# Properties

 Label 98.2.c.c.67.2 Level $98$ Weight $2$ Character 98.67 Analytic conductor $0.783$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$98 = 2 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 98.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.782533939809$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 67.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 98.67 Dual form 98.2.c.c.79.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.41421 - 2.44949i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.41421 + 2.44949i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.707107 + 1.22474i) q^{12} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.707107 - 1.22474i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.53553 + 6.12372i) q^{19} +2.82843 q^{20} -2.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.707107 - 1.22474i) q^{24} +(-1.50000 + 2.59808i) q^{25} +5.65685 q^{27} +2.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-4.24264 + 7.34847i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.41421 - 2.44949i) q^{33} -1.41421 q^{34} -1.00000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(3.53553 - 6.12372i) q^{38} +(-1.41421 - 2.44949i) q^{40} -9.89949 q^{41} +2.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(1.41421 - 2.44949i) q^{45} +(2.00000 - 3.46410i) q^{46} +(-1.41421 - 2.44949i) q^{47} -1.41421 q^{48} +3.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +(-2.82843 - 4.89898i) q^{54} -5.65685 q^{55} +10.0000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(0.707107 - 1.22474i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-1.41421 - 2.44949i) q^{61} +8.48528 q^{62} +1.00000 q^{64} +(-1.41421 + 2.44949i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(0.707107 + 1.22474i) q^{68} +5.65685 q^{69} -12.0000 q^{71} +(0.500000 + 0.866025i) q^{72} +(0.707107 - 1.22474i) q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.12132 + 3.67423i) q^{75} -7.07107 q^{76} +(2.00000 + 3.46410i) q^{79} +(-1.41421 + 2.44949i) q^{80} +(2.50000 - 4.33013i) q^{81} +(4.94975 + 8.57321i) q^{82} +9.89949 q^{83} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(1.41421 - 2.44949i) q^{87} +(1.00000 - 1.73205i) q^{88} +(3.53553 + 6.12372i) q^{89} -2.82843 q^{90} -4.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(-1.41421 + 2.44949i) q^{94} +(10.0000 - 17.3205i) q^{95} +(0.707107 + 1.22474i) q^{96} +9.89949 q^{97} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 4 q^{11} - 16 q^{15} - 2 q^{16} + 2 q^{18} - 8 q^{22} + 8 q^{23} - 6 q^{25} + 8 q^{29} + 8 q^{30} - 2 q^{32} - 4 q^{36} - 20 q^{37} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 12 q^{50} - 4 q^{51} + 4 q^{53} + 40 q^{57} - 4 q^{58} + 8 q^{60} + 4 q^{64} - 24 q^{67} - 48 q^{71} + 2 q^{72} - 20 q^{74} + 8 q^{79} + 10 q^{81} - 16 q^{85} - 4 q^{86} + 4 q^{88} - 16 q^{92} + 24 q^{93} + 40 q^{95} + 8 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ 0.707107 1.22474i 0.408248 0.707107i −0.586445 0.809989i $$-0.699473\pi$$
0.994694 + 0.102882i $$0.0328064\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.41421 2.44949i −0.632456 1.09545i −0.987048 0.160424i $$-0.948714\pi$$
0.354593 0.935021i $$-0.384620\pi$$
$$6$$ −1.41421 −0.577350
$$7$$ 0 0
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ −1.41421 + 2.44949i −0.447214 + 0.774597i
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ 0.707107 + 1.22474i 0.204124 + 0.353553i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ −4.00000 −1.03280
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0.707107 1.22474i 0.171499 0.297044i −0.767445 0.641114i $$-0.778472\pi$$
0.938944 + 0.344070i $$0.111806\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ 3.53553 + 6.12372i 0.811107 + 1.40488i 0.912090 + 0.409991i $$0.134468\pi$$
−0.100983 + 0.994888i $$0.532199\pi$$
$$20$$ 2.82843 0.632456
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0.707107 1.22474i 0.144338 0.250000i
$$25$$ −1.50000 + 2.59808i −0.300000 + 0.519615i
$$26$$ 0 0
$$27$$ 5.65685 1.08866
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 2.00000 + 3.46410i 0.365148 + 0.632456i
$$31$$ −4.24264 + 7.34847i −0.762001 + 1.31982i 0.179817 + 0.983700i $$0.442449\pi$$
−0.941818 + 0.336124i $$0.890884\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −1.41421 2.44949i −0.246183 0.426401i
$$34$$ −1.41421 −0.242536
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i $$-0.859528\pi$$
0.0821995 0.996616i $$-0.473806\pi$$
$$38$$ 3.53553 6.12372i 0.573539 0.993399i
$$39$$ 0 0
$$40$$ −1.41421 2.44949i −0.223607 0.387298i
$$41$$ −9.89949 −1.54604 −0.773021 0.634381i $$-0.781255\pi$$
−0.773021 + 0.634381i $$0.781255\pi$$
$$42$$ 0 0
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 1.00000 + 1.73205i 0.150756 + 0.261116i
$$45$$ 1.41421 2.44949i 0.210819 0.365148i
$$46$$ 2.00000 3.46410i 0.294884 0.510754i
$$47$$ −1.41421 2.44949i −0.206284 0.357295i 0.744257 0.667893i $$-0.232804\pi$$
−0.950541 + 0.310599i $$0.899470\pi$$
$$48$$ −1.41421 −0.204124
$$49$$ 0 0
$$50$$ 3.00000 0.424264
$$51$$ −1.00000 1.73205i −0.140028 0.242536i
$$52$$ 0 0
$$53$$ 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i $$-0.789471\pi$$
0.926497 + 0.376303i $$0.122805\pi$$
$$54$$ −2.82843 4.89898i −0.384900 0.666667i
$$55$$ −5.65685 −0.762770
$$56$$ 0 0
$$57$$ 10.0000 1.32453
$$58$$ −1.00000 1.73205i −0.131306 0.227429i
$$59$$ 0.707107 1.22474i 0.0920575 0.159448i −0.816319 0.577601i $$-0.803989\pi$$
0.908377 + 0.418153i $$0.137322\pi$$
$$60$$ 2.00000 3.46410i 0.258199 0.447214i
$$61$$ −1.41421 2.44949i −0.181071 0.313625i 0.761174 0.648547i $$-0.224623\pi$$
−0.942246 + 0.334922i $$0.891290\pi$$
$$62$$ 8.48528 1.07763
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −1.41421 + 2.44949i −0.174078 + 0.301511i
$$67$$ −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i $$0.428555\pi$$
−0.955588 + 0.294706i $$0.904778\pi$$
$$68$$ 0.707107 + 1.22474i 0.0857493 + 0.148522i
$$69$$ 5.65685 0.681005
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 0.707107 1.22474i 0.0827606 0.143346i −0.821674 0.569958i $$-0.806960\pi$$
0.904435 + 0.426612i $$0.140293\pi$$
$$74$$ −5.00000 + 8.66025i −0.581238 + 1.00673i
$$75$$ 2.12132 + 3.67423i 0.244949 + 0.424264i
$$76$$ −7.07107 −0.811107
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i $$-0.0944227\pi$$
−0.731307 + 0.682048i $$0.761089\pi$$
$$80$$ −1.41421 + 2.44949i −0.158114 + 0.273861i
$$81$$ 2.50000 4.33013i 0.277778 0.481125i
$$82$$ 4.94975 + 8.57321i 0.546608 + 0.946753i
$$83$$ 9.89949 1.08661 0.543305 0.839535i $$-0.317173\pi$$
0.543305 + 0.839535i $$0.317173\pi$$
$$84$$ 0 0
$$85$$ −4.00000 −0.433861
$$86$$ −1.00000 1.73205i −0.107833 0.186772i
$$87$$ 1.41421 2.44949i 0.151620 0.262613i
$$88$$ 1.00000 1.73205i 0.106600 0.184637i
$$89$$ 3.53553 + 6.12372i 0.374766 + 0.649113i 0.990292 0.139003i $$-0.0443898\pi$$
−0.615526 + 0.788116i $$0.711056\pi$$
$$90$$ −2.82843 −0.298142
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ 6.00000 + 10.3923i 0.622171 + 1.07763i
$$94$$ −1.41421 + 2.44949i −0.145865 + 0.252646i
$$95$$ 10.0000 17.3205i 1.02598 1.77705i
$$96$$ 0.707107 + 1.22474i 0.0721688 + 0.125000i
$$97$$ 9.89949 1.00514 0.502571 0.864536i $$-0.332388\pi$$
0.502571 + 0.864536i $$0.332388\pi$$
$$98$$ 0 0
$$99$$ 2.00000 0.201008
$$100$$ −1.50000 2.59808i −0.150000 0.259808i
$$101$$ −4.24264 + 7.34847i −0.422159 + 0.731200i −0.996150 0.0876610i $$-0.972061\pi$$
0.573992 + 0.818861i $$0.305394\pi$$
$$102$$ −1.00000 + 1.73205i −0.0990148 + 0.171499i
$$103$$ −1.41421 2.44949i −0.139347 0.241355i 0.787903 0.615800i $$-0.211167\pi$$
−0.927249 + 0.374444i $$0.877834\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −2.00000 −0.194257
$$107$$ 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i $$-0.104732\pi$$
−0.753010 + 0.658009i $$0.771399\pi$$
$$108$$ −2.82843 + 4.89898i −0.272166 + 0.471405i
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 2.82843 + 4.89898i 0.269680 + 0.467099i
$$111$$ −14.1421 −1.34231
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ −5.00000 8.66025i −0.468293 0.811107i
$$115$$ 5.65685 9.79796i 0.527504 0.913664i
$$116$$ −1.00000 + 1.73205i −0.0928477 + 0.160817i
$$117$$ 0 0
$$118$$ −1.41421 −0.130189
$$119$$ 0 0
$$120$$ −4.00000 −0.365148
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ −1.41421 + 2.44949i −0.128037 + 0.221766i
$$123$$ −7.00000 + 12.1244i −0.631169 + 1.09322i
$$124$$ −4.24264 7.34847i −0.381000 0.659912i
$$125$$ −5.65685 −0.505964
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 1.41421 2.44949i 0.124515 0.215666i
$$130$$ 0 0
$$131$$ −6.36396 11.0227i −0.556022 0.963058i −0.997823 0.0659452i $$-0.978994\pi$$
0.441801 0.897113i $$-0.354340\pi$$
$$132$$ 2.82843 0.246183
$$133$$ 0 0
$$134$$ 12.0000 1.03664
$$135$$ −8.00000 13.8564i −0.688530 1.19257i
$$136$$ 0.707107 1.22474i 0.0606339 0.105021i
$$137$$ −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i $$0.337990\pi$$
−0.999893 + 0.0146279i $$0.995344\pi$$
$$138$$ −2.82843 4.89898i −0.240772 0.417029i
$$139$$ 9.89949 0.839664 0.419832 0.907602i $$-0.362089\pi$$
0.419832 + 0.907602i $$0.362089\pi$$
$$140$$ 0 0
$$141$$ −4.00000 −0.336861
$$142$$ 6.00000 + 10.3923i 0.503509 + 0.872103i
$$143$$ 0 0
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ −2.82843 4.89898i −0.234888 0.406838i
$$146$$ −1.41421 −0.117041
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i $$-0.301004\pi$$
−0.994847 + 0.101391i $$0.967671\pi$$
$$150$$ 2.12132 3.67423i 0.173205 0.300000i
$$151$$ 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i $$-0.607670\pi$$
0.982873 0.184284i $$-0.0589965\pi$$
$$152$$ 3.53553 + 6.12372i 0.286770 + 0.496700i
$$153$$ 1.41421 0.114332
$$154$$ 0 0
$$155$$ 24.0000 1.92773
$$156$$ 0 0
$$157$$ 5.65685 9.79796i 0.451466 0.781962i −0.547011 0.837125i $$-0.684235\pi$$
0.998477 + 0.0551630i $$0.0175678\pi$$
$$158$$ 2.00000 3.46410i 0.159111 0.275589i
$$159$$ −1.41421 2.44949i −0.112154 0.194257i
$$160$$ 2.82843 0.223607
$$161$$ 0 0
$$162$$ −5.00000 −0.392837
$$163$$ −5.00000 8.66025i −0.391630 0.678323i 0.601035 0.799223i $$-0.294755\pi$$
−0.992665 + 0.120900i $$0.961422\pi$$
$$164$$ 4.94975 8.57321i 0.386510 0.669456i
$$165$$ −4.00000 + 6.92820i −0.311400 + 0.539360i
$$166$$ −4.94975 8.57321i −0.384175 0.665410i
$$167$$ −19.7990 −1.53209 −0.766046 0.642786i $$-0.777779\pi$$
−0.766046 + 0.642786i $$0.777779\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 2.00000 + 3.46410i 0.153393 + 0.265684i
$$171$$ −3.53553 + 6.12372i −0.270369 + 0.468293i
$$172$$ −1.00000 + 1.73205i −0.0762493 + 0.132068i
$$173$$ 8.48528 + 14.6969i 0.645124 + 1.11739i 0.984273 + 0.176655i $$0.0565276\pi$$
−0.339149 + 0.940733i $$0.610139\pi$$
$$174$$ −2.82843 −0.214423
$$175$$ 0 0
$$176$$ −2.00000 −0.150756
$$177$$ −1.00000 1.73205i −0.0751646 0.130189i
$$178$$ 3.53553 6.12372i 0.264999 0.458993i
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ 1.41421 + 2.44949i 0.105409 + 0.182574i
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ 2.00000 + 3.46410i 0.147442 + 0.255377i
$$185$$ −14.1421 + 24.4949i −1.03975 + 1.80090i
$$186$$ 6.00000 10.3923i 0.439941 0.762001i
$$187$$ −1.41421 2.44949i −0.103418 0.179124i
$$188$$ 2.82843 0.206284
$$189$$ 0 0
$$190$$ −20.0000 −1.45095
$$191$$ 2.00000 + 3.46410i 0.144715 + 0.250654i 0.929267 0.369410i $$-0.120440\pi$$
−0.784552 + 0.620063i $$0.787107\pi$$
$$192$$ 0.707107 1.22474i 0.0510310 0.0883883i
$$193$$ 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i $$-0.638004\pi$$
0.995948 0.0899262i $$-0.0286631\pi$$
$$194$$ −4.94975 8.57321i −0.355371 0.615521i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ −1.00000 1.73205i −0.0710669 0.123091i
$$199$$ −4.24264 + 7.34847i −0.300753 + 0.520919i −0.976307 0.216391i $$-0.930571\pi$$
0.675554 + 0.737311i $$0.263905\pi$$
$$200$$ −1.50000 + 2.59808i −0.106066 + 0.183712i
$$201$$ 8.48528 + 14.6969i 0.598506 + 1.03664i
$$202$$ 8.48528 0.597022
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ 14.0000 + 24.2487i 0.977802 + 1.69360i
$$206$$ −1.41421 + 2.44949i −0.0985329 + 0.170664i
$$207$$ −2.00000 + 3.46410i −0.139010 + 0.240772i
$$208$$ 0 0
$$209$$ 14.1421 0.978232
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 1.00000 + 1.73205i 0.0686803 + 0.118958i
$$213$$ −8.48528 + 14.6969i −0.581402 + 1.00702i
$$214$$ 2.00000 3.46410i 0.136717 0.236801i
$$215$$ −2.82843 4.89898i −0.192897 0.334108i
$$216$$ 5.65685 0.384900
$$217$$ 0 0
$$218$$ −2.00000 −0.135457
$$219$$ −1.00000 1.73205i −0.0675737 0.117041i
$$220$$ 2.82843 4.89898i 0.190693 0.330289i
$$221$$ 0 0
$$222$$ 7.07107 + 12.2474i 0.474579 + 0.821995i
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ −3.00000 −0.200000
$$226$$ 6.00000 + 10.3923i 0.399114 + 0.691286i
$$227$$ 10.6066 18.3712i 0.703985 1.21934i −0.263072 0.964776i $$-0.584736\pi$$
0.967057 0.254561i $$-0.0819311\pi$$
$$228$$ −5.00000 + 8.66025i −0.331133 + 0.573539i
$$229$$ 8.48528 + 14.6969i 0.560723 + 0.971201i 0.997434 + 0.0715988i $$0.0228101\pi$$
−0.436710 + 0.899602i $$0.643857\pi$$
$$230$$ −11.3137 −0.746004
$$231$$ 0 0
$$232$$ 2.00000 0.131306
$$233$$ −12.0000 20.7846i −0.786146 1.36165i −0.928312 0.371802i $$-0.878740\pi$$
0.142166 0.989843i $$-0.454593\pi$$
$$234$$ 0 0
$$235$$ −4.00000 + 6.92820i −0.260931 + 0.451946i
$$236$$ 0.707107 + 1.22474i 0.0460287 + 0.0797241i
$$237$$ 5.65685 0.367452
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 2.00000 + 3.46410i 0.129099 + 0.223607i
$$241$$ 10.6066 18.3712i 0.683231 1.18339i −0.290758 0.956797i $$-0.593907\pi$$
0.973989 0.226595i $$-0.0727593\pi$$
$$242$$ 3.50000 6.06218i 0.224989 0.389692i
$$243$$ 4.94975 + 8.57321i 0.317526 + 0.549972i
$$244$$ 2.82843 0.181071
$$245$$ 0 0
$$246$$ 14.0000 0.892607
$$247$$ 0 0
$$248$$ −4.24264 + 7.34847i −0.269408 + 0.466628i
$$249$$ 7.00000 12.1244i 0.443607 0.768350i
$$250$$ 2.82843 + 4.89898i 0.178885 + 0.309839i
$$251$$ 9.89949 0.624851 0.312425 0.949942i $$-0.398859\pi$$
0.312425 + 0.949942i $$0.398859\pi$$
$$252$$ 0 0
$$253$$ 8.00000 0.502956
$$254$$ −8.00000 13.8564i −0.501965 0.869428i
$$255$$ −2.82843 + 4.89898i −0.177123 + 0.306786i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −6.36396 11.0227i −0.396973 0.687577i 0.596378 0.802704i $$-0.296606\pi$$
−0.993351 + 0.115126i $$0.963273\pi$$
$$258$$ −2.82843 −0.176090
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 1.00000 + 1.73205i 0.0618984 + 0.107211i
$$262$$ −6.36396 + 11.0227i −0.393167 + 0.680985i
$$263$$ −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i $$-0.953967\pi$$
0.619586 + 0.784929i $$0.287301\pi$$
$$264$$ −1.41421 2.44949i −0.0870388 0.150756i
$$265$$ −5.65685 −0.347498
$$266$$ 0 0
$$267$$ 10.0000 0.611990
$$268$$ −6.00000 10.3923i −0.366508 0.634811i
$$269$$ 5.65685 9.79796i 0.344904 0.597392i −0.640432 0.768015i $$-0.721245\pi$$
0.985336 + 0.170623i $$0.0545780\pi$$
$$270$$ −8.00000 + 13.8564i −0.486864 + 0.843274i
$$271$$ −11.3137 19.5959i −0.687259 1.19037i −0.972721 0.231977i $$-0.925480\pi$$
0.285462 0.958390i $$-0.407853\pi$$
$$272$$ −1.41421 −0.0857493
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 3.00000 + 5.19615i 0.180907 + 0.313340i
$$276$$ −2.82843 + 4.89898i −0.170251 + 0.294884i
$$277$$ 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i $$-0.814196\pi$$
0.894503 + 0.447062i $$0.147530\pi$$
$$278$$ −4.94975 8.57321i −0.296866 0.514187i
$$279$$ −8.48528 −0.508001
$$280$$ 0 0
$$281$$ 16.0000 0.954480 0.477240 0.878773i $$-0.341637\pi$$
0.477240 + 0.878773i $$0.341637\pi$$
$$282$$ 2.00000 + 3.46410i 0.119098 + 0.206284i
$$283$$ 0.707107 1.22474i 0.0420331 0.0728035i −0.844243 0.535960i $$-0.819950\pi$$
0.886277 + 0.463156i $$0.153283\pi$$
$$284$$ 6.00000 10.3923i 0.356034 0.616670i
$$285$$ −14.1421 24.4949i −0.837708 1.45095i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 7.50000 + 12.9904i 0.441176 + 0.764140i
$$290$$ −2.82843 + 4.89898i −0.166091 + 0.287678i
$$291$$ 7.00000 12.1244i 0.410347 0.710742i
$$292$$ 0.707107 + 1.22474i 0.0413803 + 0.0716728i
$$293$$ −19.7990 −1.15667 −0.578335 0.815800i $$-0.696297\pi$$
−0.578335 + 0.815800i $$0.696297\pi$$
$$294$$ 0 0
$$295$$ −4.00000 −0.232889
$$296$$ −5.00000 8.66025i −0.290619 0.503367i
$$297$$ 5.65685 9.79796i 0.328244 0.568535i
$$298$$ −5.00000 + 8.66025i −0.289642 + 0.501675i
$$299$$ 0 0
$$300$$ −4.24264 −0.244949
$$301$$ 0 0
$$302$$ −16.0000 −0.920697
$$303$$ 6.00000 + 10.3923i 0.344691 + 0.597022i
$$304$$ 3.53553 6.12372i 0.202777 0.351220i
$$305$$ −4.00000 + 6.92820i −0.229039 + 0.396708i
$$306$$ −0.707107 1.22474i −0.0404226 0.0700140i
$$307$$ −9.89949 −0.564994 −0.282497 0.959268i $$-0.591163\pi$$
−0.282497 + 0.959268i $$0.591163\pi$$
$$308$$ 0 0
$$309$$ −4.00000 −0.227552
$$310$$ −12.0000 20.7846i −0.681554 1.18049i
$$311$$ 5.65685 9.79796i 0.320771 0.555591i −0.659877 0.751374i $$-0.729391\pi$$
0.980647 + 0.195783i $$0.0627248\pi$$
$$312$$ 0 0
$$313$$ −6.36396 11.0227i −0.359712 0.623040i 0.628200 0.778052i $$-0.283792\pi$$
−0.987913 + 0.155012i $$0.950459\pi$$
$$314$$ −11.3137 −0.638470
$$315$$ 0 0
$$316$$ −4.00000 −0.225018
$$317$$ −5.00000 8.66025i −0.280828 0.486408i 0.690761 0.723083i $$-0.257276\pi$$
−0.971589 + 0.236675i $$0.923942\pi$$
$$318$$ −1.41421 + 2.44949i −0.0793052 + 0.137361i
$$319$$ 2.00000 3.46410i 0.111979 0.193952i
$$320$$ −1.41421 2.44949i −0.0790569 0.136931i
$$321$$ 5.65685 0.315735
$$322$$ 0 0
$$323$$ 10.0000 0.556415
$$324$$ 2.50000 + 4.33013i 0.138889 + 0.240563i
$$325$$ 0 0
$$326$$ −5.00000 + 8.66025i −0.276924 + 0.479647i
$$327$$ −1.41421 2.44949i −0.0782062 0.135457i
$$328$$ −9.89949 −0.546608
$$329$$ 0 0
$$330$$ 8.00000 0.440386
$$331$$ −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i $$-0.255287\pi$$
−0.970091 + 0.242742i $$0.921953\pi$$
$$332$$ −4.94975 + 8.57321i −0.271653 + 0.470516i
$$333$$ 5.00000 8.66025i 0.273998 0.474579i
$$334$$ 9.89949 + 17.1464i 0.541676 + 0.938211i
$$335$$ 33.9411 1.85440
$$336$$ 0 0
$$337$$ 2.00000 0.108947 0.0544735 0.998515i $$-0.482652\pi$$
0.0544735 + 0.998515i $$0.482652\pi$$
$$338$$ 6.50000 + 11.2583i 0.353553 + 0.612372i
$$339$$ −8.48528 + 14.6969i −0.460857 + 0.798228i
$$340$$ 2.00000 3.46410i 0.108465 0.187867i
$$341$$ 8.48528 + 14.6969i 0.459504 + 0.795884i
$$342$$ 7.07107 0.382360
$$343$$ 0 0
$$344$$ 2.00000 0.107833
$$345$$ −8.00000 13.8564i −0.430706 0.746004i
$$346$$ 8.48528 14.6969i 0.456172 0.790112i
$$347$$ 15.0000 25.9808i 0.805242 1.39472i −0.110885 0.993833i $$-0.535369\pi$$
0.916127 0.400887i $$-0.131298\pi$$
$$348$$ 1.41421 + 2.44949i 0.0758098 + 0.131306i
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.00000 + 1.73205i 0.0533002 + 0.0923186i
$$353$$ 0.707107 1.22474i 0.0376355 0.0651866i −0.846594 0.532239i $$-0.821351\pi$$
0.884230 + 0.467052i $$0.154684\pi$$
$$354$$ −1.00000 + 1.73205i −0.0531494 + 0.0920575i
$$355$$ 16.9706 + 29.3939i 0.900704 + 1.56007i
$$356$$ −7.07107 −0.374766
$$357$$ 0 0
$$358$$ 12.0000 0.634220
$$359$$ 16.0000 + 27.7128i 0.844448 + 1.46263i 0.886100 + 0.463494i $$0.153404\pi$$
−0.0416523 + 0.999132i $$0.513262\pi$$
$$360$$ 1.41421 2.44949i 0.0745356 0.129099i
$$361$$ −15.5000 + 26.8468i −0.815789 + 1.41299i
$$362$$ 0 0
$$363$$ 9.89949 0.519589
$$364$$ 0 0
$$365$$ −4.00000 −0.209370
$$366$$ 2.00000 + 3.46410i 0.104542 + 0.181071i
$$367$$ −14.1421 + 24.4949i −0.738213 + 1.27862i 0.215086 + 0.976595i $$0.430997\pi$$
−0.953299 + 0.302028i $$0.902336\pi$$
$$368$$ 2.00000 3.46410i 0.104257 0.180579i
$$369$$ −4.94975 8.57321i −0.257674 0.446304i
$$370$$ 28.2843 1.47043
$$371$$ 0 0
$$372$$ −12.0000 −0.622171
$$373$$ −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i $$-0.250023\pi$$
−0.965945 + 0.258748i $$0.916690\pi$$
$$374$$ −1.41421 + 2.44949i −0.0731272 + 0.126660i
$$375$$ −4.00000 + 6.92820i −0.206559 + 0.357771i
$$376$$ −1.41421 2.44949i −0.0729325 0.126323i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −26.0000 −1.33553 −0.667765 0.744372i $$-0.732749\pi$$
−0.667765 + 0.744372i $$0.732749\pi$$
$$380$$ 10.0000 + 17.3205i 0.512989 + 0.888523i
$$381$$ 11.3137 19.5959i 0.579619 1.00393i
$$382$$ 2.00000 3.46410i 0.102329 0.177239i
$$383$$ 18.3848 + 31.8434i 0.939418 + 1.62712i 0.766559 + 0.642173i $$0.221967\pi$$
0.172859 + 0.984947i $$0.444700\pi$$
$$384$$ −1.41421 −0.0721688
$$385$$ 0 0
$$386$$ −16.0000 −0.814379
$$387$$ 1.00000 + 1.73205i 0.0508329 + 0.0880451i
$$388$$ −4.94975 + 8.57321i −0.251285 + 0.435239i
$$389$$ −13.0000 + 22.5167i −0.659126 + 1.14164i 0.321716 + 0.946836i $$0.395740\pi$$
−0.980842 + 0.194804i $$0.937593\pi$$
$$390$$ 0 0
$$391$$ 5.65685 0.286079
$$392$$ 0 0
$$393$$ −18.0000 −0.907980
$$394$$ −1.00000 1.73205i −0.0503793 0.0872595i
$$395$$ 5.65685 9.79796i 0.284627 0.492989i
$$396$$ −1.00000 + 1.73205i −0.0502519 + 0.0870388i
$$397$$ −11.3137 19.5959i −0.567819 0.983491i −0.996781 0.0801687i $$-0.974454\pi$$
0.428963 0.903322i $$-0.358879\pi$$
$$398$$ 8.48528 0.425329
$$399$$ 0 0
$$400$$ 3.00000 0.150000
$$401$$ 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i $$-0.0182907\pi$$
−0.548911 + 0.835881i $$0.684957\pi$$
$$402$$ 8.48528 14.6969i 0.423207 0.733017i
$$403$$ 0 0
$$404$$ −4.24264 7.34847i −0.211079 0.365600i
$$405$$ −14.1421 −0.702728
$$406$$ 0 0
$$407$$ −20.0000 −0.991363
$$408$$ −1.00000 1.73205i −0.0495074 0.0857493i
$$409$$ −19.0919 + 33.0681i −0.944033 + 1.63511i −0.186357 + 0.982482i $$0.559668\pi$$
−0.757676 + 0.652631i $$0.773665\pi$$
$$410$$ 14.0000 24.2487i 0.691411 1.19756i
$$411$$ 8.48528 + 14.6969i 0.418548 + 0.724947i
$$412$$ 2.82843 0.139347
$$413$$ 0 0
$$414$$ 4.00000 0.196589
$$415$$ −14.0000 24.2487i −0.687233 1.19032i
$$416$$ 0 0
$$417$$ 7.00000 12.1244i 0.342791 0.593732i
$$418$$ −7.07107 12.2474i −0.345857 0.599042i
$$419$$ −9.89949 −0.483622 −0.241811 0.970323i $$-0.577741\pi$$
−0.241811 + 0.970323i $$0.577741\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 6.00000 + 10.3923i 0.292075 + 0.505889i
$$423$$ 1.41421 2.44949i 0.0687614 0.119098i
$$424$$ 1.00000 1.73205i 0.0485643 0.0841158i
$$425$$ 2.12132 + 3.67423i 0.102899 + 0.178227i
$$426$$ 16.9706 0.822226
$$427$$ 0 0
$$428$$ −4.00000 −0.193347
$$429$$ 0 0
$$430$$ −2.82843 + 4.89898i −0.136399 + 0.236250i
$$431$$ −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i $$-0.926659\pi$$
0.684564 + 0.728953i $$0.259993\pi$$
$$432$$ −2.82843 4.89898i −0.136083 0.235702i
$$433$$ −29.6985 −1.42722 −0.713609 0.700544i $$-0.752941\pi$$
−0.713609 + 0.700544i $$0.752941\pi$$
$$434$$ 0 0
$$435$$ −8.00000 −0.383571
$$436$$ 1.00000 + 1.73205i 0.0478913 + 0.0829502i
$$437$$ −14.1421 + 24.4949i −0.676510 + 1.17175i
$$438$$ −1.00000 + 1.73205i −0.0477818 + 0.0827606i
$$439$$ 8.48528 + 14.6969i 0.404980 + 0.701447i 0.994319 0.106439i $$-0.0339450\pi$$
−0.589339 + 0.807886i $$0.700612\pi$$
$$440$$ −5.65685 −0.269680
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i $$-0.136374\pi$$
−0.814595 + 0.580030i $$0.803041\pi$$
$$444$$ 7.07107 12.2474i 0.335578 0.581238i
$$445$$ 10.0000 17.3205i 0.474045 0.821071i
$$446$$ 0 0
$$447$$ −14.1421 −0.668900
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 1.50000 + 2.59808i 0.0707107 + 0.122474i
$$451$$ −9.89949 + 17.1464i −0.466149 + 0.807394i
$$452$$ 6.00000 10.3923i 0.282216 0.488813i
$$453$$ −11.3137 19.5959i −0.531564 0.920697i
$$454$$ −21.2132 −0.995585
$$455$$ 0 0
$$456$$ 10.0000 0.468293
$$457$$ −12.0000 20.7846i −0.561336 0.972263i −0.997380 0.0723376i $$-0.976954\pi$$
0.436044 0.899925i $$-0.356379\pi$$
$$458$$ 8.48528 14.6969i 0.396491 0.686743i
$$459$$ 4.00000 6.92820i 0.186704 0.323381i
$$460$$ 5.65685 + 9.79796i 0.263752 + 0.456832i
$$461$$ 39.5980 1.84426 0.922131 0.386878i $$-0.126447\pi$$
0.922131 + 0.386878i $$0.126447\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −1.00000 1.73205i −0.0464238 0.0804084i
$$465$$ 16.9706 29.3939i 0.786991 1.36311i
$$466$$ −12.0000 + 20.7846i −0.555889 + 0.962828i
$$467$$ −16.2635 28.1691i −0.752583 1.30351i −0.946567 0.322507i $$-0.895474\pi$$
0.193984 0.981005i $$-0.437859\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 8.00000 0.369012
$$471$$ −8.00000 13.8564i −0.368621 0.638470i
$$472$$ 0.707107 1.22474i 0.0325472 0.0563735i
$$473$$ 2.00000 3.46410i 0.0919601 0.159280i
$$474$$ −2.82843 4.89898i −0.129914 0.225018i
$$475$$ −21.2132 −0.973329
$$476$$ 0 0
$$477$$ 2.00000 0.0915737
$$478$$ 6.00000 + 10.3923i 0.274434 + 0.475333i
$$479$$ 15.5563 26.9444i 0.710788 1.23112i −0.253774 0.967264i $$-0.581672\pi$$
0.964562 0.263857i $$-0.0849947\pi$$
$$480$$ 2.00000 3.46410i 0.0912871 0.158114i
$$481$$ 0 0
$$482$$ −21.2132 −0.966235
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −14.0000 24.2487i −0.635707 1.10108i
$$486$$ 4.94975 8.57321i 0.224525 0.388889i
$$487$$ −6.00000 + 10.3923i −0.271886 + 0.470920i −0.969345 0.245705i $$-0.920981\pi$$
0.697459 + 0.716625i $$0.254314\pi$$
$$488$$ −1.41421 2.44949i −0.0640184 0.110883i
$$489$$ −14.1421 −0.639529
$$490$$ 0 0
$$491$$ −12.0000 −0.541552 −0.270776 0.962642i $$-0.587280\pi$$
−0.270776 + 0.962642i $$0.587280\pi$$
$$492$$ −7.00000 12.1244i −0.315584 0.546608i
$$493$$ 1.41421 2.44949i 0.0636930 0.110319i
$$494$$ 0 0
$$495$$ −2.82843 4.89898i −0.127128 0.220193i
$$496$$ 8.48528 0.381000
$$497$$ 0 0
$$498$$ −14.0000 −0.627355
$$499$$ 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i $$-0.138129\pi$$
−0.817781 + 0.575529i $$0.804796\pi$$
$$500$$ 2.82843 4.89898i 0.126491 0.219089i
$$501$$ −14.0000 + 24.2487i −0.625474 + 1.08335i
$$502$$ −4.94975 8.57321i −0.220918 0.382641i
$$503$$ 39.5980 1.76559 0.882793 0.469762i $$-0.155660\pi$$
0.882793 + 0.469762i $$0.155660\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ −4.00000 6.92820i −0.177822 0.307996i
$$507$$ −9.19239 + 15.9217i −0.408248 + 0.707107i
$$508$$ −8.00000 + 13.8564i −0.354943 + 0.614779i
$$509$$ −11.3137 19.5959i −0.501471 0.868574i −0.999999 0.00169976i $$-0.999459\pi$$
0.498527 0.866874i $$-0.333874\pi$$
$$510$$ 5.65685 0.250490
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 20.0000 + 34.6410i 0.883022 + 1.52944i
$$514$$ −6.36396 + 11.0227i −0.280702 + 0.486191i
$$515$$ −4.00000 + 6.92820i −0.176261 + 0.305293i
$$516$$ 1.41421 + 2.44949i 0.0622573 + 0.107833i
$$517$$ −5.65685 −0.248788
$$518$$ 0 0
$$519$$ 24.0000 1.05348
$$520$$ 0 0
$$521$$ 0.707107 1.22474i 0.0309789 0.0536570i −0.850120 0.526589i $$-0.823471\pi$$
0.881099 + 0.472931i $$0.156804\pi$$
$$522$$ 1.00000 1.73205i 0.0437688 0.0758098i
$$523$$ −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i $$-0.256430\pi$$
−0.970957 + 0.239256i $$0.923097\pi$$
$$524$$ 12.7279 0.556022
$$525$$ 0 0
$$526$$ 12.0000 0.523225
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ −1.41421 + 2.44949i −0.0615457 + 0.106600i
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 2.82843 + 4.89898i 0.122859 + 0.212798i
$$531$$ 1.41421 0.0613716
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −5.00000 8.66025i −0.216371 0.374766i
$$535$$ 5.65685 9.79796i 0.244567 0.423603i
$$536$$ −6.00000 + 10.3923i −0.259161 + 0.448879i
$$537$$ 8.48528 + 14.6969i 0.366167 + 0.634220i
$$538$$ −11.3137 −0.487769
$$539$$ 0 0
$$540$$ 16.0000 0.688530
$$541$$ −5.00000 8.66025i −0.214967 0.372333i 0.738296 0.674477i $$-0.235631\pi$$
−0.953262 + 0.302144i $$0.902298\pi$$
$$542$$ −11.3137 + 19.5959i −0.485965 + 0.841717i
$$543$$ 0 0
$$544$$ 0.707107 + 1.22474i 0.0303170 + 0.0525105i
$$545$$ −5.65685 −0.242313
$$546$$ 0 0
$$547$$ −26.0000 −1.11168 −0.555840 0.831289i $$-0.687603\pi$$
−0.555840 + 0.831289i $$0.687603\pi$$
$$548$$ −6.00000 10.3923i −0.256307 0.443937i
$$549$$ 1.41421 2.44949i 0.0603572 0.104542i
$$550$$ 3.00000 5.19615i 0.127920 0.221565i
$$551$$ 7.07107 + 12.2474i 0.301238 + 0.521759i
$$552$$ 5.65685 0.240772
$$553$$ 0 0
$$554$$ −2.00000 −0.0849719
$$555$$ 20.0000 + 34.6410i 0.848953 + 1.47043i
$$556$$ −4.94975 + 8.57321i −0.209916 + 0.363585i
$$557$$ 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i $$-0.614098\pi$$
0.986394 0.164399i $$-0.0525683\pi$$
$$558$$ 4.24264 + 7.34847i 0.179605 + 0.311086i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −4.00000 −0.168880
$$562$$ −8.00000 13.8564i −0.337460 0.584497i
$$563$$ 0.707107 1.22474i 0.0298010 0.0516168i −0.850740 0.525586i $$-0.823846\pi$$
0.880541 + 0.473970i $$0.157179\pi$$
$$564$$ 2.00000 3.46410i 0.0842152 0.145865i
$$565$$ 16.9706 + 29.3939i 0.713957 + 1.23661i
$$566$$ −1.41421 −0.0594438
$$567$$ 0 0
$$568$$ −12.0000 −0.503509
$$569$$ −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i $$-0.233886\pi$$
−0.951592 + 0.307364i $$0.900553\pi$$
$$570$$ −14.1421 + 24.4949i −0.592349 + 1.02598i
$$571$$ 1.00000 1.73205i 0.0418487 0.0724841i −0.844342 0.535804i $$-0.820009\pi$$
0.886191 + 0.463320i $$0.153342\pi$$
$$572$$ 0 0
$$573$$ 5.65685 0.236318
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ 10.6066 18.3712i 0.441559 0.764802i −0.556247 0.831017i $$-0.687759\pi$$
0.997805 + 0.0662152i $$0.0210924\pi$$
$$578$$ 7.50000 12.9904i 0.311959 0.540329i
$$579$$ −11.3137 19.5959i −0.470182 0.814379i
$$580$$ 5.65685 0.234888
$$581$$ 0 0
$$582$$ −14.0000 −0.580319
$$583$$ −2.00000 3.46410i −0.0828315 0.143468i
$$584$$ 0.707107 1.22474i 0.0292603 0.0506803i
$$585$$ 0 0
$$586$$ 9.89949 + 17.1464i 0.408944 + 0.708312i
$$587$$ −29.6985 −1.22579 −0.612894 0.790165i $$-0.709995\pi$$
−0.612894 + 0.790165i $$0.709995\pi$$
$$588$$ 0 0
$$589$$ −60.0000 −2.47226
$$590$$ 2.00000 + 3.46410i 0.0823387 + 0.142615i
$$591$$ 1.41421 2.44949i 0.0581730 0.100759i
$$592$$ −5.00000 + 8.66025i −0.205499 + 0.355934i
$$593$$ 3.53553 + 6.12372i 0.145187 + 0.251471i 0.929443 0.368967i $$-0.120288\pi$$
−0.784256 + 0.620438i $$0.786955\pi$$
$$594$$ −11.3137 −0.464207
$$595$$ 0 0
$$596$$ 10.0000 0.409616
$$597$$ 6.00000 + 10.3923i 0.245564 + 0.425329i
$$598$$ 0 0
$$599$$ 8.00000 13.8564i 0.326871 0.566157i −0.655018 0.755613i $$-0.727339\pi$$
0.981889 + 0.189456i $$0.0606724\pi$$
$$600$$ 2.12132 + 3.67423i 0.0866025 + 0.150000i
$$601$$ 29.6985 1.21143 0.605713 0.795683i $$-0.292888\pi$$
0.605713 + 0.795683i $$0.292888\pi$$
$$602$$ 0 0
$$603$$ −12.0000 −0.488678
$$604$$ 8.00000 + 13.8564i 0.325515 + 0.563809i
$$605$$ 9.89949 17.1464i 0.402472 0.697101i
$$606$$ 6.00000 10.3923i 0.243733 0.422159i
$$607$$ 8.48528 + 14.6969i 0.344407 + 0.596530i 0.985246 0.171145i $$-0.0547467\pi$$
−0.640839 + 0.767675i $$0.721413\pi$$
$$608$$ −7.07107 −0.286770
$$609$$ 0 0
$$610$$ 8.00000 0.323911
$$611$$ 0 0
$$612$$ −0.707107 + 1.22474i −0.0285831 + 0.0495074i
$$613$$ 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i $$-0.626169\pi$$
0.991917 0.126885i $$-0.0404979\pi$$
$$614$$ 4.94975 + 8.57321i 0.199756 + 0.345987i
$$615$$ 39.5980 1.59674
$$616$$ 0 0
$$617$$ −26.0000 −1.04672 −0.523360 0.852111i $$-0.675322\pi$$
−0.523360 + 0.852111i $$0.675322\pi$$
$$618$$ 2.00000 + 3.46410i 0.0804518 + 0.139347i
$$619$$ −9.19239 + 15.9217i −0.369473 + 0.639946i −0.989483 0.144647i $$-0.953795\pi$$
0.620010 + 0.784594i $$0.287129\pi$$
$$620$$ −12.0000 + 20.7846i −0.481932 + 0.834730i
$$621$$ 11.3137 + 19.5959i 0.454003 + 0.786357i
$$622$$ −11.3137 −0.453638
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15.5000 + 26.8468i 0.620000 + 1.07387i
$$626$$ −6.36396 + 11.0227i −0.254355 + 0.440556i
$$627$$ 10.0000 17.3205i 0.399362 0.691714i
$$628$$ 5.65685 + 9.79796i 0.225733 + 0.390981i
$$629$$ −14.1421 −0.563884
$$630$$ 0 0
$$631$$ 44.0000 1.75161 0.875806 0.482663i $$-0.160330\pi$$
0.875806 + 0.482663i $$0.160330\pi$$
$$632$$ 2.00000 + 3.46410i 0.0795557 + 0.137795i
$$633$$ −8.48528 + 14.6969i −0.337260 + 0.584151i
$$634$$ −5.00000 + 8.66025i −0.198575 + 0.343943i
$$635$$ −22.6274 39.1918i −0.897942 1.55528i
$$636$$ 2.82843 0.112154
$$637$$ 0 0
$$638$$ −4.00000 −0.158362
$$639$$ −6.00000 10.3923i −0.237356 0.411113i
$$640$$ −1.41421 + 2.44949i −0.0559017 + 0.0968246i
$$641$$ −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i $$0.338307\pi$$
−0.999878 + 0.0156233i $$0.995027\pi$$
$$642$$ −2.82843 4.89898i −0.111629 0.193347i
$$643$$ 9.89949 0.390398 0.195199 0.980764i $$-0.437465\pi$$
0.195199 + 0.980764i $$0.437465\pi$$
$$644$$ 0 0
$$645$$ −8.00000 −0.315000
$$646$$ −5.00000 8.66025i −0.196722 0.340733i
$$647$$ −4.24264 + 7.34847i −0.166795 + 0.288898i −0.937291 0.348547i $$-0.886675\pi$$
0.770496 + 0.637445i $$0.220009\pi$$
$$648$$ 2.50000 4.33013i 0.0982093 0.170103i
$$649$$ −1.41421 2.44949i −0.0555127 0.0961509i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 10.0000 0.391630
$$653$$ 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i $$-0.0521013\pi$$
−0.634437 + 0.772975i $$0.718768\pi$$
$$654$$ −1.41421 + 2.44949i −0.0553001 + 0.0957826i
$$655$$ −18.0000 + 31.1769i −0.703318 + 1.21818i
$$656$$ 4.94975 + 8.57321i 0.193255 + 0.334728i
$$657$$ 1.41421 0.0551737
$$658$$ 0 0
$$659$$ 30.0000 1.16863 0.584317 0.811525i $$-0.301362\pi$$
0.584317 + 0.811525i $$0.301362\pi$$
$$660$$ −4.00000 6.92820i −0.155700 0.269680i
$$661$$ −4.24264 + 7.34847i −0.165020 + 0.285822i −0.936662 0.350234i $$-0.886102\pi$$
0.771643 + 0.636056i $$0.219435\pi$$
$$662$$ −5.00000 + 8.66025i −0.194331 + 0.336590i
$$663$$ 0 0
$$664$$ 9.89949 0.384175
$$665$$ 0 0
$$666$$ −10.0000 −0.387492
$$667$$ 4.00000 + 6.92820i 0.154881 + 0.268261i
$$668$$ 9.89949 17.1464i 0.383023 0.663415i
$$669$$ 0 0
$$670$$ −16.9706 29.3939i −0.655630 1.13558i
$$671$$ −5.65685 −0.218380
$$672$$ 0 0
$$673$$ −12.0000 −0.462566 −0.231283 0.972887i $$-0.574292\pi$$
−0.231283 + 0.972887i $$0.574292\pi$$
$$674$$ −1.00000 1.73205i −0.0385186 0.0667161i
$$675$$ −8.48528 + 14.6969i −0.326599 + 0.565685i
$$676$$ 6.50000 11.2583i 0.250000 0.433013i
$$677$$ 8.48528 + 14.6969i 0.326116 + 0.564849i 0.981738 0.190240i $$-0.0609267\pi$$
−0.655622 + 0.755090i $$0.727593\pi$$
$$678$$ 16.9706 0.651751
$$679$$ 0 0
$$680$$ −4.00000 −0.153393
$$681$$ −15.0000 25.9808i −0.574801 0.995585i
$$682$$ 8.48528 14.6969i 0.324918 0.562775i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ −3.53553 6.12372i −0.135185 0.234146i
$$685$$ 33.9411 1.29682
$$686$$ 0 0
$$687$$ 24.0000 0.915657
$$688$$ −1.00000 1.73205i −0.0381246 0.0660338i
$$689$$ 0 0
$$690$$ −8.00000 + 13.8564i −0.304555 + 0.527504i
$$691$$ −6.36396 11.0227i −0.242096 0.419323i 0.719215 0.694788i $$-0.244502\pi$$
−0.961311 + 0.275464i $$0.911168\pi$$
$$692$$ −16.9706 −0.645124
$$693$$ 0 0
$$694$$ −30.0000 −1.13878
$$695$$ −14.0000 24.2487i −0.531050 0.919806i
$$696$$ 1.41421 2.44949i 0.0536056 0.0928477i
$$697$$ −7.00000 + 12.1244i −0.265144 + 0.459243i
$$698$$ 0 0
$$699$$ −33.9411 −1.28377
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 35.3553 61.2372i 1.33345 2.30961i
$$704$$ 1.00000 1.73205i 0.0376889 0.0652791i
$$705$$ 5.65685 + 9.79796i 0.213049 + 0.369012i
$$706$$ −1.41421 −0.0532246
$$707$$ 0 0
$$708$$ 2.00000 0.0751646
$$709$$ −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i $$-0.226796\pi$$
−0.944509 + 0.328484i $$0.893462\pi$$
$$710$$ 16.9706 29.3939i 0.636894 1.10313i
$$711$$ −2.00000 + 3.46410i −0.0750059 + 0.129914i
$$712$$ 3.53553 + 6.12372i 0.132500 + 0.229496i
$$713$$ −33.9411 −1.27111
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ −8.48528 + 14.6969i −0.316889 + 0.548867i
$$718$$ 16.0000 27.7128i 0.597115 1.03423i
$$719$$ −1.41421 2.44949i −0.0527413 0.0913506i 0.838449 0.544979i $$-0.183463\pi$$
−0.891191 + 0.453629i $$0.850129\pi$$
$$720$$ −2.82843 −0.105409
$$721$$ 0 0
$$722$$ 31.0000 1.15370
$$723$$ −15.0000 25.9808i −0.557856 0.966235i
$$724$$ 0 0
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ −4.94975 8.57321i −0.183702 0.318182i
$$727$$ −19.7990 −0.734304 −0.367152 0.930161i $$-0.619667\pi$$
−0.367152 + 0.930161i $$0.619667\pi$$
$$728$$ 0 0
$$729$$ 29.0000 1.07407
$$730$$ 2.00000 + 3.46410i 0.0740233 + 0.128212i
$$731$$ 1.41421 2.44949i 0.0523066 0.0905977i
$$732$$ 2.00000 3.46410i 0.0739221 0.128037i
$$733$$ −21.2132 36.7423i −0.783528 1.35711i −0.929875 0.367876i $$-0.880085\pi$$
0.146347 0.989233i $$-0.453248\pi$$
$$734$$ 28.2843 1.04399
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ 12.0000 + 20.7846i 0.442026 + 0.765611i
$$738$$ −4.94975 + 8.57321i −0.182203 + 0.315584i
$$739$$ 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i $$-0.647281\pi$$
0.998146 0.0608653i $$-0.0193860\pi$$
$$740$$ −14.1421 24.4949i −0.519875 0.900450i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 16.0000 0.586983 0.293492 0.955962i $$-0.405183\pi$$
0.293492 + 0.955962i $$0.405183\pi$$
$$744$$ 6.00000 + 10.3923i 0.219971 + 0.381000i
$$745$$ −14.1421 + 24.4949i −0.518128 + 0.897424i
$$746$$ −5.00000 + 8.66025i −0.183063 + 0.317074i
$$747$$ 4.94975 + 8.57321i 0.181102 + 0.313678i
$$748$$ 2.82843 0.103418
$$749$$ 0 0
$$750$$ 8.00000 0.292119
$$751$$ 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i $$-0.143415\pi$$
−0.827225 + 0.561870i $$0.810082\pi$$
$$752$$ −1.41421 + 2.44949i −0.0515711 + 0.0893237i
$$753$$ 7.00000 12.1244i 0.255094 0.441836i
$$754$$ 0 0
$$755$$ −45.2548 −1.64699
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 13.0000 + 22.5167i 0.472181 + 0.817842i
$$759$$ 5.65685 9.79796i 0.205331 0.355643i
$$760$$ 10.0000 17.3205i 0.362738 0.628281i
$$761$$ 3.53553 + 6.12372i 0.128163 + 0.221985i 0.922965 0.384884i $$-0.125759\pi$$
−0.794802 + 0.606869i $$0.792425\pi$$
$$762$$ −22.6274 −0.819705
$$763$$ 0 0
$$764$$ −4.00000 −0.144715
$$765$$ −2.00000 3.46410i −0.0723102 0.125245i
$$766$$ 18.3848 31.8434i 0.664269 1.15055i
$$767$$ 0 0
$$768$$ 0.707107 + 1.22474i 0.0255155 + 0.0441942i
$$769$$ 29.6985 1.07095 0.535477 0.844550i $$-0.320132\pi$$
0.535477 + 0.844550i $$0.320132\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 8.00000 + 13.8564i 0.287926 + 0.498703i
$$773$$ −24.0416 + 41.6413i −0.864717 + 1.49773i 0.00261021 + 0.999997i $$0.499169\pi$$
−0.867328 + 0.497738i $$0.834164\pi$$
$$774$$ 1.00000 1.73205i 0.0359443 0.0622573i
$$775$$ −12.7279 22.0454i −0.457200 0.791894i
$$776$$ 9.89949 0.355371
$$777$$ 0 0
$$778$$ 26.0000 0.932145
$$779$$ −35.0000 60.6218i −1.25401 2.17200i
$$780$$ 0 0
$$781$$ −12.0000 + 20.7846i −0.429394 + 0.743732i
$$782$$ −2.82843 4.89898i −0.101144 0.175187i
$$783$$ 11.3137 0.404319
$$784$$ 0 0
$$785$$ −32.0000 −1.14213
$$786$$ 9.00000 + 15.5885i 0.321019 + 0.556022i
$$787$$ 0.707107 1.22474i 0.0252056