{57} - 5 q^{58} + 15 q^{59} - 17 q^{61} + 9 q^{62} - 4 q^{63} - 7 q^{64} - 14 q^{66} + 12 q^{67} + 4 q^{68} - 11 q^{69} + 3 q^{71} + 10 q^{72} - 9 q^{73} + 6 q^{74} + 20 q^{76} - 6 q^{77} - 3 q^{78} - 10 q^{79} - q^{81} + 4 q^{82} + q^{83} + q^{84} - 12 q^{86} - 5 q^{87} - 20 q^{88} + 20 q^{89} + 3 q^{91} - 23 q^{92} + 12 q^{93} + q^{94} - 7 q^{96} + 7 q^{97} + 19 q^{98} + 24 q^{99}+O(q^{100})$$ 4 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^6 + 2 * q^7 - 5 * q^8 + 2 * q^9 + 8 * q^11 + 2 * q^12 + 6 * q^13 + q^14 + 9 * q^16 + 2 * q^17 - 4 * q^18 + 10 * q^19 + 3 * q^21 - 6 * q^22 + q^23 - 12 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^31 - 18 * q^32 + 2 * q^33 - 14 * q^34 + 4 * q^36 - 3 * q^37 - 6 * q^39 - 2 * q^41 - q^42 + 6 * q^43 - 4 * q^44 - 12 * q^46 - 3 * q^47 - 9 * q^48 - 22 * q^49 - 12 * q^51 - 3 * q^52 + 11 * q^53 + 10 * q^54 - 5 * q^56 + 10 * q^57 - 5 * q^58 + 15 * q^59 - 17 * q^61 + 9 * q^62 - 4 * q^63 - 7 * q^64 - 14 * q^66 + 12 * q^67 + 4 * q^68 - 11 * q^69 + 3 * q^71 + 10 * q^72 - 9 * q^73 + 6 * q^74 + 20 * q^76 - 6 * q^77 - 3 * q^78 - 10 * q^79 - q^81 + 4 * q^82 + q^83 + q^84 - 12 * q^86 - 5 * q^87 - 20 * q^88 + 20 * q^89 + 3 * q^91 - 23 * q^92 + 12 * q^93 + q^94 - 7 * q^96 + 7 * q^97 + 19 * q^98 + 24 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{4}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.30902 + 0.951057i −0.925615 + 0.672499i −0.944915 0.327315i $$-0.893856\pi$$
0.0193004 + 0.999814i $$0.493856\pi$$
$$3$$ −0.309017 + 0.951057i −0.178411 + 0.549093i −0.999773 0.0213149i $$-0.993215\pi$$
0.821362 + 0.570408i $$0.193215\pi$$
$$4$$ 0.190983 0.587785i 0.0954915 0.293893i
$$5$$ 0 0
$$6$$ −0.500000 1.53884i −0.204124 0.628230i
$$7$$ −0.618034 −0.233595 −0.116797 0.993156i $$-0.537263\pi$$
−0.116797 + 0.993156i $$0.537263\pi$$
$$8$$ −0.690983 2.12663i −0.244299 0.751876i
$$9$$ 1.61803 + 1.17557i 0.539345 + 0.391857i
$$10$$ 0 0
$$11$$ 4.23607 3.07768i 1.27722 0.927957i 0.277757 0.960651i $$-0.410409\pi$$
0.999465 + 0.0326948i $$0.0104089\pi$$
$$12$$ 0.500000 + 0.363271i 0.144338 + 0.104867i
$$13$$ 1.50000 + 1.08981i 0.416025 + 0.302260i 0.776037 0.630688i $$-0.217227\pi$$
−0.360011 + 0.932948i $$0.617227\pi$$
$$14$$ 0.809017 0.587785i 0.216219 0.157092i
$$15$$ 0 0
$$16$$ 3.92705 + 2.85317i 0.981763 + 0.713292i
$$17$$ 1.61803 + 4.97980i 0.392431 + 1.20778i 0.930944 + 0.365161i $$0.118986\pi$$
−0.538513 + 0.842617i $$0.681014\pi$$
$$18$$ −3.23607 −0.762749
$$19$$ 0.263932 + 0.812299i 0.0605502 + 0.186354i 0.976756 0.214353i $$-0.0687644\pi$$
−0.916206 + 0.400707i $$0.868764\pi$$
$$20$$ 0 0
$$21$$ 0.190983 0.587785i 0.0416759 0.128265i
$$22$$ −2.61803 + 8.05748i −0.558167 + 1.71786i
$$23$$ 3.04508 2.21238i 0.634944 0.461314i −0.223165 0.974781i $$-0.571639\pi$$
0.858110 + 0.513467i $$0.171639\pi$$
$$24$$ 2.23607 0.456435
$$25$$ 0 0
$$26$$ −3.00000 −0.588348
$$27$$ −4.04508 + 2.93893i −0.778477 + 0.565597i
$$28$$ −0.118034 + 0.363271i −0.0223063 + 0.0686518i
$$29$$ −1.11803 + 3.44095i −0.207614 + 0.638969i 0.791982 + 0.610544i $$0.209049\pi$$
−0.999596 + 0.0284251i $$0.990951\pi$$
$$30$$ 0 0
$$31$$ −0.927051 2.85317i −0.166503 0.512444i 0.832641 0.553814i $$-0.186828\pi$$
−0.999144 + 0.0413693i $$0.986828\pi$$
$$32$$ −3.38197 −0.597853
$$33$$ 1.61803 + 4.97980i 0.281664 + 0.866871i
$$34$$ −6.85410 4.97980i −1.17547 0.854028i
$$35$$ 0 0
$$36$$ 1.00000 0.726543i 0.166667 0.121090i
$$37$$ −0.190983 0.138757i −0.0313974 0.0228116i 0.571976 0.820270i $$-0.306177\pi$$
−0.603373 + 0.797459i $$0.706177\pi$$
$$38$$ −1.11803 0.812299i −0.181369 0.131772i
$$39$$ −1.50000 + 1.08981i −0.240192 + 0.174510i
$$40$$ 0 0
$$41$$ 0.618034 + 0.449028i 0.0965207 + 0.0701264i 0.634999 0.772513i $$-0.281001\pi$$
−0.538478 + 0.842639i $$0.681001\pi$$
$$42$$ 0.309017 + 0.951057i 0.0476824 + 0.146751i
$$43$$ 4.85410 0.740244 0.370122 0.928983i $$-0.379316\pi$$
0.370122 + 0.928983i $$0.379316\pi$$
$$44$$ −1.00000 3.07768i −0.150756 0.463978i
$$45$$ 0 0
$$46$$ −1.88197 + 5.79210i −0.277481 + 0.853998i
$$47$$ −0.190983 + 0.587785i −0.0278577 + 0.0857373i −0.964019 0.265834i $$-0.914353\pi$$
0.936161 + 0.351572i $$0.114353\pi$$
$$48$$ −3.92705 + 2.85317i −0.566821 + 0.411820i
$$49$$ −6.61803 −0.945433
$$50$$ 0 0
$$51$$ −5.23607 −0.733196
$$52$$ 0.927051 0.673542i 0.128559 0.0934035i
$$53$$ 1.07295 3.30220i 0.147381 0.453592i −0.849929 0.526898i $$-0.823355\pi$$
0.997309 + 0.0733062i $$0.0233550\pi$$
$$54$$ 2.50000 7.69421i 0.340207 1.04705i
$$55$$ 0 0
$$56$$ 0.427051 + 1.31433i 0.0570671 + 0.175634i
$$57$$ −0.854102 −0.113129
$$58$$ −1.80902 5.56758i −0.237536 0.731059i
$$59$$ 8.78115 + 6.37988i 1.14321 + 0.830590i 0.987563 0.157223i $$-0.0502542\pi$$
0.155646 + 0.987813i $$0.450254\pi$$
$$60$$ 0 0
$$61$$ −7.04508 + 5.11855i −0.902031 + 0.655364i −0.938987 0.343953i $$-0.888234\pi$$
0.0369561 + 0.999317i $$0.488234\pi$$
$$62$$ 3.92705 + 2.85317i 0.498736 + 0.362353i
$$63$$ −1.00000 0.726543i −0.125988 0.0915358i
$$64$$ −3.42705 + 2.48990i −0.428381 + 0.311237i
$$65$$ 0 0
$$66$$ −6.85410 4.97980i −0.843682 0.612971i
$$67$$ −1.47214 4.53077i −0.179850 0.553521i 0.819972 0.572404i $$-0.193989\pi$$
−0.999822 + 0.0188826i $$0.993989\pi$$
$$68$$ 3.23607 0.392431
$$69$$ 1.16312 + 3.57971i 0.140023 + 0.430947i
$$70$$ 0 0
$$71$$ −2.04508 + 6.29412i −0.242707 + 0.746975i 0.753298 + 0.657679i $$0.228462\pi$$
−0.996005 + 0.0892960i $$0.971538\pi$$
$$72$$ 1.38197 4.25325i 0.162866 0.501251i
$$73$$ −7.28115 + 5.29007i −0.852194 + 0.619156i −0.925750 0.378136i $$-0.876565\pi$$
0.0735557 + 0.997291i $$0.476565\pi$$
$$74$$ 0.381966 0.0444026
$$75$$ 0 0
$$76$$ 0.527864 0.0605502
$$77$$ −2.61803 + 1.90211i −0.298353 + 0.216766i
$$78$$ 0.927051 2.85317i 0.104968 0.323058i
$$79$$ −2.50000 + 7.69421i −0.281272 + 0.865666i 0.706219 + 0.707993i $$0.250399\pi$$
−0.987491 + 0.157673i $$0.949601\pi$$
$$80$$ 0 0
$$81$$ 0.309017 + 0.951057i 0.0343352 + 0.105673i
$$82$$ −1.23607 −0.136501
$$83$$ 1.92705 + 5.93085i 0.211521 + 0.650996i 0.999382 + 0.0351426i $$0.0111885\pi$$
−0.787861 + 0.615853i $$0.788811\pi$$
$$84$$ −0.309017 0.224514i −0.0337165 0.0244965i
$$85$$ 0 0
$$86$$ −6.35410 + 4.61653i −0.685180 + 0.497813i
$$87$$ −2.92705 2.12663i −0.313813 0.227998i
$$88$$ −9.47214 6.88191i −1.00973 0.733614i
$$89$$ 7.23607 5.25731i 0.767022 0.557274i −0.134034 0.990977i $$-0.542793\pi$$
0.901056 + 0.433703i $$0.142793\pi$$
$$90$$ 0 0
$$91$$ −0.927051 0.673542i −0.0971813 0.0706064i
$$92$$ −0.718847 2.21238i −0.0749450 0.230657i
$$93$$ 3.00000 0.311086
$$94$$ −0.309017 0.951057i −0.0318727 0.0980940i
$$95$$ 0 0
$$96$$ 1.04508 3.21644i 0.106664 0.328277i
$$97$$ 1.19098 3.66547i 0.120926 0.372172i −0.872211 0.489130i $$-0.837314\pi$$
0.993137 + 0.116958i $$0.0373143\pi$$
$$98$$ 8.66312 6.29412i 0.875107 0.635803i
$$99$$ 10.4721 1.05249
$$100$$ 0 0
$$101$$ 1.47214 0.146483 0.0732415 0.997314i $$-0.476666\pi$$
0.0732415 + 0.997314i $$0.476666\pi$$
$$102$$ 6.85410 4.97980i 0.678657 0.493073i
$$103$$ −2.64590 + 8.14324i −0.260708 + 0.802377i 0.731943 + 0.681366i $$0.238614\pi$$
−0.992651 + 0.121011i $$0.961386\pi$$
$$104$$ 1.28115 3.94298i 0.125627 0.386641i
$$105$$ 0 0
$$106$$ 1.73607 + 5.34307i 0.168622 + 0.518965i
$$107$$ 16.4164 1.58703 0.793517 0.608548i $$-0.208248\pi$$
0.793517 + 0.608548i $$0.208248\pi$$
$$108$$ 0.954915 + 2.93893i 0.0918867 + 0.282798i
$$109$$ −8.09017 5.87785i −0.774898 0.562996i 0.128546 0.991704i $$-0.458969\pi$$
−0.903443 + 0.428707i $$0.858969\pi$$
$$110$$ 0 0
$$111$$ 0.190983 0.138757i 0.0181273 0.0131703i
$$112$$ −2.42705 1.76336i −0.229335 0.166621i
$$113$$ 13.6353 + 9.90659i 1.28270 + 0.931934i 0.999631 0.0271666i $$-0.00864846\pi$$
0.283066 + 0.959100i $$0.408648\pi$$
$$114$$ 1.11803 0.812299i 0.104713 0.0760788i
$$115$$ 0 0
$$116$$ 1.80902 + 1.31433i 0.167963 + 0.122032i
$$117$$ 1.14590 + 3.52671i 0.105938 + 0.326045i
$$118$$ −17.5623 −1.61674
$$119$$ −1.00000 3.07768i −0.0916698 0.282131i
$$120$$ 0 0
$$121$$ 5.07295 15.6129i 0.461177 1.41936i
$$122$$ 4.35410 13.4005i 0.394202 1.21323i
$$123$$ −0.618034 + 0.449028i −0.0557262 + 0.0404875i
$$124$$ −1.85410 −0.166503
$$125$$ 0 0
$$126$$ 2.00000 0.178174
$$127$$ 16.0902 11.6902i 1.42777 1.03734i 0.437346 0.899294i $$-0.355919\pi$$
0.990426 0.138043i $$-0.0440813\pi$$
$$128$$ 4.20820 12.9515i 0.371956 1.14476i
$$129$$ −1.50000 + 4.61653i −0.132068 + 0.406462i
$$130$$ 0 0
$$131$$ 2.10081 + 6.46564i 0.183549 + 0.564905i 0.999920 0.0126218i $$-0.00401775\pi$$
−0.816371 + 0.577527i $$0.804018\pi$$
$$132$$ 3.23607 0.281664
$$133$$ −0.163119 0.502029i −0.0141442 0.0435314i
$$134$$ 6.23607 + 4.53077i 0.538714 + 0.391399i
$$135$$ 0 0
$$136$$ 9.47214 6.88191i 0.812229 0.590119i
$$137$$ −9.66312 7.02067i −0.825576 0.599816i 0.0927283 0.995691i $$-0.470441\pi$$
−0.918304 + 0.395875i $$0.870441\pi$$
$$138$$ −4.92705 3.57971i −0.419418 0.304725i
$$139$$ −4.04508 + 2.93893i −0.343100 + 0.249276i −0.745968 0.665981i $$-0.768013\pi$$
0.402869 + 0.915258i $$0.368013\pi$$
$$140$$ 0 0
$$141$$ −0.500000 0.363271i −0.0421076 0.0305930i
$$142$$ −3.30902 10.1841i −0.277687 0.854631i
$$143$$ 9.70820 0.811841
$$144$$ 3.00000 + 9.23305i 0.250000 + 0.769421i
$$145$$ 0 0
$$146$$ 4.50000 13.8496i 0.372423 1.14620i
$$147$$ 2.04508 6.29412i 0.168676 0.519131i
$$148$$ −0.118034 + 0.0857567i −0.00970233 + 0.00704916i
$$149$$ −3.94427 −0.323127 −0.161564 0.986862i $$-0.551654\pi$$
−0.161564 + 0.986862i $$0.551654\pi$$
$$150$$ 0 0
$$151$$ 14.5623 1.18506 0.592532 0.805547i $$-0.298128\pi$$
0.592532 + 0.805547i $$0.298128\pi$$
$$152$$ 1.54508 1.12257i 0.125323 0.0910524i
$$153$$ −3.23607 + 9.95959i −0.261621 + 0.805185i
$$154$$ 1.61803 4.97980i 0.130385 0.401283i
$$155$$ 0 0
$$156$$ 0.354102 + 1.08981i 0.0283508 + 0.0872549i
$$157$$ −13.1803 −1.05191 −0.525953 0.850514i $$-0.676291\pi$$
−0.525953 + 0.850514i $$0.676291\pi$$
$$158$$ −4.04508 12.4495i −0.321810 0.990428i
$$159$$ 2.80902 + 2.04087i 0.222770 + 0.161852i
$$160$$ 0 0
$$161$$ −1.88197 + 1.36733i −0.148320 + 0.107761i
$$162$$ −1.30902 0.951057i −0.102846 0.0747221i
$$163$$ 8.89919 + 6.46564i 0.697038 + 0.506428i 0.878966 0.476884i $$-0.158234\pi$$
−0.181928 + 0.983312i $$0.558234\pi$$
$$164$$ 0.381966 0.277515i 0.0298265 0.0216702i
$$165$$ 0 0
$$166$$ −8.16312 5.93085i −0.633581 0.460323i
$$167$$ −4.50000 13.8496i −0.348220 1.07171i −0.959837 0.280558i $$-0.909480\pi$$
0.611617 0.791154i $$-0.290520\pi$$
$$168$$ −1.38197 −0.106621
$$169$$ −2.95492 9.09429i −0.227301 0.699561i
$$170$$ 0 0
$$171$$ −0.527864 + 1.62460i −0.0403668 + 0.124236i
$$172$$ 0.927051 2.85317i 0.0706870 0.217552i
$$173$$ 15.2812 11.1024i 1.16180 0.844100i 0.171799 0.985132i $$-0.445042\pi$$
0.990005 + 0.141032i $$0.0450419\pi$$
$$174$$ 5.85410 0.443798
$$175$$ 0 0
$$176$$ 25.4164 1.91583
$$177$$ −8.78115 + 6.37988i −0.660032 + 0.479541i
$$178$$ −4.47214 + 13.7638i −0.335201 + 1.03164i
$$179$$ −0.163119 + 0.502029i −0.0121921 + 0.0375234i −0.956967 0.290195i $$-0.906280\pi$$
0.944775 + 0.327719i $$0.106280\pi$$
$$180$$ 0 0
$$181$$ 0.0901699 + 0.277515i 0.00670228 + 0.0206275i 0.954352 0.298685i $$-0.0965480\pi$$
−0.947649 + 0.319313i $$0.896548\pi$$
$$182$$ 1.85410 0.137435
$$183$$ −2.69098 8.28199i −0.198923 0.612223i
$$184$$ −6.80902 4.94704i −0.501967 0.364701i
$$185$$ 0 0
$$186$$ −3.92705 + 2.85317i −0.287945 + 0.209205i
$$187$$ 22.1803 + 16.1150i 1.62199 + 1.17844i
$$188$$ 0.309017 + 0.224514i 0.0225374 + 0.0163744i
$$189$$ 2.50000 1.81636i 0.181848 0.132120i
$$190$$ 0 0
$$191$$ 1.47214 + 1.06957i 0.106520 + 0.0773913i 0.639770 0.768566i $$-0.279030\pi$$
−0.533250 + 0.845958i $$0.679030\pi$$
$$192$$ −1.30902 4.02874i −0.0944702 0.290749i
$$193$$ −7.70820 −0.554849 −0.277424 0.960747i $$-0.589481\pi$$
−0.277424 + 0.960747i $$0.589481\pi$$
$$194$$ 1.92705 + 5.93085i 0.138354 + 0.425810i
$$195$$ 0 0
$$196$$ −1.26393 + 3.88998i −0.0902809 + 0.277856i
$$197$$ −1.14590 + 3.52671i −0.0816419 + 0.251268i −0.983543 0.180675i $$-0.942172\pi$$
0.901901 + 0.431943i $$0.142172\pi$$
$$198$$ −13.7082 + 9.95959i −0.974200 + 0.707797i
$$199$$ −17.5623 −1.24496 −0.622479 0.782636i $$-0.713875\pi$$
−0.622479 + 0.782636i $$0.713875\pi$$
$$200$$ 0 0
$$201$$ 4.76393 0.336022
$$202$$ −1.92705 + 1.40008i −0.135587 + 0.0985096i
$$203$$ 0.690983 2.12663i 0.0484975 0.149260i
$$204$$ −1.00000 + 3.07768i −0.0700140 + 0.215481i
$$205$$ 0 0
$$206$$ −4.28115 13.1760i −0.298282 0.918018i
$$207$$ 7.52786 0.523223
$$208$$ 2.78115 + 8.55951i 0.192838 + 0.593495i
$$209$$ 3.61803 + 2.62866i 0.250265 + 0.181828i
$$210$$ 0 0
$$211$$ 7.42705 5.39607i 0.511299 0.371481i −0.302017 0.953303i $$-0.597660\pi$$
0.813316 + 0.581822i $$0.197660\pi$$
$$212$$ −1.73607 1.26133i −0.119234 0.0866283i
$$213$$ −5.35410 3.88998i −0.366857 0.266537i
$$214$$ −21.4894 + 15.6129i −1.46898 + 1.06728i
$$215$$ 0 0
$$216$$ 9.04508 + 6.57164i 0.615440 + 0.447143i
$$217$$ 0.572949 + 1.76336i 0.0388943 + 0.119704i
$$218$$ 16.1803 1.09587
$$219$$ −2.78115 8.55951i −0.187933 0.578398i
$$220$$ 0 0
$$221$$ −3.00000 + 9.23305i −0.201802 + 0.621082i
$$222$$ −0.118034 + 0.363271i −0.00792192 + 0.0243812i
$$223$$ −0.145898 + 0.106001i −0.00977005 + 0.00709836i −0.592660 0.805453i $$-0.701922\pi$$
0.582890 + 0.812551i $$0.301922\pi$$
$$224$$ 2.09017 0.139655
$$225$$ 0 0
$$226$$ −27.2705 −1.81401
$$227$$ 11.9443 8.67802i 0.792769 0.575981i −0.116015 0.993247i $$-0.537012\pi$$
0.908784 + 0.417267i $$0.137012\pi$$
$$228$$ −0.163119 + 0.502029i −0.0108028 + 0.0332477i
$$229$$ 6.70820 20.6457i 0.443291 1.36431i −0.441057 0.897479i $$-0.645396\pi$$
0.884348 0.466829i $$-0.154604\pi$$
$$230$$ 0 0
$$231$$ −1.00000 3.07768i −0.0657952 0.202497i
$$232$$ 8.09017 0.531146
$$233$$ 0.909830 + 2.80017i 0.0596049 + 0.183445i 0.976426 0.215854i $$-0.0692535\pi$$
−0.916821 + 0.399299i $$0.869254\pi$$
$$234$$ −4.85410 3.52671i −0.317323 0.230548i
$$235$$ 0 0
$$236$$ 5.42705 3.94298i 0.353271 0.256666i
$$237$$ −6.54508 4.75528i −0.425149 0.308889i
$$238$$ 4.23607 + 3.07768i 0.274584 + 0.199497i
$$239$$ 16.6074 12.0660i 1.07424 0.780483i 0.0975727 0.995228i $$-0.468892\pi$$
0.976670 + 0.214745i $$0.0688921\pi$$
$$240$$ 0 0
$$241$$ −2.04508 1.48584i −0.131736 0.0957114i 0.519966 0.854187i $$-0.325945\pi$$
−0.651702 + 0.758475i $$0.725945\pi$$
$$242$$ 8.20820 + 25.2623i 0.527643 + 1.62392i
$$243$$ −16.0000 −1.02640
$$244$$ 1.66312 + 5.11855i 0.106470 + 0.327682i
$$245$$ 0 0
$$246$$ 0.381966 1.17557i 0.0243533 0.0749516i
$$247$$ −0.489357 + 1.50609i −0.0311370 + 0.0958299i
$$248$$ −5.42705 + 3.94298i −0.344618 + 0.250380i
$$249$$ −6.23607 −0.395195
$$250$$ 0 0
$$251$$ −29.1803 −1.84185 −0.920923 0.389744i $$-0.872564\pi$$
−0.920923 + 0.389744i $$0.872564\pi$$
$$252$$ −0.618034 + 0.449028i −0.0389325 + 0.0282861i
$$253$$ 6.09017 18.7436i 0.382886 1.17840i
$$254$$ −9.94427 + 30.6053i −0.623959 + 1.92035i
$$255$$ 0 0
$$256$$ 4.19098 + 12.8985i 0.261936 + 0.806157i
$$257$$ −22.8541 −1.42560 −0.712800 0.701367i $$-0.752573\pi$$
−0.712800 + 0.701367i $$0.752573\pi$$
$$258$$ −2.42705 7.46969i −0.151102 0.465043i
$$259$$ 0.118034 + 0.0857567i 0.00733428 + 0.00532866i
$$260$$ 0 0
$$261$$ −5.85410 + 4.25325i −0.362360 + 0.263270i
$$262$$ −8.89919 6.46564i −0.549794 0.399448i
$$263$$ −8.82624 6.41264i −0.544249 0.395420i 0.281412 0.959587i $$-0.409197\pi$$
−0.825661 + 0.564167i $$0.809197\pi$$
$$264$$ 9.47214 6.88191i 0.582970 0.423552i
$$265$$ 0 0
$$266$$ 0.690983 + 0.502029i 0.0423669 + 0.0307813i
$$267$$ 2.76393 + 8.50651i 0.169150 + 0.520590i
$$268$$ −2.94427 −0.179850
$$269$$ −3.94427 12.1392i −0.240487 0.740141i −0.996346 0.0854076i $$-0.972781\pi$$
0.755860 0.654734i $$-0.227219\pi$$
$$270$$ 0 0
$$271$$ −2.47214 + 7.60845i −0.150172 + 0.462181i −0.997640 0.0686657i $$-0.978126\pi$$
0.847468 + 0.530846i $$0.178126\pi$$
$$272$$ −7.85410 + 24.1724i −0.476225 + 1.46567i
$$273$$ 0.927051 0.673542i 0.0561077 0.0407646i
$$274$$ 19.3262 1.16754
$$275$$ 0 0
$$276$$ 2.32624 0.140023
$$277$$ −19.9894 + 14.5231i −1.20104 + 0.872610i −0.994387 0.105804i $$-0.966258\pi$$
−0.206657 + 0.978413i $$0.566258\pi$$
$$278$$ 2.50000 7.69421i 0.149940 0.461468i
$$279$$ 1.85410 5.70634i 0.111002 0.341630i
$$280$$ 0 0
$$281$$ 3.11803 + 9.59632i 0.186006 + 0.572469i 0.999964 0.00845524i $$-0.00269142\pi$$
−0.813958 + 0.580924i $$0.802691\pi$$
$$282$$ 1.00000 0.0595491
$$283$$ 9.22542 + 28.3929i 0.548395 + 1.68778i 0.712779 + 0.701389i $$0.247436\pi$$
−0.164384 + 0.986396i $$0.552564\pi$$
$$284$$ 3.30902 + 2.40414i 0.196354 + 0.142660i
$$285$$ 0 0
$$286$$ −12.7082 + 9.23305i −0.751452 + 0.545962i
$$287$$ −0.381966 0.277515i −0.0225467 0.0163812i
$$288$$ −5.47214 3.97574i −0.322449 0.234273i
$$289$$ −8.42705 + 6.12261i −0.495709 + 0.360154i
$$290$$ 0 0
$$291$$ 3.11803 + 2.26538i 0.182782 + 0.132799i
$$292$$ 1.71885 + 5.29007i 0.100588 + 0.309578i
$$293$$ 19.5279 1.14083 0.570415 0.821357i $$-0.306782\pi$$
0.570415 + 0.821357i $$0.306782\pi$$
$$294$$ 3.30902 + 10.1841i 0.192986 + 0.593949i
$$295$$ 0 0
$$296$$ −0.163119 + 0.502029i −0.00948110 + 0.0291798i
$$297$$ −8.09017 + 24.8990i −0.469439 + 1.44479i
$$298$$ 5.16312 3.75123i 0.299091 0.217303i
$$299$$ 6.97871 0.403589
$$300$$ 0 0
$$301$$ −3.00000 −0.172917
$$302$$ −19.0623 + 13.8496i −1.09691 + 0.796954i
$$303$$ −0.454915 + 1.40008i −0.0261342 + 0.0804328i
$$304$$ −1.28115 + 3.94298i −0.0734792 + 0.226146i
$$305$$ 0 0
$$306$$ −5.23607 16.1150i −0.299326 0.921231i
$$307$$ −9.23607 −0.527130 −0.263565 0.964642i $$-0.584898\pi$$
−0.263565 + 0.964642i $$0.584898\pi$$
$$308$$ 0.618034 + 1.90211i 0.0352158 + 0.108383i
$$309$$ −6.92705 5.03280i −0.394066 0.286306i
$$310$$ 0 0
$$311$$ −6.88197 + 5.00004i −0.390240 + 0.283526i −0.765554 0.643372i $$-0.777535\pi$$
0.375314 + 0.926898i $$0.377535\pi$$
$$312$$ 3.35410 + 2.43690i 0.189889 + 0.137962i
$$313$$ −13.5623 9.85359i −0.766587 0.556958i 0.134337 0.990936i $$-0.457110\pi$$
−0.900924 + 0.433978i $$0.857110\pi$$
$$314$$ 17.2533 12.5352i 0.973659 0.707405i
$$315$$ 0 0
$$316$$ 4.04508 + 2.93893i 0.227554 + 0.165328i
$$317$$ −2.36475 7.27794i −0.132817 0.408770i 0.862427 0.506182i $$-0.168944\pi$$
−0.995244 + 0.0974121i $$0.968944\pi$$
$$318$$ −5.61803 −0.315044
$$319$$ 5.85410 + 18.0171i 0.327767 + 1.00876i
$$320$$ 0 0
$$321$$ −5.07295 + 15.6129i −0.283144 + 0.871429i
$$322$$ 1.16312 3.57971i 0.0648181 0.199490i
$$323$$ −3.61803 + 2.62866i −0.201313 + 0.146262i
$$324$$ 0.618034 0.0343352
$$325$$ 0 0
$$326$$ −17.7984 −0.985761
$$327$$ 8.09017 5.87785i 0.447387 0.325046i
$$328$$ 0.527864 1.62460i 0.0291464 0.0897034i
$$329$$ 0.118034 0.363271i 0.00650742 0.0200278i
$$330$$ 0 0
$$331$$ −7.14590 21.9928i −0.392774 1.20883i −0.930682 0.365830i $$-0.880785\pi$$
0.537907 0.843004i $$-0.319215\pi$$
$$332$$ 3.85410 0.211521
$$333$$ −0.145898 0.449028i −0.00799516 0.0246066i
$$334$$ 19.0623 + 13.8496i 1.04304 + 0.757815i
$$335$$ 0 0
$$336$$ 2.42705 1.76336i 0.132406 0.0961989i
$$337$$ 6.35410 + 4.61653i 0.346130 + 0.251478i 0.747244 0.664550i $$-0.231377\pi$$
−0.401114 + 0.916028i $$0.631377\pi$$
$$338$$ 12.5172 + 9.09429i 0.680847 + 0.494664i
$$339$$ −13.6353 + 9.90659i −0.740565 + 0.538052i
$$340$$ 0 0
$$341$$ −12.7082 9.23305i −0.688188 0.499998i
$$342$$ −0.854102 2.62866i −0.0461845 0.142141i
$$343$$ 8.41641 0.454443
$$344$$ −3.35410 10.3229i −0.180841 0.556572i
$$345$$ 0 0
$$346$$ −9.44427 + 29.0665i −0.507727 + 1.56262i
$$347$$ 6.15248 18.9354i 0.330282 1.01650i −0.638717 0.769441i $$-0.720535\pi$$
0.969000 0.247063i $$-0.0794653\pi$$
$$348$$ −1.80902 + 1.31433i −0.0969735 + 0.0704554i
$$349$$ 21.7082 1.16201 0.581007 0.813899i $$-0.302659\pi$$
0.581007 + 0.813899i $$0.302659\pi$$
$$350$$ 0 0
$$351$$ −9.27051 −0.494823
$$352$$ −14.3262 + 10.4086i −0.763591 + 0.554781i
$$353$$ −3.98936 + 12.2780i −0.212332 + 0.653491i 0.787000 + 0.616953i $$0.211633\pi$$
−0.999332 + 0.0365381i $$0.988367\pi$$
$$354$$ 5.42705 16.7027i 0.288445 0.887741i
$$355$$ 0 0
$$356$$ −1.70820 5.25731i −0.0905346 0.278637i
$$357$$ 3.23607 0.171271
$$358$$ −0.263932 0.812299i −0.0139492 0.0429313i
$$359$$ −11.1180 8.07772i −0.586787 0.426326i 0.254377 0.967105i $$-0.418130\pi$$
−0.841165 + 0.540779i $$0.818130\pi$$
$$360$$ 0 0
$$361$$ 14.7812 10.7391i 0.777955 0.565218i
$$362$$ −0.381966 0.277515i −0.0200757 0.0145858i
$$363$$ 13.2812 + 9.64932i 0.697080 + 0.506458i
$$364$$ −0.572949 + 0.416272i −0.0300307 + 0.0218186i
$$365$$ 0 0
$$366$$ 11.3992 + 8.28199i 0.595845 + 0.432907i
$$367$$ 7.89919 + 24.3112i 0.412334 + 1.26903i 0.914614 + 0.404329i $$0.132495\pi$$
−0.502279 + 0.864705i $$0.667505\pi$$
$$368$$ 18.2705 0.952416
$$369$$ 0.472136 + 1.45309i 0.0245784 + 0.0756446i
$$370$$ 0 0
$$371$$ −0.663119 + 2.04087i −0.0344274 + 0.105957i
$$372$$ 0.572949 1.76336i 0.0297060 0.0914257i
$$373$$ −22.8713 + 16.6170i −1.18423 + 0.860395i −0.992643 0.121080i $$-0.961364\pi$$
−0.191589 + 0.981475i $$0.561364\pi$$
$$374$$ −44.3607 −2.29384
$$375$$ 0 0
$$376$$ 1.38197 0.0712695
$$377$$ −5.42705 + 3.94298i −0.279507 + 0.203074i
$$378$$ −1.54508 + 4.75528i −0.0794706 + 0.244585i
$$379$$ 4.51064 13.8823i 0.231696 0.713087i −0.765846 0.643024i $$-0.777680\pi$$
0.997543 0.0700639i $$-0.0223203\pi$$
$$380$$ 0 0
$$381$$ 6.14590 + 18.9151i 0.314864 + 0.969051i
$$382$$ −2.94427 −0.150642
$$383$$ −10.3090 31.7279i −0.526766 1.62122i −0.760797 0.648990i $$-0.775192\pi$$
0.234031 0.972229i $$-0.424808\pi$$
$$384$$ 11.0172 + 8.00448i 0.562220 + 0.408477i
$$385$$ 0 0
$$386$$ 10.0902 7.33094i 0.513576 0.373135i
$$387$$ 7.85410 + 5.70634i 0.399246 + 0.290070i
$$388$$ −1.92705 1.40008i −0.0978312 0.0710785i
$$389$$ −12.1353 + 8.81678i −0.615282 + 0.447028i −0.851270 0.524727i $$-0.824167\pi$$
0.235988 + 0.971756i $$0.424167\pi$$
$$390$$ 0 0
$$391$$ 15.9443 + 11.5842i 0.806336 + 0.585838i
$$392$$ 4.57295 + 14.0741i 0.230969 + 0.710849i
$$393$$ −6.79837 −0.342933
$$394$$ −1.85410 5.70634i −0.0934083 0.287481i
$$395$$ 0 0
$$396$$ 2.00000 6.15537i 0.100504 0.309319i
$$397$$ −8.97214 + 27.6134i −0.450299 + 1.38588i 0.426268 + 0.904597i $$0.359828\pi$$
−0.876567 + 0.481280i $$0.840172\pi$$
$$398$$ 22.9894 16.7027i 1.15235 0.837233i
$$399$$ 0.527864 0.0264263
$$400$$ 0 0
$$401$$ 26.5967 1.32818 0.664089 0.747653i $$-0.268820\pi$$
0.664089 + 0.747653i $$0.268820\pi$$
$$402$$ −6.23607 + 4.53077i −0.311027 + 0.225974i
$$403$$ 1.71885 5.29007i 0.0856219 0.263517i
$$404$$ 0.281153 0.865300i 0.0139879 0.0430503i
$$405$$ 0 0
$$406$$ 1.11803 + 3.44095i 0.0554871 + 0.170772i
$$407$$ −1.23607 −0.0612696
$$408$$ 3.61803 + 11.1352i 0.179119 + 0.551273i
$$409$$ −1.28115 0.930812i −0.0633489 0.0460257i 0.555660 0.831410i $$-0.312466\pi$$
−0.619009 + 0.785384i $$0.712466\pi$$
$$410$$ 0 0
$$411$$ 9.66312 7.02067i 0.476647 0.346304i
$$412$$ 4.28115 + 3.11044i 0.210917 + 0.153240i
$$413$$ −5.42705 3.94298i −0.267048 0.194022i
$$414$$ −9.85410 + 7.15942i −0.484303 + 0.351867i
$$415$$ 0 0
$$416$$ −5.07295 3.68571i −0.248722 0.180707i
$$417$$ −1.54508 4.75528i −0.0756631 0.232867i
$$418$$ −7.23607 −0.353928
$$419$$ −2.92705 9.00854i −0.142996 0.440096i 0.853752 0.520680i $$-0.174321\pi$$
−0.996748 + 0.0805840i $$0.974321\pi$$
$$420$$ 0 0
$$421$$ 9.88854 30.4338i 0.481938 1.48325i −0.354429 0.935083i $$-0.615325\pi$$
0.836367 0.548170i $$-0.184675\pi$$
$$422$$ −4.59017 + 14.1271i −0.223446 + 0.687696i
$$423$$ −1.00000 + 0.726543i −0.0486217 + 0.0353257i
$$424$$ −7.76393 −0.377050
$$425$$ 0 0
$$426$$ 10.7082 0.518814
$$427$$ 4.35410 3.16344i 0.210710 0.153090i
$$428$$ 3.13525 9.64932i 0.151548 0.466418i
$$429$$ −3.00000 + 9.23305i −0.144841 + 0.445776i
$$430$$ 0 0
$$431$$ −9.21885 28.3727i −0.444056 1.36666i −0.883515 0.468402i $$-0.844830\pi$$
0.439459 0.898263i $$-0.355170\pi$$
$$432$$ −24.2705 −1.16772
$$433$$ −8.29837 25.5398i −0.398794 1.22736i −0.925967 0.377605i $$-0.876748\pi$$
0.527173 0.849758i $$-0.323252\pi$$
$$434$$ −2.42705 1.76336i −0.116502 0.0846438i
$$435$$ 0 0
$$436$$ −5.00000 + 3.63271i −0.239457 + 0.173975i
$$437$$ 2.60081 + 1.88960i 0.124414 + 0.0903919i
$$438$$ 11.7812 + 8.55951i 0.562925 + 0.408989i
$$439$$ 33.1525 24.0867i 1.58228 1.14959i 0.668261 0.743927i $$-0.267039\pi$$
0.914021 0.405667i $$-0.132961\pi$$
$$440$$ 0 0
$$441$$ −10.7082 7.77997i −0.509914 0.370475i
$$442$$ −4.85410 14.9394i −0.230886 0.710594i
$$443$$ −29.9443 −1.42270 −0.711348 0.702840i $$-0.751915\pi$$
−0.711348 + 0.702840i $$0.751915\pi$$
$$444$$ −0.0450850 0.138757i −0.00213964 0.00658513i
$$445$$ 0 0
$$446$$ 0.0901699 0.277515i 0.00426967 0.0131407i
$$447$$ 1.21885 3.75123i 0.0576495 0.177427i
$$448$$ 2.11803 1.53884i 0.100068 0.0727034i
$$449$$ 4.67376 0.220568 0.110284 0.993900i $$-0.464824\pi$$
0.110284 + 0.993900i $$0.464824\pi$$
$$450$$ 0 0
$$451$$ 4.00000 0.188353
$$452$$ 8.42705 6.12261i 0.396375 0.287983i
$$453$$ −4.50000 + 13.8496i −0.211428 + 0.650710i
$$454$$ −7.38197 + 22.7194i −0.346453 + 1.06627i
$$455$$ 0 0
$$456$$ 0.590170 + 1.81636i 0.0276372 + 0.0850587i
$$457$$ 21.4164 1.00182 0.500909 0.865500i $$-0.332999\pi$$
0.500909 + 0.865500i $$0.332999\pi$$
$$458$$ 10.8541 + 33.4055i 0.507179 + 1.56094i
$$459$$ −21.1803 15.3884i −0.988614 0.718270i
$$460$$ 0 0
$$461$$ −0.663119 + 0.481784i −0.0308845 + 0.0224389i −0.603120 0.797650i $$-0.706076\pi$$
0.572236 + 0.820089i $$0.306076\pi$$
$$462$$ 4.23607 + 3.07768i 0.197080 + 0.143187i
$$463$$ −19.5172 14.1801i −0.907042 0.659005i 0.0332229 0.999448i $$-0.489423\pi$$
−0.940265 + 0.340443i $$0.889423\pi$$
$$464$$ −14.2082 + 10.3229i −0.659599 + 0.479227i
$$465$$ 0 0
$$466$$ −3.85410 2.80017i −0.178538 0.129715i
$$467$$ −8.48278 26.1073i −0.392536 1.20810i −0.930864 0.365367i $$-0.880944\pi$$
0.538328 0.842736i $$-0.319056\pi$$
$$468$$ 2.29180 0.105938
$$469$$ 0.909830 + 2.80017i 0.0420120 + 0.129300i
$$470$$ 0 0
$$471$$ 4.07295 12.5352i 0.187672 0.577594i
$$472$$ 7.50000 23.0826i 0.345215 1.06246i
$$473$$ 20.5623 14.9394i 0.945456 0.686914i
$$474$$ 13.0902 0.601251
$$475$$ 0 0
$$476$$ −2.00000 −0.0916698
$$477$$ 5.61803 4.08174i 0.257232 0.186890i
$$478$$ −10.2639 + 31.5891i −0.469461 + 1.44485i
$$479$$ −3.35410 + 10.3229i −0.153253 + 0.471664i −0.997980 0.0635340i $$-0.979763\pi$$
0.844727 + 0.535198i $$0.179763\pi$$
$$480$$ 0 0
$$481$$ −0.135255 0.416272i −0.00616709 0.0189804i
$$482$$ 4.09017 0.186302
$$483$$ −0.718847 2.21238i −0.0327087 0.100667i
$$484$$ −8.20820 5.96361i −0.373100 0.271073i
$$485$$ 0 0
$$486$$ 20.9443 15.2169i 0.950051 0.690253i
$$487$$ −29.4615 21.4050i −1.33503 0.969954i −0.999611 0.0278844i $$-0.991123\pi$$
−0.335417 0.942070i $$-0.608877\pi$$
$$488$$ 15.7533 + 11.4454i 0.713118 + 0.518110i
$$489$$ −8.89919 + 6.46564i −0.402435 + 0.292386i
$$490$$ 0 0
$$491$$ 34.9894 + 25.4213i 1.57905 + 1.14725i 0.917776 + 0.397099i $$0.129983\pi$$
0.661272 + 0.750147i $$0.270017\pi$$
$$492$$ 0.145898 + 0.449028i 0.00657759 + 0.0202437i
$$493$$ −18.9443 −0.853207
$$494$$ −0.791796 2.43690i −0.0356246 0.109641i
$$495$$ 0 0
$$496$$ 4.50000 13.8496i 0.202056 0.621864i
$$497$$ 1.26393 3.88998i 0.0566951 0.174490i
$$498$$ 8.16312 5.93085i 0.365798 0.265768i
$$499$$ 7.56231 0.338535 0.169268 0.985570i $$-0.445860\pi$$
0.169268 + 0.985570i $$0.445860\pi$$
$$500$$ 0 0
$$501$$ 14.5623 0.650596
$$502$$ 38.1976 27.7522i 1.70484 1.23864i
$$503$$ 11.5623 35.5851i 0.515538 1.58666i −0.266764 0.963762i $$-0.585954\pi$$
0.782301 0.622900i $$-0.214046\pi$$
$$504$$ −0.854102 + 2.62866i −0.0380447 + 0.117090i
$$505$$ 0 0
$$506$$ 9.85410 + 30.3278i 0.438068 + 1.34824i
$$507$$ 9.56231 0.424677
$$508$$ −3.79837 11.6902i −0.168526 0.518668i
$$509$$ 16.4443 + 11.9475i 0.728880 + 0.529562i 0.889209 0.457502i $$-0.151256\pi$$
−0.160329 + 0.987064i $$0.551256\pi$$
$$510$$ 0 0
$$511$$ 4.50000 3.26944i 0.199068 0.144632i
$$512$$ 4.28115 + 3.11044i 0.189202 + 0.137463i
$$513$$ −3.45492 2.51014i −0.152538 0.110826i
$$514$$ 29.9164 21.7355i 1.31956 0.958714i
$$515$$ 0 0
$$516$$ 2.42705 + 1.76336i 0.106845 + 0.0776274i
$$517$$ 1.00000 + 3.07768i 0.0439799 + 0.135356i
$$518$$ −0.236068 −0.0103722
$$519$$ 5.83688 + 17.9641i 0.256211 + 0.788535i
$$520$$ 0 0
$$521$$ 9.07295 27.9237i 0.397493 1.22336i −0.529510 0.848304i $$-0.677624\pi$$
0.927003 0.375054i $$-0.122376\pi$$
$$522$$ 3.61803 11.1352i 0.158357 0.487373i
$$523$$ −10.6353 + 7.72696i −0.465047 + 0.337877i −0.795508 0.605943i $$-0.792796\pi$$
0.330461 + 0.943820i $$0.392796\pi$$
$$524$$ 4.20163 0.183549
$$525$$ 0 0
$$526$$ 17.6525 0.769685
$$527$$ 12.7082 9.23305i 0.553578 0.402198i
$$528$$ −7.85410 + 24.1724i −0.341806 + 1.05197i
$$529$$ −2.72949 + 8.40051i −0.118673 + 0.365239i
$$530$$ 0 0
$$531$$ 6.70820 + 20.6457i 0.291111 + 0.895948i
$$532$$ −0.326238 −0.0141442
$$533$$ 0.437694 + 1.34708i 0.0189586 + 0.0583487i
$$534$$ −11.7082 8.50651i −0.506664 0.368113i
$$535$$ 0 0
$$536$$ −8.61803 + 6.26137i −0.372242 + 0.270450i
$$537$$ −0.427051 0.310271i −0.0184286 0.0133892i
$$538$$ 16.7082 + 12.1392i 0.720342 + 0.523359i
$$539$$ −28.0344 + 20.3682i −1.20753 + 0.877321i
$$540$$ 0 0
$$541$$ −21.9443 15.9434i −0.943458 0.685462i 0.00579261 0.999983i $$-0.498156\pi$$
−0.949251 + 0.314521i $$0.898156\pi$$
$$542$$ −4.00000 12.3107i −0.171815 0.528791i
$$543$$ −0.291796 −0.0125222
$$544$$ −5.47214 16.8415i −0.234616 0.722073i
$$545$$ 0 0
$$546$$ −0.572949 + 1.76336i −0.0245200 + 0.0754647i
$$547$$ 6.57953 20.2497i 0.281320 0.865815i −0.706157 0.708055i $$-0.749573\pi$$
0.987478 0.157760i $$-0.0504271\pi$$
$$548$$ −5.97214 + 4.33901i −0.255117 + 0.185353i
$$549$$ −17.4164 −0.743314
$$550$$ 0 0
$$551$$ −3.09017 −0.131646
$$552$$ 6.80902 4.94704i 0.289811 0.210560i
$$553$$ 1.54508 4.75528i 0.0657037 0.202215i
$$554$$ 12.3541 38.0220i 0.524875 1.61540i
$$555$$ 0 0
$$556$$ 0.954915 + 2.93893i 0.0404974 + 0.124638i
$$557$$ −4.76393 −0.201854 −0.100927 0.994894i $$-0.532181\pi$$
−0.100927 + 0.994894i $$0.532181\pi$$
$$558$$ 3.00000 + 9.23305i 0.127000 + 0.390866i
$$559$$ 7.28115 + 5.29007i 0.307960 + 0.223746i
$$560$$ 0 0
$$561$$ −22.1803 + 16.1150i −0.936455 + 0.680374i
$$562$$ −13.2082 9.59632i −0.557154 0.404796i
$$563$$ 5.97214 + 4.33901i 0.251696 + 0.182868i 0.706478 0.707735i $$-0.250283\pi$$
−0.454782 + 0.890603i $$0.650283\pi$$
$$564$$ −0.309017 + 0.224514i −0.0130120 + 0.00945374i
$$565$$ 0 0
$$566$$ −39.0795 28.3929i −1.64264 1.19344i
$$567$$ −0.190983 0.587785i −0.00802053 0.0246847i
$$568$$ 14.7984 0.620926
$$569$$ 6.34346 + 19.5232i 0.265932 + 0.818453i 0.991477 + 0.130279i $$0.0415874\pi$$
−0.725546 + 0.688174i $$0.758413\pi$$
$$570$$ 0 0
$$571$$ −2.51064 + 7.72696i −0.105067 + 0.323363i −0.989746 0.142837i $$-0.954377\pi$$
0.884679 + 0.466201i $$0.154377\pi$$
$$572$$ 1.85410 5.70634i 0.0775239 0.238594i
$$573$$ −1.47214 + 1.06957i −0.0614994 + 0.0446819i
$$574$$ 0.763932 0.0318859
$$575$$ 0 0
$$576$$ −8.47214 −0.353006
$$577$$ −27.3262 + 19.8537i −1.13761 + 0.826519i −0.986784 0.162042i $$-0.948192\pi$$
−0.150822 + 0.988561i $$0.548192\pi$$
$$578$$ 5.20820 16.0292i 0.216633 0.666727i
$$579$$ 2.38197 7.33094i 0.0989911 0.304663i
$$580$$ 0 0
$$581$$ −1.19098 3.66547i −0.0494103 0.152069i
$$582$$ −6.23607 −0.258493
$$583$$ −5.61803 17.2905i −0.232675 0.716101i
$$584$$ 16.2812 + 11.8290i 0.673719 + 0.489485i
$$585$$ 0 0
$$586$$ −25.5623 + 18.5721i −1.05597 + 0.767206i
$$587$$ 4.28115 + 3.11044i 0.176702 + 0.128382i 0.672621 0.739987i $$-0.265169\pi$$
−0.495919 + 0.868369i $$0.665169\pi$$
$$588$$ −3.30902 2.40414i −0.136462 0.0991451i
$$589$$ 2.07295 1.50609i 0.0854144 0.0620572i
$$590$$ 0 0
$$591$$ −3.00000 2.17963i −0.123404 0.0896579i
$$592$$ −0.354102 1.08981i −0.0145535 0.0447911i
$$593$$ 10.9098 0.448013 0.224007 0.974588i $$-0.428086\pi$$
0.224007 + 0.974588i $$0.428086\pi$$
$$594$$ −13.0902 40.2874i −0.537096 1.65301i
$$595$$ 0 0
$$596$$ −0.753289 + 2.31838i −0.0308559 + 0.0949647i
$$597$$ 5.42705 16.7027i 0.222114 0.683598i
$$598$$ −9.13525 + 6.63715i −0.373568 + 0.271413i
$$599$$ −9.47214 −0.387021 −0.193510 0.981098i $$-0.561987\pi$$
−0.193510 + 0.981098i $$0.561987\pi$$
$$600$$ 0 0
$$601$$ 2.72949 0.111338 0.0556691 0.998449i $$-0.482271\pi$$
0.0556691 + 0.998449i $$0.482271\pi$$
$$602$$ 3.92705 2.85317i 0.160055 0.116287i
$$603$$ 2.94427 9.06154i 0.119900 0.369014i
$$604$$ 2.78115 8.55951i 0.113164 0.348281i
$$605$$ 0 0
$$606$$ −0.736068 2.26538i −0.0299007 0.0920249i
$$607$$ 35.5623 1.44343 0.721715 0.692191i $$-0.243354\pi$$
0.721715 + 0.692191i $$0.243354\pi$$
$$608$$ −0.892609 2.74717i −0.0362001 0.111412i
$$609$$ 1.80902 + 1.31433i 0.0733051 + 0.0532592i
$$610$$ 0 0
$$611$$ −0.927051 + 0.673542i −0.0375045 + 0.0272486i
$$612$$ 5.23607 + 3.80423i 0.211656 + 0.153777i
$$613$$ −12.1180 8.80427i −0.489443 0.355601i 0.315527 0.948917i $$-0.397819\pi$$
−0.804970 + 0.593316i $$0.797819\pi$$
$$614$$ 12.0902 8.78402i 0.487920 0.354494i
$$615$$ 0 0
$$616$$ 5.85410 + 4.25325i 0.235868 + 0.171368i
$$617$$ −4.39919 13.5393i −0.177105 0.545072i 0.822619 0.568593i $$-0.192512\pi$$
−0.999723 + 0.0235215i $$0.992512\pi$$
$$618$$ 13.8541 0.557294
$$619$$ 9.43363 + 29.0337i 0.379170 + 1.16696i 0.940622 + 0.339455i $$0.110243\pi$$
−0.561453 + 0.827509i $$0.689757\pi$$
$$620$$ 0 0
$$621$$ −5.81559 + 17.8986i −0.233372 + 0.718244i
$$622$$ 4.25329 13.0903i 0.170541 0.524872i
$$623$$ −4.47214 + 3.24920i −0.179172 + 0.130176i
$$624$$ −9.00000 −0.360288
$$625$$ 0 0
$$626$$ 27.1246 1.08412
$$627$$ −3.61803 + 2.62866i −0.144490 + 0.104978i
$$628$$ −2.51722 + 7.74721i −0.100448 + 0.309147i
$$629$$ 0.381966 1.17557i 0.0152300 0.0468731i
$$630$$ 0 0
$$631$$ −3.16312 9.73508i −0.125922 0.387547i 0.868146 0.496309i $$-0.165312\pi$$
−0.994068 + 0.108761i $$0.965312\pi$$
$$632$$ 18.0902 0.719588
$$633$$ 2.83688 + 8.73102i 0.112756 + 0.347027i
$$634$$ 10.0172 + 7.27794i 0.397835 + 0.289044i
$$635$$ 0 0
$$636$$ 1.73607 1.26133i 0.0688396 0.0500149i
$$637$$ −9.92705 7.21242i −0.393324 0.285767i
$$638$$ −24.7984 18.0171i −0.981777 0.713303i
$$639$$ −10.7082 + 7.77997i −0.423610 + 0.307771i
$$640$$ 0 0
$$641$$ 0.881966 + 0.640786i 0.0348356 + 0.0253095i 0.605067 0.796175i $$-0.293146\pi$$
−0.570231 + 0.821484i $$0.693146\pi$$
$$642$$ −8.20820 25.2623i −0.323952 0.997022i
$$643$$ 30.8328 1.21593 0.607964 0.793965i $$-0.291987\pi$$
0.607964 + 0.793965i $$0.291987\pi$$
$$644$$ 0.444272 + 1.36733i 0.0175068 + 0.0538803i
$$645$$ 0 0
$$646$$ 2.23607 6.88191i 0.0879769 0.270765i
$$647$$ 11.2918 34.7526i 0.443926 1.36626i −0.439731 0.898130i $$-0.644926\pi$$
0.883657 0.468135i $$-0.155074\pi$$
$$648$$ 1.80902 1.31433i 0.0710649 0.0516317i
$$649$$ 56.8328 2.23088
$$650$$ 0 0
$$651$$ −1.85410 −0.0726680
$$652$$ 5.50000 3.99598i 0.215397 0.156495i
$$653$$ −5.89919 + 18.1558i −0.230853 + 0.710493i 0.766791 + 0.641896i $$0.221852\pi$$
−0.997645 + 0.0685963i $$0.978148\pi$$
$$654$$ −5.00000 + 15.3884i −0.195515 + 0.601735i
$$655$$ 0 0
$$656$$ 1.14590 + 3.52671i 0.0447398 + 0.137695i
$$657$$ −18.0000 −0.702247
$$658$$ 0.190983 + 0.587785i 0.00744529 + 0.0229143i
$$659$$ −12.5623 9.12705i −0.489358 0.355539i 0.315579 0.948899i $$-0.397801\pi$$
−0.804937 + 0.593360i $$0.797801\pi$$
$$660$$ 0 0
$$661$$ −15.9271 + 11.5717i −0.619490 + 0.450086i −0.852744 0.522330i $$-0.825063\pi$$
0.233253 + 0.972416i $$0.425063\pi$$
$$662$$ 30.2705 + 21.9928i 1.17650 + 0.854775i
$$663$$ −7.85410 5.70634i −0.305028 0.221616i
$$664$$ 11.2812 8.19624i 0.437794 0.318076i
$$665$$ 0 0
$$666$$ 0.618034 + 0.449028i 0.0239483 + 0.0173995i
$$667$$ 4.20820 + 12.9515i 0.162942 + 0.501485i
$$668$$ −9.00000 −0.348220
$$669$$ −0.0557281 0.171513i −0.00215457 0.00663109i
$$670$$ 0 0
$$671$$ −14.0902 + 43.3651i −0.543945 + 1.67409i
$$672$$ −0.645898 + 1.98787i −0.0249161 + 0.0766837i
$$673$$ 9.85410 7.15942i 0.379848 0.275976i −0.381435 0.924396i $$-0.624570\pi$$
0.761283 + 0.648420i $$0.224570\pi$$
$$674$$ −12.7082 −0.489502
$$675$$ 0 0
$$676$$ −5.90983 −0.227301
$$677$$ 8.59017 6.24112i 0.330147 0.239866i −0.410346 0.911930i $$-0.634592\pi$$
0.740493 + 0.672064i $$0.234592\pi$$
$$678$$ 8.42705 25.9358i 0.323639 0.996058i
$$679$$ −0.736068 + 2.26538i −0.0282477 + 0.0869375i
$$680$$ 0 0
$$681$$ 4.56231 + 14.0413i 0.174828 + 0.538065i
$$682$$ 25.4164 0.973245
$$683$$ 4.16312 + 12.8128i 0.159297 + 0.490267i 0.998571 0.0534426i $$-0.0170194\pi$$
−0.839274 + 0.543709i $$0.817019\pi$$
$$684$$ 0.854102 + 0.620541i 0.0326574 + 0.0237270i
$$685$$ 0 0
$$686$$ −11.0172 + 8.00448i −0.420639 + 0.305612i
$$687$$ 17.5623 + 12.7598i 0.670044 + 0.486815i
$$688$$ 19.0623 + 13.8496i 0.726744 + 0.528010i
$$689$$ 5.20820 3.78398i 0.198417 0.144158i
$$690$$ 0 0
$$691$$ −29.3435 21.3193i −1.11628 0.811023i −0.132637 0.991165i $$-0.542344\pi$$
−0.983641 + 0.180141i $$0.942344\pi$$
$$692$$ −3.60739 11.1024i −0.137132 0.422050i
$$693$$ −6.47214 −0.245856
$$694$$ 9.95492 + 30.6381i 0.377883 + 1.16301i
$$695$$ 0 0
$$696$$ −2.50000 + 7.69421i −0.0947623 + 0.291648i
$$697$$ −1.23607 + 3.80423i −0.0468194 + 0.144095i
$$698$$ −28.4164 + 20.6457i −1.07558 + 0.781452i
$$699$$ −2.94427 −0.111363
$$700$$ 0 0
$$701$$ −41.0132 −1.54905 −0.774523 0.632546i $$-0.782010\pi$$
−0.774523 + 0.632546i $$0.782010\pi$$
$$702$$ 12.1353 8.81678i 0.458016 0.332768i
$$703$$ 0.0623059 0.191758i 0.00234991 0.00723228i
$$704$$ −6.85410 + 21.0948i −0.258324 + 0.795039i
$$705$$ 0 0
$$706$$ −6.45492 19.8662i −0.242934 0.747674i
$$707$$ −0.909830 −0.0342177
$$708$$ 2.07295 + 6.37988i 0.0779062 + 0.239771i
$$709$$ 27.1353 + 19.7149i 1.01909 + 0.740409i 0.966095 0.258186i $$-0.0831247\pi$$
0.0529906 + 0.998595i $$0.483125\pi$$
$$710$$ 0 0
$$711$$ −13.0902 + 9.51057i −0.490920 + 0.356674i
$$712$$ −16.1803 11.7557i −0.606384 0.440564i
$$713$$ −9.13525 6.63715i −0.342118 0.248563i
$$714$$ −4.23607 + 3.07768i −0.158531 + 0.115179i
$$715$$ 0 0
$$716$$ 0.263932 + 0.191758i 0.00986360 + 0.00716633i
$$717$$ 6.34346 + 19.5232i 0.236901 + 0.729106i
$$718$$ 22.2361 0.829843
$$719$$ −7.19756 22.1518i −0.268424 0.826123i −0.990885 0.134712i $$-0.956989\pi$$
0.722461 0.691412i $$-0.243011\pi$$
$$720$$ 0 0
$$721$$ 1.63525 5.03280i 0.0609001 0.187431i
$$722$$ −9.13525 + 28.1154i −0.339979 + 1.04635i
$$723$$ 2.04508 1.48584i 0.0760575 0.0552590i
$$724$$ 0.180340 0.00670228
$$725$$ 0 0
$$726$$ −26.5623 −0.985820
$$727$$ 19.8713 14.4374i 0.736987 0.535452i −0.154779 0.987949i $$-0.549467\pi$$
0.891766 + 0.452497i $$0.149467\pi$$
$$728$$ −0.791796 + 2.43690i −0.0293459 + 0.0903174i
$$729$$ 4.01722 12.3637i 0.148786 0.457916i
$$730$$ 0 0
$$731$$ 7.85410 + 24.1724i 0.290494 + 0.894050i
$$732$$ −5.38197 −0.198923
$$733$$ 6.17376 + 19.0009i 0.228033 + 0.701814i 0.997970 + 0.0636931i $$0.0202879\pi$$
−0.769936 + 0.638121i $$0.779712\pi$$
$$734$$ −33.4615 24.3112i −1.23509 0.897343i
$$735$$ 0 0
$$736$$ −10.2984 + 7.48221i −0.379603 + 0.275798i
$$737$$ −20.1803 14.6619i −0.743352 0.540077i
$$738$$ −2.00000 1.45309i −0.0736210 0.0534888i
$$739$$ −12.9271 + 9.39205i −0.475529 + 0.345492i −0.799592 0.600543i $$-0.794951\pi$$
0.324063 + 0.946036i $$0.394951\pi$$
$$740$$ 0 0
$$741$$ −1.28115 0.930812i −0.0470643 0.0341942i
$$742$$ −1.07295 3.30220i −0.0393892 0.121227i
$$743$$ −28.3607 −1.04045 −0.520226 0.854029i $$-0.674152\pi$$
−0.520226 + 0.854029i $$0.674152\pi$$
$$744$$ −2.07295 6.37988i −0.0759980 0.233898i
$$745$$ 0 0
$$746$$ 14.1353 43.5038i 0.517528 1.59279i
$$747$$ −3.85410 + 11.8617i −0.141014 + 0.433997i
$$748$$ 13.7082 9.95959i 0.501222 0.364159i
$$749$$ −10.1459 −0.370723
$$750$$ 0 0
$$751$$ −5.11146 −0.186520 −0.0932598 0.995642i $$-0.529729\pi$$
−0.0932598 + 0.995642i $$0.529729\pi$$
$$752$$ −2.42705 + 1.76336i −0.0885054 + 0.0643030i
$$753$$ 9.01722 27.7522i 0.328606 1.01134i
$$754$$ 3.35410 10.3229i 0.122149 0.375937i
$$755$$ 0 0
$$756$$ −0.590170 1.81636i −0.0214643 0.0660602i
$$757$$ −30.4164 −1.10550 −0.552752 0.833346i $$-0.686422\pi$$
−0.552752 + 0.833346i $$0.686422\pi$$
$$758$$ 7.29837 + 22.4621i 0.265089 + 0.815860i
$$759$$ 15.9443 + 11.5842i 0.578740 + 0.420480i
$$760$$ 0 0
$$761$$ 14.9271 10.8451i 0.541105 0.393136i −0.283390 0.959005i $$-0.591459\pi$$
0.824495 + 0.565869i $$0.191459\pi$$
$$762$$ −26.0344 18.9151i −0.943128 0.685223i
$$763$$ 5.00000 + 3.63271i 0.181012 + 0.131513i
$$764$$ 0.909830 0.661030i 0.0329165 0.0239152i
$$765$$ 0 0
$$766$$ 43.6697 + 31.7279i 1.57785 + 1.14638i
$$767$$ 6.21885 + 19.1396i 0.224550 + 0.691092i
$$768$$ −13.5623 −0.489388
$$769$$ 4.14590 + 12.7598i 0.149505 + 0.460129i 0.997563 0.0697749i $$-0.0222281\pi$$
−0.848058 + 0.529904i $$0.822228\pi$$
$$770$$ 0 0
$$771$$ 7.06231 21.7355i 0.254343 0.782786i
$$772$$ −1.47214 + 4.53077i −0.0529833 + 0.163066i
$$773$$ −29.2533 + 21.2538i −1.05217 + 0.764445i −0.972623 0.232387i $$-0.925346\pi$$
−0.0795442 + 0.996831i $$0.525346\pi$$
$$774$$ −15.7082 −0.564620
$$775$$ 0 0
$$776$$ −8.61803 −0.309369
$$777$$ −0.118034 + 0.0857567i −0.00423445 + 0.00307650i
$$778$$ 7.50000 23.0826i 0.268888 0.827552i
$$779$$ −0.201626 + 0.620541i −0.00722401 + 0.0222332i
$$780$$ 0 0