# Properties

 Label 70.2.c.a.29.1 Level $70$ Weight $2$ Character 70.29 Analytic conductor $0.559$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$70 = 2 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 70.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.558952814149$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 29.1 Root $$1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 70.29 Dual form 70.2.c.a.29.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} -2.44949 q^{6} -1.00000i q^{7} +1.00000i q^{8} -3.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-0.224745 + 2.22474i) q^{5} -2.44949 q^{6} -1.00000i q^{7} +1.00000i q^{8} -3.00000 q^{9} +(2.22474 + 0.224745i) q^{10} +4.89898 q^{11} +2.44949i q^{12} +0.449490i q^{13} -1.00000 q^{14} +(5.44949 + 0.550510i) q^{15} +1.00000 q^{16} +2.00000i q^{17} +3.00000i q^{18} -6.44949 q^{19} +(0.224745 - 2.22474i) q^{20} -2.44949 q^{21} -4.89898i q^{22} +6.89898i q^{23} +2.44949 q^{24} +(-4.89898 - 1.00000i) q^{25} +0.449490 q^{26} +1.00000i q^{28} +2.89898 q^{29} +(0.550510 - 5.44949i) q^{30} -0.898979 q^{31} -1.00000i q^{32} -12.0000i q^{33} +2.00000 q^{34} +(2.22474 + 0.224745i) q^{35} +3.00000 q^{36} +2.00000i q^{37} +6.44949i q^{38} +1.10102 q^{39} +(-2.22474 - 0.224745i) q^{40} -10.8990 q^{41} +2.44949i q^{42} -8.89898i q^{43} -4.89898 q^{44} +(0.674235 - 6.67423i) q^{45} +6.89898 q^{46} -0.898979i q^{47} -2.44949i q^{48} -1.00000 q^{49} +(-1.00000 + 4.89898i) q^{50} +4.89898 q^{51} -0.449490i q^{52} +1.10102i q^{53} +(-1.10102 + 10.8990i) q^{55} +1.00000 q^{56} +15.7980i q^{57} -2.89898i q^{58} +6.44949 q^{59} +(-5.44949 - 0.550510i) q^{60} +8.44949 q^{61} +0.898979i q^{62} +3.00000i q^{63} -1.00000 q^{64} +(-1.00000 - 0.101021i) q^{65} -12.0000 q^{66} -8.00000i q^{67} -2.00000i q^{68} +16.8990 q^{69} +(0.224745 - 2.22474i) q^{70} -10.8990 q^{71} -3.00000i q^{72} +6.89898i q^{73} +2.00000 q^{74} +(-2.44949 + 12.0000i) q^{75} +6.44949 q^{76} -4.89898i q^{77} -1.10102i q^{78} +2.89898 q^{79} +(-0.224745 + 2.22474i) q^{80} -9.00000 q^{81} +10.8990i q^{82} -2.44949i q^{83} +2.44949 q^{84} +(-4.44949 - 0.449490i) q^{85} -8.89898 q^{86} -7.10102i q^{87} +4.89898i q^{88} +10.0000 q^{89} +(-6.67423 - 0.674235i) q^{90} +0.449490 q^{91} -6.89898i q^{92} +2.20204i q^{93} -0.898979 q^{94} +(1.44949 - 14.3485i) q^{95} -2.44949 q^{96} -3.79796i q^{97} +1.00000i q^{98} -14.6969 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + O(q^{10})$$ $$4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + 4 q^{10} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 16 q^{19} - 4 q^{20} - 8 q^{26} - 8 q^{29} + 12 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 24 q^{39} - 4 q^{40} - 24 q^{41} - 12 q^{45} + 8 q^{46} - 4 q^{49} - 4 q^{50} - 24 q^{55} + 4 q^{56} + 16 q^{59} - 12 q^{60} + 24 q^{61} - 4 q^{64} - 4 q^{65} - 48 q^{66} + 48 q^{69} - 4 q^{70} - 24 q^{71} + 8 q^{74} + 16 q^{76} - 8 q^{79} + 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} + 40 q^{89} - 12 q^{90} - 8 q^{91} + 16 q^{94} - 4 q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$57$$ $$\chi(n)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 2.44949i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ −0.224745 + 2.22474i −0.100509 + 0.994936i
$$6$$ −2.44949 −1.00000
$$7$$ 1.00000i 0.377964i
$$8$$ 1.00000i 0.353553i
$$9$$ −3.00000 −1.00000
$$10$$ 2.22474 + 0.224745i 0.703526 + 0.0710706i
$$11$$ 4.89898 1.47710 0.738549 0.674200i $$-0.235511\pi$$
0.738549 + 0.674200i $$0.235511\pi$$
$$12$$ 2.44949i 0.707107i
$$13$$ 0.449490i 0.124666i 0.998055 + 0.0623330i $$0.0198541\pi$$
−0.998055 + 0.0623330i $$0.980146\pi$$
$$14$$ −1.00000 −0.267261
$$15$$ 5.44949 + 0.550510i 1.40705 + 0.142141i
$$16$$ 1.00000 0.250000
$$17$$ 2.00000i 0.485071i 0.970143 + 0.242536i $$0.0779791\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 3.00000i 0.707107i
$$19$$ −6.44949 −1.47961 −0.739807 0.672819i $$-0.765083\pi$$
−0.739807 + 0.672819i $$0.765083\pi$$
$$20$$ 0.224745 2.22474i 0.0502545 0.497468i
$$21$$ −2.44949 −0.534522
$$22$$ 4.89898i 1.04447i
$$23$$ 6.89898i 1.43854i 0.694732 + 0.719268i $$0.255523\pi$$
−0.694732 + 0.719268i $$0.744477\pi$$
$$24$$ 2.44949 0.500000
$$25$$ −4.89898 1.00000i −0.979796 0.200000i
$$26$$ 0.449490 0.0881522
$$27$$ 0 0
$$28$$ 1.00000i 0.188982i
$$29$$ 2.89898 0.538327 0.269163 0.963095i $$-0.413253\pi$$
0.269163 + 0.963095i $$0.413253\pi$$
$$30$$ 0.550510 5.44949i 0.100509 0.994936i
$$31$$ −0.898979 −0.161461 −0.0807307 0.996736i $$-0.525725\pi$$
−0.0807307 + 0.996736i $$0.525725\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 12.0000i 2.08893i
$$34$$ 2.00000 0.342997
$$35$$ 2.22474 + 0.224745i 0.376051 + 0.0379888i
$$36$$ 3.00000 0.500000
$$37$$ 2.00000i 0.328798i 0.986394 + 0.164399i $$0.0525685\pi$$
−0.986394 + 0.164399i $$0.947432\pi$$
$$38$$ 6.44949i 1.04625i
$$39$$ 1.10102 0.176304
$$40$$ −2.22474 0.224745i −0.351763 0.0355353i
$$41$$ −10.8990 −1.70213 −0.851067 0.525057i $$-0.824044\pi$$
−0.851067 + 0.525057i $$0.824044\pi$$
$$42$$ 2.44949i 0.377964i
$$43$$ 8.89898i 1.35708i −0.734563 0.678541i $$-0.762613\pi$$
0.734563 0.678541i $$-0.237387\pi$$
$$44$$ −4.89898 −0.738549
$$45$$ 0.674235 6.67423i 0.100509 0.994936i
$$46$$ 6.89898 1.01720
$$47$$ 0.898979i 0.131130i −0.997848 0.0655648i $$-0.979115\pi$$
0.997848 0.0655648i $$-0.0208849\pi$$
$$48$$ 2.44949i 0.353553i
$$49$$ −1.00000 −0.142857
$$50$$ −1.00000 + 4.89898i −0.141421 + 0.692820i
$$51$$ 4.89898 0.685994
$$52$$ 0.449490i 0.0623330i
$$53$$ 1.10102i 0.151237i 0.997137 + 0.0756184i $$0.0240931\pi$$
−0.997137 + 0.0756184i $$0.975907\pi$$
$$54$$ 0 0
$$55$$ −1.10102 + 10.8990i −0.148462 + 1.46962i
$$56$$ 1.00000 0.133631
$$57$$ 15.7980i 2.09249i
$$58$$ 2.89898i 0.380655i
$$59$$ 6.44949 0.839652 0.419826 0.907605i $$-0.362091\pi$$
0.419826 + 0.907605i $$0.362091\pi$$
$$60$$ −5.44949 0.550510i −0.703526 0.0710706i
$$61$$ 8.44949 1.08185 0.540923 0.841072i $$-0.318075\pi$$
0.540923 + 0.841072i $$0.318075\pi$$
$$62$$ 0.898979i 0.114171i
$$63$$ 3.00000i 0.377964i
$$64$$ −1.00000 −0.125000
$$65$$ −1.00000 0.101021i −0.124035 0.0125301i
$$66$$ −12.0000 −1.47710
$$67$$ 8.00000i 0.977356i −0.872464 0.488678i $$-0.837479\pi$$
0.872464 0.488678i $$-0.162521\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 16.8990 2.03440
$$70$$ 0.224745 2.22474i 0.0268622 0.265908i
$$71$$ −10.8990 −1.29347 −0.646735 0.762714i $$-0.723866\pi$$
−0.646735 + 0.762714i $$0.723866\pi$$
$$72$$ 3.00000i 0.353553i
$$73$$ 6.89898i 0.807464i 0.914877 + 0.403732i $$0.132287\pi$$
−0.914877 + 0.403732i $$0.867713\pi$$
$$74$$ 2.00000 0.232495
$$75$$ −2.44949 + 12.0000i −0.282843 + 1.38564i
$$76$$ 6.44949 0.739807
$$77$$ 4.89898i 0.558291i
$$78$$ 1.10102i 0.124666i
$$79$$ 2.89898 0.326161 0.163080 0.986613i $$-0.447857\pi$$
0.163080 + 0.986613i $$0.447857\pi$$
$$80$$ −0.224745 + 2.22474i −0.0251272 + 0.248734i
$$81$$ −9.00000 −1.00000
$$82$$ 10.8990i 1.20359i
$$83$$ 2.44949i 0.268866i −0.990923 0.134433i $$-0.957079\pi$$
0.990923 0.134433i $$-0.0429214\pi$$
$$84$$ 2.44949 0.267261
$$85$$ −4.44949 0.449490i −0.482615 0.0487540i
$$86$$ −8.89898 −0.959602
$$87$$ 7.10102i 0.761309i
$$88$$ 4.89898i 0.522233i
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ −6.67423 0.674235i −0.703526 0.0710706i
$$91$$ 0.449490 0.0471193
$$92$$ 6.89898i 0.719268i
$$93$$ 2.20204i 0.228341i
$$94$$ −0.898979 −0.0927227
$$95$$ 1.44949 14.3485i 0.148715 1.47212i
$$96$$ −2.44949 −0.250000
$$97$$ 3.79796i 0.385624i −0.981236 0.192812i $$-0.938239\pi$$
0.981236 0.192812i $$-0.0617608\pi$$
$$98$$ 1.00000i 0.101015i
$$99$$ −14.6969 −1.47710
$$100$$ 4.89898 + 1.00000i 0.489898 + 0.100000i
$$101$$ 8.44949 0.840756 0.420378 0.907349i $$-0.361898\pi$$
0.420378 + 0.907349i $$0.361898\pi$$
$$102$$ 4.89898i 0.485071i
$$103$$ 3.10102i 0.305553i −0.988261 0.152776i $$-0.951179\pi$$
0.988261 0.152776i $$-0.0488214\pi$$
$$104$$ −0.449490 −0.0440761
$$105$$ 0.550510 5.44949i 0.0537243 0.531816i
$$106$$ 1.10102 0.106941
$$107$$ 8.00000i 0.773389i −0.922208 0.386695i $$-0.873617\pi$$
0.922208 0.386695i $$-0.126383\pi$$
$$108$$ 0 0
$$109$$ 2.89898 0.277672 0.138836 0.990315i $$-0.455664\pi$$
0.138836 + 0.990315i $$0.455664\pi$$
$$110$$ 10.8990 + 1.10102i 1.03918 + 0.104978i
$$111$$ 4.89898 0.464991
$$112$$ 1.00000i 0.0944911i
$$113$$ 0.202041i 0.0190064i −0.999955 0.00950321i $$-0.996975\pi$$
0.999955 0.00950321i $$-0.00302501\pi$$
$$114$$ 15.7980 1.47961
$$115$$ −15.3485 1.55051i −1.43125 0.144586i
$$116$$ −2.89898 −0.269163
$$117$$ 1.34847i 0.124666i
$$118$$ 6.44949i 0.593724i
$$119$$ 2.00000 0.183340
$$120$$ −0.550510 + 5.44949i −0.0502545 + 0.497468i
$$121$$ 13.0000 1.18182
$$122$$ 8.44949i 0.764981i
$$123$$ 26.6969i 2.40718i
$$124$$ 0.898979 0.0807307
$$125$$ 3.32577 10.6742i 0.297465 0.954733i
$$126$$ 3.00000 0.267261
$$127$$ 5.10102i 0.452642i −0.974053 0.226321i $$-0.927330\pi$$
0.974053 0.226321i $$-0.0726699\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −21.7980 −1.91920
$$130$$ −0.101021 + 1.00000i −0.00886009 + 0.0877058i
$$131$$ −1.55051 −0.135469 −0.0677344 0.997703i $$-0.521577\pi$$
−0.0677344 + 0.997703i $$0.521577\pi$$
$$132$$ 12.0000i 1.04447i
$$133$$ 6.44949i 0.559242i
$$134$$ −8.00000 −0.691095
$$135$$ 0 0
$$136$$ −2.00000 −0.171499
$$137$$ 17.7980i 1.52058i 0.649582 + 0.760291i $$0.274944\pi$$
−0.649582 + 0.760291i $$0.725056\pi$$
$$138$$ 16.8990i 1.43854i
$$139$$ −6.44949 −0.547039 −0.273519 0.961867i $$-0.588188\pi$$
−0.273519 + 0.961867i $$0.588188\pi$$
$$140$$ −2.22474 0.224745i −0.188025 0.0189944i
$$141$$ −2.20204 −0.185445
$$142$$ 10.8990i 0.914622i
$$143$$ 2.20204i 0.184144i
$$144$$ −3.00000 −0.250000
$$145$$ −0.651531 + 6.44949i −0.0541067 + 0.535601i
$$146$$ 6.89898 0.570964
$$147$$ 2.44949i 0.202031i
$$148$$ 2.00000i 0.164399i
$$149$$ −15.7980 −1.29422 −0.647110 0.762397i $$-0.724022\pi$$
−0.647110 + 0.762397i $$0.724022\pi$$
$$150$$ 12.0000 + 2.44949i 0.979796 + 0.200000i
$$151$$ −19.5959 −1.59469 −0.797347 0.603522i $$-0.793764\pi$$
−0.797347 + 0.603522i $$0.793764\pi$$
$$152$$ 6.44949i 0.523123i
$$153$$ 6.00000i 0.485071i
$$154$$ −4.89898 −0.394771
$$155$$ 0.202041 2.00000i 0.0162283 0.160644i
$$156$$ −1.10102 −0.0881522
$$157$$ 8.44949i 0.674343i 0.941443 + 0.337171i $$0.109470\pi$$
−0.941443 + 0.337171i $$0.890530\pi$$
$$158$$ 2.89898i 0.230630i
$$159$$ 2.69694 0.213881
$$160$$ 2.22474 + 0.224745i 0.175882 + 0.0177676i
$$161$$ 6.89898 0.543716
$$162$$ 9.00000i 0.707107i
$$163$$ 16.8990i 1.32363i 0.749667 + 0.661815i $$0.230214\pi$$
−0.749667 + 0.661815i $$0.769786\pi$$
$$164$$ 10.8990 0.851067
$$165$$ 26.6969 + 2.69694i 2.07835 + 0.209956i
$$166$$ −2.44949 −0.190117
$$167$$ 4.89898i 0.379094i 0.981872 + 0.189547i $$0.0607020\pi$$
−0.981872 + 0.189547i $$0.939298\pi$$
$$168$$ 2.44949i 0.188982i
$$169$$ 12.7980 0.984458
$$170$$ −0.449490 + 4.44949i −0.0344743 + 0.341260i
$$171$$ 19.3485 1.47961
$$172$$ 8.89898i 0.678541i
$$173$$ 18.2474i 1.38733i −0.720299 0.693664i $$-0.755995\pi$$
0.720299 0.693664i $$-0.244005\pi$$
$$174$$ −7.10102 −0.538327
$$175$$ −1.00000 + 4.89898i −0.0755929 + 0.370328i
$$176$$ 4.89898 0.369274
$$177$$ 15.7980i 1.18745i
$$178$$ 10.0000i 0.749532i
$$179$$ 5.79796 0.433360 0.216680 0.976243i $$-0.430477\pi$$
0.216680 + 0.976243i $$0.430477\pi$$
$$180$$ −0.674235 + 6.67423i −0.0502545 + 0.497468i
$$181$$ 14.2474 1.05900 0.529502 0.848309i $$-0.322379\pi$$
0.529502 + 0.848309i $$0.322379\pi$$
$$182$$ 0.449490i 0.0333184i
$$183$$ 20.6969i 1.52996i
$$184$$ −6.89898 −0.508600
$$185$$ −4.44949 0.449490i −0.327133 0.0330471i
$$186$$ 2.20204 0.161461
$$187$$ 9.79796i 0.716498i
$$188$$ 0.898979i 0.0655648i
$$189$$ 0 0
$$190$$ −14.3485 1.44949i −1.04095 0.105157i
$$191$$ −16.6969 −1.20815 −0.604074 0.796928i $$-0.706457\pi$$
−0.604074 + 0.796928i $$0.706457\pi$$
$$192$$ 2.44949i 0.176777i
$$193$$ 17.5959i 1.26658i −0.773914 0.633291i $$-0.781704\pi$$
0.773914 0.633291i $$-0.218296\pi$$
$$194$$ −3.79796 −0.272678
$$195$$ −0.247449 + 2.44949i −0.0177202 + 0.175412i
$$196$$ 1.00000 0.0714286
$$197$$ 9.10102i 0.648421i 0.945985 + 0.324210i $$0.105099\pi$$
−0.945985 + 0.324210i $$0.894901\pi$$
$$198$$ 14.6969i 1.04447i
$$199$$ −7.10102 −0.503378 −0.251689 0.967808i $$-0.580986\pi$$
−0.251689 + 0.967808i $$0.580986\pi$$
$$200$$ 1.00000 4.89898i 0.0707107 0.346410i
$$201$$ −19.5959 −1.38219
$$202$$ 8.44949i 0.594504i
$$203$$ 2.89898i 0.203468i
$$204$$ −4.89898 −0.342997
$$205$$ 2.44949 24.2474i 0.171080 1.69352i
$$206$$ −3.10102 −0.216058
$$207$$ 20.6969i 1.43854i
$$208$$ 0.449490i 0.0311665i
$$209$$ −31.5959 −2.18554
$$210$$ −5.44949 0.550510i −0.376051 0.0379888i
$$211$$ 12.0000 0.826114 0.413057 0.910705i $$-0.364461\pi$$
0.413057 + 0.910705i $$0.364461\pi$$
$$212$$ 1.10102i 0.0756184i
$$213$$ 26.6969i 1.82924i
$$214$$ −8.00000 −0.546869
$$215$$ 19.7980 + 2.00000i 1.35021 + 0.136399i
$$216$$ 0 0
$$217$$ 0.898979i 0.0610267i
$$218$$ 2.89898i 0.196344i
$$219$$ 16.8990 1.14193
$$220$$ 1.10102 10.8990i 0.0742308 0.734809i
$$221$$ −0.898979 −0.0604719
$$222$$ 4.89898i 0.328798i
$$223$$ 4.00000i 0.267860i 0.990991 + 0.133930i $$0.0427597\pi$$
−0.990991 + 0.133930i $$0.957240\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ 14.6969 + 3.00000i 0.979796 + 0.200000i
$$226$$ −0.202041 −0.0134396
$$227$$ 7.34847i 0.487735i −0.969809 0.243868i $$-0.921584\pi$$
0.969809 0.243868i $$-0.0784162\pi$$
$$228$$ 15.7980i 1.04625i
$$229$$ −15.1464 −1.00090 −0.500452 0.865764i $$-0.666833\pi$$
−0.500452 + 0.865764i $$0.666833\pi$$
$$230$$ −1.55051 + 15.3485i −0.102238 + 1.01205i
$$231$$ −12.0000 −0.789542
$$232$$ 2.89898i 0.190327i
$$233$$ 10.2020i 0.668358i −0.942510 0.334179i $$-0.891541\pi$$
0.942510 0.334179i $$-0.108459\pi$$
$$234$$ −1.34847 −0.0881522
$$235$$ 2.00000 + 0.202041i 0.130466 + 0.0131797i
$$236$$ −6.44949 −0.419826
$$237$$ 7.10102i 0.461261i
$$238$$ 2.00000i 0.129641i
$$239$$ 25.7980 1.66873 0.834366 0.551211i $$-0.185834\pi$$
0.834366 + 0.551211i $$0.185834\pi$$
$$240$$ 5.44949 + 0.550510i 0.351763 + 0.0355353i
$$241$$ 20.6969 1.33321 0.666604 0.745412i $$-0.267747\pi$$
0.666604 + 0.745412i $$0.267747\pi$$
$$242$$ 13.0000i 0.835672i
$$243$$ 22.0454i 1.41421i
$$244$$ −8.44949 −0.540923
$$245$$ 0.224745 2.22474i 0.0143584 0.142134i
$$246$$ 26.6969 1.70213
$$247$$ 2.89898i 0.184458i
$$248$$ 0.898979i 0.0570853i
$$249$$ −6.00000 −0.380235
$$250$$ −10.6742 3.32577i −0.675098 0.210340i
$$251$$ −1.55051 −0.0978673 −0.0489337 0.998802i $$-0.515582\pi$$
−0.0489337 + 0.998802i $$0.515582\pi$$
$$252$$ 3.00000i 0.188982i
$$253$$ 33.7980i 2.12486i
$$254$$ −5.10102 −0.320066
$$255$$ −1.10102 + 10.8990i −0.0689486 + 0.682521i
$$256$$ 1.00000 0.0625000
$$257$$ 20.6969i 1.29104i 0.763744 + 0.645520i $$0.223359\pi$$
−0.763744 + 0.645520i $$0.776641\pi$$
$$258$$ 21.7980i 1.35708i
$$259$$ 2.00000 0.124274
$$260$$ 1.00000 + 0.101021i 0.0620174 + 0.00626503i
$$261$$ −8.69694 −0.538327
$$262$$ 1.55051i 0.0957908i
$$263$$ 9.79796i 0.604168i 0.953281 + 0.302084i $$0.0976823\pi$$
−0.953281 + 0.302084i $$0.902318\pi$$
$$264$$ 12.0000 0.738549
$$265$$ −2.44949 0.247449i −0.150471 0.0152007i
$$266$$ 6.44949 0.395444
$$267$$ 24.4949i 1.49906i
$$268$$ 8.00000i 0.488678i
$$269$$ 15.1464 0.923494 0.461747 0.887012i $$-0.347223\pi$$
0.461747 + 0.887012i $$0.347223\pi$$
$$270$$ 0 0
$$271$$ 12.0000 0.728948 0.364474 0.931214i $$-0.381249\pi$$
0.364474 + 0.931214i $$0.381249\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 1.10102i 0.0666368i
$$274$$ 17.7980 1.07521
$$275$$ −24.0000 4.89898i −1.44725 0.295420i
$$276$$ −16.8990 −1.01720
$$277$$ 5.10102i 0.306491i −0.988188 0.153245i $$-0.951028\pi$$
0.988188 0.153245i $$-0.0489725\pi$$
$$278$$ 6.44949i 0.386815i
$$279$$ 2.69694 0.161461
$$280$$ −0.224745 + 2.22474i −0.0134311 + 0.132954i
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 2.20204i 0.131130i
$$283$$ 28.2474i 1.67914i −0.543254 0.839568i $$-0.682808\pi$$
0.543254 0.839568i $$-0.317192\pi$$
$$284$$ 10.8990 0.646735
$$285$$ −35.1464 3.55051i −2.08189 0.210314i
$$286$$ 2.20204 0.130209
$$287$$ 10.8990i 0.643346i
$$288$$ 3.00000i 0.176777i
$$289$$ 13.0000 0.764706
$$290$$ 6.44949 + 0.651531i 0.378727 + 0.0382592i
$$291$$ −9.30306 −0.545355
$$292$$ 6.89898i 0.403732i
$$293$$ 6.24745i 0.364980i 0.983208 + 0.182490i $$0.0584157\pi$$
−0.983208 + 0.182490i $$0.941584\pi$$
$$294$$ 2.44949 0.142857
$$295$$ −1.44949 + 14.3485i −0.0843926 + 0.835400i
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ 15.7980i 0.915151i
$$299$$ −3.10102 −0.179337
$$300$$ 2.44949 12.0000i 0.141421 0.692820i
$$301$$ −8.89898 −0.512929
$$302$$ 19.5959i 1.12762i
$$303$$ 20.6969i 1.18901i
$$304$$ −6.44949 −0.369904
$$305$$ −1.89898 + 18.7980i −0.108735 + 1.07637i
$$306$$ −6.00000 −0.342997
$$307$$ 4.24745i 0.242415i 0.992627 + 0.121207i $$0.0386766\pi$$
−0.992627 + 0.121207i $$0.961323\pi$$
$$308$$ 4.89898i 0.279145i
$$309$$ −7.59592 −0.432117
$$310$$ −2.00000 0.202041i −0.113592 0.0114752i
$$311$$ 12.0000 0.680458 0.340229 0.940343i $$-0.389495\pi$$
0.340229 + 0.940343i $$0.389495\pi$$
$$312$$ 1.10102i 0.0623330i
$$313$$ 17.5959i 0.994580i −0.867584 0.497290i $$-0.834328\pi$$
0.867584 0.497290i $$-0.165672\pi$$
$$314$$ 8.44949 0.476832
$$315$$ −6.67423 0.674235i −0.376051 0.0379888i
$$316$$ −2.89898 −0.163080
$$317$$ 26.4949i 1.48810i 0.668123 + 0.744051i $$0.267098\pi$$
−0.668123 + 0.744051i $$0.732902\pi$$
$$318$$ 2.69694i 0.151237i
$$319$$ 14.2020 0.795162
$$320$$ 0.224745 2.22474i 0.0125636 0.124367i
$$321$$ −19.5959 −1.09374
$$322$$ 6.89898i 0.384465i
$$323$$ 12.8990i 0.717718i
$$324$$ 9.00000 0.500000
$$325$$ 0.449490 2.20204i 0.0249332 0.122147i
$$326$$ 16.8990 0.935948
$$327$$ 7.10102i 0.392687i
$$328$$ 10.8990i 0.601795i
$$329$$ −0.898979 −0.0495623
$$330$$ 2.69694 26.6969i 0.148462 1.46962i
$$331$$ 10.6969 0.587957 0.293978 0.955812i $$-0.405021\pi$$
0.293978 + 0.955812i $$0.405021\pi$$
$$332$$ 2.44949i 0.134433i
$$333$$ 6.00000i 0.328798i
$$334$$ 4.89898 0.268060
$$335$$ 17.7980 + 1.79796i 0.972406 + 0.0982330i
$$336$$ −2.44949 −0.133631
$$337$$ 29.5959i 1.61219i −0.591785 0.806096i $$-0.701576\pi$$
0.591785 0.806096i $$-0.298424\pi$$
$$338$$ 12.7980i 0.696117i
$$339$$ −0.494897 −0.0268791
$$340$$ 4.44949 + 0.449490i 0.241307 + 0.0243770i
$$341$$ −4.40408 −0.238494
$$342$$ 19.3485i 1.04625i
$$343$$ 1.00000i 0.0539949i
$$344$$ 8.89898 0.479801
$$345$$ −3.79796 + 37.5959i −0.204475 + 2.02410i
$$346$$ −18.2474 −0.980989
$$347$$ 19.1010i 1.02540i 0.858569 + 0.512698i $$0.171354\pi$$
−0.858569 + 0.512698i $$0.828646\pi$$
$$348$$ 7.10102i 0.380655i
$$349$$ 3.55051 0.190054 0.0950272 0.995475i $$-0.469706\pi$$
0.0950272 + 0.995475i $$0.469706\pi$$
$$350$$ 4.89898 + 1.00000i 0.261861 + 0.0534522i
$$351$$ 0 0
$$352$$ 4.89898i 0.261116i
$$353$$ 13.1010i 0.697297i −0.937254 0.348648i $$-0.886641\pi$$
0.937254 0.348648i $$-0.113359\pi$$
$$354$$ −15.7980 −0.839652
$$355$$ 2.44949 24.2474i 0.130005 1.28692i
$$356$$ −10.0000 −0.529999
$$357$$ 4.89898i 0.259281i
$$358$$ 5.79796i 0.306432i
$$359$$ −11.5959 −0.612009 −0.306005 0.952030i $$-0.598992\pi$$
−0.306005 + 0.952030i $$0.598992\pi$$
$$360$$ 6.67423 + 0.674235i 0.351763 + 0.0355353i
$$361$$ 22.5959 1.18926
$$362$$ 14.2474i 0.748829i
$$363$$ 31.8434i 1.67134i
$$364$$ −0.449490 −0.0235597
$$365$$ −15.3485 1.55051i −0.803376 0.0811574i
$$366$$ −20.6969 −1.08185
$$367$$ 32.0000i 1.67039i 0.549957 + 0.835193i $$0.314644\pi$$
−0.549957 + 0.835193i $$0.685356\pi$$
$$368$$ 6.89898i 0.359634i
$$369$$ 32.6969 1.70213
$$370$$ −0.449490 + 4.44949i −0.0233679 + 0.231318i
$$371$$ 1.10102 0.0571621
$$372$$ 2.20204i 0.114171i
$$373$$ 24.6969i 1.27876i −0.768891 0.639380i $$-0.779191\pi$$
0.768891 0.639380i $$-0.220809\pi$$
$$374$$ 9.79796 0.506640
$$375$$ −26.1464 8.14643i −1.35020 0.420680i
$$376$$ 0.898979 0.0463613
$$377$$ 1.30306i 0.0671111i
$$378$$ 0 0
$$379$$ −1.30306 −0.0669338 −0.0334669 0.999440i $$-0.510655\pi$$
−0.0334669 + 0.999440i $$0.510655\pi$$
$$380$$ −1.44949 + 14.3485i −0.0743573 + 0.736061i
$$381$$ −12.4949 −0.640133
$$382$$ 16.6969i 0.854290i
$$383$$ 16.8990i 0.863498i 0.901994 + 0.431749i $$0.142103\pi$$
−0.901994 + 0.431749i $$0.857897\pi$$
$$384$$ 2.44949 0.125000
$$385$$ 10.8990 + 1.10102i 0.555463 + 0.0561132i
$$386$$ −17.5959 −0.895609
$$387$$ 26.6969i 1.35708i
$$388$$ 3.79796i 0.192812i
$$389$$ −22.8990 −1.16102 −0.580512 0.814252i $$-0.697148\pi$$
−0.580512 + 0.814252i $$0.697148\pi$$
$$390$$ 2.44949 + 0.247449i 0.124035 + 0.0125301i
$$391$$ −13.7980 −0.697793
$$392$$ 1.00000i 0.0505076i
$$393$$ 3.79796i 0.191582i
$$394$$ 9.10102 0.458503
$$395$$ −0.651531 + 6.44949i −0.0327821 + 0.324509i
$$396$$ 14.6969 0.738549
$$397$$ 17.3485i 0.870695i −0.900263 0.435347i $$-0.856626\pi$$
0.900263 0.435347i $$-0.143374\pi$$
$$398$$ 7.10102i 0.355942i
$$399$$ 15.7980 0.790887
$$400$$ −4.89898 1.00000i −0.244949 0.0500000i
$$401$$ 29.3939 1.46786 0.733930 0.679225i $$-0.237684\pi$$
0.733930 + 0.679225i $$0.237684\pi$$
$$402$$ 19.5959i 0.977356i
$$403$$ 0.404082i 0.0201288i
$$404$$ −8.44949 −0.420378
$$405$$ 2.02270 20.0227i 0.100509 0.994936i
$$406$$ −2.89898 −0.143874
$$407$$ 9.79796i 0.485667i
$$408$$ 4.89898i 0.242536i
$$409$$ 14.4949 0.716727 0.358363 0.933582i $$-0.383335\pi$$
0.358363 + 0.933582i $$0.383335\pi$$
$$410$$ −24.2474 2.44949i −1.19750 0.120972i
$$411$$ 43.5959 2.15043
$$412$$ 3.10102i 0.152776i
$$413$$ 6.44949i 0.317359i
$$414$$ −20.6969 −1.01720
$$415$$ 5.44949 + 0.550510i 0.267505 + 0.0270235i
$$416$$ 0.449490 0.0220380
$$417$$ 15.7980i 0.773629i
$$418$$ 31.5959i 1.54541i
$$419$$ 6.44949 0.315078 0.157539 0.987513i $$-0.449644\pi$$
0.157539 + 0.987513i $$0.449644\pi$$
$$420$$ −0.550510 + 5.44949i −0.0268622 + 0.265908i
$$421$$ −23.7980 −1.15984 −0.579921 0.814673i $$-0.696917\pi$$
−0.579921 + 0.814673i $$0.696917\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 2.69694i 0.131130i
$$424$$ −1.10102 −0.0534703
$$425$$ 2.00000 9.79796i 0.0970143 0.475271i
$$426$$ 26.6969 1.29347
$$427$$ 8.44949i 0.408899i
$$428$$ 8.00000i 0.386695i
$$429$$ 5.39388 0.260419
$$430$$ 2.00000 19.7980i 0.0964486 0.954742i
$$431$$ 17.7980 0.857298 0.428649 0.903471i $$-0.358990\pi$$
0.428649 + 0.903471i $$0.358990\pi$$
$$432$$ 0 0
$$433$$ 19.7980i 0.951429i 0.879600 + 0.475715i $$0.157810\pi$$
−0.879600 + 0.475715i $$0.842190\pi$$
$$434$$ 0.898979 0.0431524
$$435$$ 15.7980 + 1.59592i 0.757454 + 0.0765184i
$$436$$ −2.89898 −0.138836
$$437$$ 44.4949i 2.12848i
$$438$$ 16.8990i 0.807464i
$$439$$ −37.3939 −1.78471 −0.892356 0.451332i $$-0.850949\pi$$
−0.892356 + 0.451332i $$0.850949\pi$$
$$440$$ −10.8990 1.10102i −0.519588 0.0524891i
$$441$$ 3.00000 0.142857
$$442$$ 0.898979i 0.0427601i
$$443$$ 9.79796i 0.465515i 0.972535 + 0.232758i $$0.0747749\pi$$
−0.972535 + 0.232758i $$0.925225\pi$$
$$444$$ −4.89898 −0.232495
$$445$$ −2.24745 + 22.2474i −0.106539 + 1.05463i
$$446$$ 4.00000 0.189405
$$447$$ 38.6969i 1.83030i
$$448$$ 1.00000i 0.0472456i
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 3.00000 14.6969i 0.141421 0.692820i
$$451$$ −53.3939 −2.51422
$$452$$ 0.202041i 0.00950321i
$$453$$ 48.0000i 2.25524i
$$454$$ −7.34847 −0.344881
$$455$$ −0.101021 + 1.00000i −0.00473591 + 0.0468807i
$$456$$ −15.7980 −0.739807
$$457$$ 9.59592i 0.448878i −0.974488 0.224439i $$-0.927945\pi$$
0.974488 0.224439i $$-0.0720550\pi$$
$$458$$ 15.1464i 0.707746i
$$459$$ 0 0
$$460$$ 15.3485 + 1.55051i 0.715626 + 0.0722929i
$$461$$ 2.65153 0.123494 0.0617470 0.998092i $$-0.480333\pi$$
0.0617470 + 0.998092i $$0.480333\pi$$
$$462$$ 12.0000i 0.558291i
$$463$$ 35.5959i 1.65428i 0.561994 + 0.827141i $$0.310034\pi$$
−0.561994 + 0.827141i $$0.689966\pi$$
$$464$$ 2.89898 0.134582
$$465$$ −4.89898 0.494897i −0.227185 0.0229503i
$$466$$ −10.2020 −0.472600
$$467$$ 5.55051i 0.256847i 0.991719 + 0.128423i $$0.0409917\pi$$
−0.991719 + 0.128423i $$0.959008\pi$$
$$468$$ 1.34847i 0.0623330i
$$469$$ −8.00000 −0.369406
$$470$$ 0.202041 2.00000i 0.00931946 0.0922531i
$$471$$ 20.6969 0.953665
$$472$$ 6.44949i 0.296862i
$$473$$ 43.5959i 2.00454i
$$474$$ −7.10102 −0.326161
$$475$$ 31.5959 + 6.44949i 1.44972 + 0.295923i
$$476$$ −2.00000 −0.0916698
$$477$$ 3.30306i 0.151237i
$$478$$ 25.7980i 1.17997i
$$479$$ −38.6969 −1.76811 −0.884054 0.467385i $$-0.845196\pi$$
−0.884054 + 0.467385i $$0.845196\pi$$
$$480$$ 0.550510 5.44949i 0.0251272 0.248734i
$$481$$ −0.898979 −0.0409899
$$482$$ 20.6969i 0.942720i
$$483$$ 16.8990i 0.768930i
$$484$$ −13.0000 −0.590909
$$485$$ 8.44949 + 0.853572i 0.383672 + 0.0387587i
$$486$$ 22.0454 1.00000
$$487$$ 36.6969i 1.66290i −0.555602 0.831449i $$-0.687512\pi$$
0.555602 0.831449i $$-0.312488\pi$$
$$488$$ 8.44949i 0.382490i
$$489$$ 41.3939 1.87190
$$490$$ −2.22474 0.224745i −0.100504 0.0101529i
$$491$$ −19.5959 −0.884351 −0.442176 0.896928i $$-0.645793\pi$$
−0.442176 + 0.896928i $$0.645793\pi$$
$$492$$ 26.6969i 1.20359i
$$493$$ 5.79796i 0.261127i
$$494$$ −2.89898 −0.130431
$$495$$ 3.30306 32.6969i 0.148462 1.46962i
$$496$$ −0.898979 −0.0403654
$$497$$ 10.8990i 0.488886i
$$498$$ 6.00000i 0.268866i
$$499$$ −25.7980 −1.15488 −0.577438 0.816435i $$-0.695947\pi$$
−0.577438 + 0.816435i $$0.695947\pi$$
$$500$$ −3.32577 + 10.6742i −0.148733 + 0.477366i
$$501$$ 12.0000 0.536120
$$502$$ 1.55051i 0.0692027i
$$503$$ 4.00000i 0.178351i 0.996016 + 0.0891756i $$0.0284232\pi$$
−0.996016 + 0.0891756i $$0.971577\pi$$
$$504$$ −3.00000 −0.133631
$$505$$ −1.89898 + 18.7980i −0.0845035 + 0.836498i
$$506$$ 33.7980 1.50250
$$507$$ 31.3485i 1.39223i
$$508$$ 5.10102i 0.226321i
$$509$$ 36.4495 1.61560 0.807798 0.589460i $$-0.200659\pi$$
0.807798 + 0.589460i $$0.200659\pi$$
$$510$$ 10.8990 + 1.10102i 0.482615 + 0.0487540i
$$511$$ 6.89898 0.305193
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 20.6969 0.912903
$$515$$ 6.89898 + 0.696938i 0.304005 + 0.0307108i
$$516$$ 21.7980 0.959602
$$517$$ 4.40408i 0.193691i
$$518$$ 2.00000i 0.0878750i
$$519$$ −44.6969 −1.96198
$$520$$ 0.101021 1.00000i 0.00443004 0.0438529i
$$521$$ 3.30306 0.144710 0.0723549 0.997379i $$-0.476949\pi$$
0.0723549 + 0.997379i $$0.476949\pi$$
$$522$$ 8.69694i 0.380655i
$$523$$ 1.14643i 0.0501298i −0.999686 0.0250649i $$-0.992021\pi$$
0.999686 0.0250649i $$-0.00797924\pi$$
$$524$$ 1.55051 0.0677344
$$525$$ 12.0000 + 2.44949i 0.523723 + 0.106904i
$$526$$ 9.79796 0.427211
$$527$$ 1.79796i 0.0783203i
$$528$$ 12.0000i 0.522233i
$$529$$ −24.5959 −1.06939
$$530$$ −0.247449 + 2.44949i −0.0107485 + 0.106399i
$$531$$ −19.3485 −0.839652
$$532$$ 6.44949i 0.279621i
$$533$$ 4.89898i 0.212198i
$$534$$ −24.4949 −1.06000
$$535$$ 17.7980 + 1.79796i 0.769473 + 0.0777325i
$$536$$ 8.00000 0.345547
$$537$$ 14.2020i 0.612863i
$$538$$ 15.1464i 0.653009i
$$539$$ −4.89898 −0.211014
$$540$$ 0 0
$$541$$ −29.5959 −1.27243 −0.636214 0.771513i $$-0.719500\pi$$
−0.636214 + 0.771513i $$0.719500\pi$$
$$542$$ 12.0000i 0.515444i
$$543$$ 34.8990i 1.49766i
$$544$$ 2.00000 0.0857493
$$545$$ −0.651531 + 6.44949i −0.0279085 + 0.276266i
$$546$$ −1.10102 −0.0471193
$$547$$ 10.6969i 0.457368i 0.973501 + 0.228684i $$0.0734423\pi$$
−0.973501 + 0.228684i $$0.926558\pi$$
$$548$$ 17.7980i 0.760291i
$$549$$ −25.3485 −1.08185
$$550$$ −4.89898 + 24.0000i −0.208893 + 1.02336i
$$551$$ −18.6969 −0.796516
$$552$$ 16.8990i 0.719268i
$$553$$ 2.89898i 0.123277i
$$554$$ −5.10102 −0.216722
$$555$$ −1.10102 + 10.8990i −0.0467357 + 0.462636i
$$556$$ 6.44949 0.273519
$$557$$ 16.6969i 0.707472i −0.935345 0.353736i $$-0.884911\pi$$
0.935345 0.353736i $$-0.115089\pi$$
$$558$$ 2.69694i 0.114171i
$$559$$ 4.00000 0.169182
$$560$$ 2.22474 + 0.224745i 0.0940126 + 0.00949720i
$$561$$ 24.0000 1.01328
$$562$$ 18.0000i 0.759284i
$$563$$ 14.0454i 0.591943i −0.955197 0.295972i $$-0.904357\pi$$
0.955197 0.295972i $$-0.0956434\pi$$
$$564$$ 2.20204 0.0927227
$$565$$ 0.449490 + 0.0454077i 0.0189102 + 0.00191032i
$$566$$ −28.2474 −1.18733
$$567$$ 9.00000i 0.377964i
$$568$$ 10.8990i 0.457311i
$$569$$ −14.2020 −0.595381 −0.297690 0.954663i $$-0.596216\pi$$
−0.297690 + 0.954663i $$0.596216\pi$$
$$570$$ −3.55051 + 35.1464i −0.148715 + 1.47212i
$$571$$ −20.8990 −0.874595 −0.437298 0.899317i $$-0.644064\pi$$
−0.437298 + 0.899317i $$0.644064\pi$$
$$572$$ 2.20204i 0.0920720i
$$573$$ 40.8990i 1.70858i
$$574$$ 10.8990 0.454915
$$575$$ 6.89898 33.7980i 0.287707 1.40947i
$$576$$ 3.00000 0.125000
$$577$$ 46.4949i 1.93561i 0.251705 + 0.967804i $$0.419009\pi$$
−0.251705 + 0.967804i $$0.580991\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ −43.1010 −1.79122
$$580$$ 0.651531 6.44949i 0.0270533 0.267800i
$$581$$ −2.44949 −0.101622
$$582$$ 9.30306i 0.385624i
$$583$$ 5.39388i 0.223392i
$$584$$ −6.89898 −0.285482
$$585$$ 3.00000 + 0.303062i 0.124035 + 0.0125301i
$$586$$ 6.24745 0.258080
$$587$$ 33.1464i 1.36810i −0.729435 0.684050i $$-0.760217\pi$$
0.729435 0.684050i $$-0.239783\pi$$
$$588$$ 2.44949i 0.101015i
$$589$$ 5.79796 0.238901
$$590$$ 14.3485 + 1.44949i 0.590717 + 0.0596745i
$$591$$ 22.2929 0.917006
$$592$$ 2.00000i 0.0821995i
$$593$$ 1.10102i 0.0452135i 0.999744 + 0.0226067i $$0.00719656\pi$$
−0.999744 + 0.0226067i $$0.992803\pi$$
$$594$$ 0 0
$$595$$ −0.449490 + 4.44949i −0.0184273 + 0.182411i
$$596$$ 15.7980 0.647110
$$597$$ 17.3939i 0.711884i
$$598$$ 3.10102i 0.126810i
$$599$$ 22.8990 0.935627 0.467813 0.883827i $$-0.345042\pi$$
0.467813 + 0.883827i $$0.345042\pi$$
$$600$$ −12.0000 2.44949i −0.489898 0.100000i
$$601$$ 19.3939 0.791093 0.395546 0.918446i $$-0.370555\pi$$
0.395546 + 0.918446i $$0.370555\pi$$
$$602$$ 8.89898i 0.362695i
$$603$$ 24.0000i 0.977356i
$$604$$ 19.5959 0.797347
$$605$$ −2.92168 + 28.9217i −0.118783 + 1.17583i
$$606$$ −20.6969 −0.840756
$$607$$ 25.3939i 1.03071i −0.856978 0.515353i $$-0.827661\pi$$
0.856978 0.515353i $$-0.172339\pi$$
$$608$$ 6.44949i 0.261561i
$$609$$ −7.10102 −0.287748
$$610$$ 18.7980 + 1.89898i 0.761107 + 0.0768874i
$$611$$ 0.404082 0.0163474
$$612$$ 6.00000i 0.242536i
$$613$$ 8.20204i 0.331277i 0.986187 + 0.165639i $$0.0529685\pi$$
−0.986187 + 0.165639i $$0.947031\pi$$
$$614$$ 4.24745 0.171413
$$615$$ −59.3939 6.00000i −2.39499 0.241943i
$$616$$ 4.89898 0.197386
$$617$$ 9.59592i 0.386317i −0.981168 0.193159i $$-0.938127\pi$$
0.981168 0.193159i $$-0.0618732\pi$$
$$618$$ 7.59592i 0.305553i
$$619$$ 46.4495 1.86696 0.933481 0.358626i $$-0.116755\pi$$
0.933481 + 0.358626i $$0.116755\pi$$
$$620$$ −0.202041 + 2.00000i −0.00811416 + 0.0803219i
$$621$$ 0 0
$$622$$ 12.0000i 0.481156i
$$623$$ 10.0000i 0.400642i
$$624$$ 1.10102 0.0440761
$$625$$ 23.0000 + 9.79796i 0.920000 + 0.391918i
$$626$$ −17.5959 −0.703274
$$627$$ 77.3939i 3.09081i
$$628$$ 8.44949i 0.337171i
$$629$$ −4.00000 −0.159490
$$630$$ −0.674235 + 6.67423i −0.0268622 + 0.265908i
$$631$$ 6.49490 0.258558 0.129279 0.991608i $$-0.458734\pi$$
0.129279 + 0.991608i $$0.458734\pi$$
$$632$$ 2.89898i 0.115315i
$$633$$ 29.3939i 1.16830i
$$634$$ 26.4949 1.05225
$$635$$ 11.3485 + 1.14643i 0.450350 + 0.0454946i
$$636$$ −2.69694 −0.106941
$$637$$ 0.449490i 0.0178094i
$$638$$ 14.2020i 0.562264i
$$639$$ 32.6969 1.29347
$$640$$ −2.22474 0.224745i −0.0879408 0.00888382i
$$641$$ 6.20204 0.244966 0.122483 0.992471i $$-0.460914\pi$$
0.122483 + 0.992471i $$0.460914\pi$$
$$642$$ 19.5959i 0.773389i
$$643$$ 9.14643i 0.360700i 0.983603 + 0.180350i $$0.0577230\pi$$
−0.983603 + 0.180350i $$0.942277\pi$$
$$644$$ −6.89898 −0.271858
$$645$$ 4.89898 48.4949i 0.192897 1.90948i
$$646$$ −12.8990 −0.507504
$$647$$ 22.2929i 0.876423i 0.898872 + 0.438211i $$0.144388\pi$$
−0.898872 + 0.438211i $$0.855612\pi$$
$$648$$ 9.00000i 0.353553i
$$649$$ 31.5959 1.24025
$$650$$ −2.20204 0.449490i −0.0863712 0.0176304i
$$651$$ 2.20204 0.0863048
$$652$$ 16.8990i 0.661815i
$$653$$ 39.7980i 1.55741i 0.627387 + 0.778707i $$0.284124\pi$$
−0.627387 + 0.778707i $$0.715876\pi$$
$$654$$ −7.10102 −0.277672
$$655$$ 0.348469 3.44949i 0.0136158 0.134783i
$$656$$ −10.8990 −0.425534
$$657$$ 20.6969i 0.807464i
$$658$$ 0.898979i 0.0350459i
$$659$$ −7.10102 −0.276616 −0.138308 0.990389i $$-0.544166\pi$$
−0.138308 + 0.990389i $$0.544166\pi$$
$$660$$ −26.6969 2.69694i −1.03918 0.104978i
$$661$$ 12.9444 0.503478 0.251739 0.967795i $$-0.418997\pi$$
0.251739 + 0.967795i $$0.418997\pi$$
$$662$$ 10.6969i 0.415748i
$$663$$ 2.20204i 0.0855202i
$$664$$ 2.44949 0.0950586
$$665$$ −14.3485 1.44949i −0.556410 0.0562088i
$$666$$ −6.00000 −0.232495
$$667$$ 20.0000i 0.774403i
$$668$$ 4.89898i 0.189547i
$$669$$ 9.79796 0.378811
$$670$$ 1.79796 17.7980i 0.0694612 0.687595i
$$671$$ 41.3939 1.59799
$$672$$ 2.44949i 0.0944911i
$$673$$ 1.79796i 0.0693062i −0.999399 0.0346531i $$-0.988967\pi$$
0.999399 0.0346531i $$-0.0110326\pi$$
$$674$$ −29.5959 −1.13999
$$675$$ 0 0
$$676$$ −12.7980 −0.492229
$$677$$ 31.5505i 1.21258i −0.795242 0.606292i $$-0.792656\pi$$
0.795242 0.606292i $$-0.207344\pi$$
$$678$$ 0.494897i 0.0190064i
$$679$$ −3.79796 −0.145752
$$680$$ 0.449490 4.44949i 0.0172371 0.170630i
$$681$$ −18.0000 −0.689761
$$682$$ 4.40408i 0.168641i
$$683$$ 35.5959i 1.36204i 0.732265 + 0.681020i $$0.238463\pi$$
−0.732265 + 0.681020i $$0.761537\pi$$
$$684$$ −19.3485 −0.739807
$$685$$ −39.5959 4.00000i −1.51288 0.152832i
$$686$$ 1.00000 0.0381802
$$687$$ 37.1010i 1.41549i
$$688$$ 8.89898i 0.339270i
$$689$$ −0.494897 −0.0188541
$$690$$ 37.5959 + 3.79796i 1.43125 + 0.144586i
$$691$$ −13.1464 −0.500114 −0.250057 0.968231i $$-0.580449\pi$$
−0.250057 + 0.968231i $$0.580449\pi$$
$$692$$ 18.2474i 0.693664i
$$693$$ 14.6969i 0.558291i
$$694$$ 19.1010 0.725065
$$695$$ 1.44949 14.3485i 0.0549823 0.544268i
$$696$$ 7.10102 0.269163
$$697$$ 21.7980i 0.825657i
$$698$$ 3.55051i 0.134389i
$$699$$ −24.9898 −0.945201
$$700$$ 1.00000 4.89898i 0.0377964 0.185164i
$$701$$ 40.6969 1.53710 0.768551 0.639788i $$-0.220978\pi$$
0.768551 + 0.639788i $$0.220978\pi$$
$$702$$ 0 0
$$703$$ 12.8990i 0.486494i
$$704$$ −4.89898 −0.184637
$$705$$ 0.494897 4.89898i 0.0186389 0.184506i
$$706$$ −13.1010 −0.493063
$$707$$ 8.44949i 0.317776i
$$708$$ 15.7980i 0.593724i
$$709$$ −40.2929 −1.51323 −0.756615 0.653861i $$-0.773148\pi$$
−0.756615 + 0.653861i $$0.773148\pi$$
$$710$$ −24.2474 2.44949i −0.909991 0.0919277i
$$711$$ −8.69694 −0.326161
$$712$$ 10.0000i 0.374766i
$$713$$ 6.20204i 0.232268i
$$714$$ −4.89898 −0.183340
$$715$$ −4.89898 0.494897i −0.183211 0.0185081i
$$716$$ −5.79796 −0.216680
$$717$$ 63.1918i 2.35994i
$$718$$ 11.5959i 0.432756i
$$719$$ −44.4949 −1.65938 −0.829690 0.558225i $$-0.811483\pi$$
−0.829690 + 0.558225i $$0.811483\pi$$
$$720$$ 0.674235 6.67423i 0.0251272 0.248734i
$$721$$ −3.10102 −0.115488
$$722$$ 22.5959i 0.840933i
$$723$$ 50.6969i 1.88544i
$$724$$ −14.2474 −0.529502
$$725$$ −14.2020 2.89898i −0.527451 0.107665i
$$726$$ −31.8434 −1.18182
$$727$$ 6.69694i 0.248376i −0.992259 0.124188i $$-0.960367\pi$$
0.992259 0.124188i $$-0.0396325\pi$$
$$728$$ 0.449490i 0.0166592i
$$729$$ 27.0000 1.00000
$$730$$ −1.55051 + 15.3485i −0.0573870 + 0.568072i
$$731$$ 17.7980 0.658281
$$732$$ 20.6969i 0.764981i
$$733$$ 43.6413i 1.61193i 0.591964 + 0.805965i $$0.298353\pi$$
−0.591964 + 0.805965i $$0.701647\pi$$
$$734$$ 32.0000 1.18114
$$735$$ −5.44949 0.550510i −0.201007 0.0203059i
$$736$$ 6.89898 0.254300
$$737$$ 39.1918i 1.44365i
$$738$$ 32.6969i 1.20359i
$$739$$ 44.4949 1.63677 0.818386 0.574669i $$-0.194869\pi$$
0.818386 + 0.574669i $$0.194869\pi$$
$$740$$ 4.44949 + 0.449490i 0.163566 + 0.0165236i
$$741$$ −7.10102 −0.260863
$$742$$ 1.10102i 0.0404197i
$$743$$ 15.3031i 0.561415i 0.959793 + 0.280707i $$0.0905691\pi$$
−0.959793 + 0.280707i $$0.909431\pi$$
$$744$$ −2.20204 −0.0807307
$$745$$ 3.55051 35.1464i 0.130081 1.28767i
$$746$$ −24.6969 −0.904219
$$747$$ 7.34847i 0.268866i
$$748$$ 9.79796i 0.358249i
$$749$$ −8.00000 −0.292314
$$750$$ −8.14643 + 26.1464i −0.297465 + 0.954733i
$$751$$ −22.2020 −0.810164 −0.405082 0.914280i $$-0.632757\pi$$
−0.405082 + 0.914280i $$0.632757\pi$$
$$752$$ 0.898979i 0.0327824i
$$753$$ 3.79796i 0.138405i
$$754$$ 1.30306 0.0474547
$$755$$ 4.40408 43.5959i 0.160281 1.58662i
$$756$$ 0 0
$$757$$ 32.2020i 1.17040i −0.810888 0.585202i $$-0.801015\pi$$
0.810888 0.585202i $$-0.198985\pi$$
$$758$$ 1.30306i 0.0473293i
$$759$$ 82.7878 3.00501
$$760$$ 14.3485 + 1.44949i 0.520474 + 0.0525785i
$$761$$ −30.8990 −1.12009 −0.560044 0.828463i $$-0.689216\pi$$
−0.560044 + 0.828463i $$0.689216\pi$$
$$762$$ 12.4949i 0.452642i
$$763$$ 2.89898i 0.104950i
$$764$$ 16.6969 0.604074
$$765$$ 13.3485 + 1.34847i 0.482615 + 0.0487540i
$$766$$ 16.8990 0.610585
$$767$$ 2.89898i 0.104676i
$$768$$ 2.44949i 0.0883883i
$$769$$ 11.3031 0.407599 0.203799 0.979013i $$-0.434671\pi$$
0.203799 + 0.979013i $$0.434671\pi$$
$$770$$ 1.10102 10.8990i 0.0396780 0.392772i
$$771$$ 50.6969 1.82581
$$772$$ 17.5959i 0.633291i
$$773$$ 13.3485i 0.480111i 0.970759 + 0.240056i $$0.0771657\pi$$
−0.970759 + 0.240056i $$0.922834\pi$$
$$774$$ 26.6969 0.959602
$$775$$ 4.40408 + 0.898979i 0.158199 + 0.0322923i
$$776$$ 3.79796 0.136339
$$777$$ 4.89898i 0.175750i
$$778$$ 22.8990i 0.820968i
$$779$$ 70.2929 2.51850
$$780$$ 0.247449 2.44949i 0.00886009 0.0877058i
$$781$$ −53.3939 −1.91058
$$782$$ 13.7980i 0.493414i
$$783$$ 0 0
$$784$$ −1.00000 −0.0357143
$$785$$ −18.7980 1.89898i −0.670928 0.0677775i
$$786$$ 3.79796 0.135469
$$787$$ 45.5505i 1.62370i 0.583866 + 0.811850i $$0.301539\pi$$
−0.583866 + 0.811850i $$0.698461\pi$$
$$788$$ 9.10102i