Properties

 Label 98.2.c.c.67.1 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: $$x^{4} + 2x^{2} + 4$$ 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 67.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 98.67 Dual form 98.2.c.c.79.1

$q$-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 $$4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 4 q^{11} - 16 q^{15} - 2 q^{16} + 2 q^{18} - 8 q^{22} + 8 q^{23} - 6 q^{25} + 8 q^{29} + 8 q^{30} - 2 q^{32} - 4 q^{36} - 20 q^{37} + 8 q^{43} + 4 q^{44} + 8 q^{46} + 12 q^{50} - 4 q^{51} + 4 q^{53} + 40 q^{57} - 4 q^{58} + 8 q^{60} + 4 q^{64} - 24 q^{67} - 48 q^{71} + 2 q^{72} - 20 q^{74} + 8 q^{79} + 10 q^{81} - 16 q^{85} - 4 q^{86} + 4 q^{88} - 16 q^{92} + 24 q^{93} + 40 q^{95} + 8 q^{99}+O(q^{100})$$ 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

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 −0.994694 0.102882i $$-0.967194\pi$$
0.586445 + 0.809989i $$0.300527\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 1.41421 + 2.44949i 0.632456 + 1.09545i 0.987048 + 0.160424i $$0.0512862\pi$$
−0.354593 + 0.935021i $$0.615380\pi$$
$$6$$ 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 −0.938944 0.344070i $$-0.888194\pi$$
0.767445 + 0.641114i $$0.221528\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ −3.53553 6.12372i −0.811107 1.40488i −0.912090 0.409991i $$-0.865532\pi$$
0.100983 0.994888i $$-0.467801\pi$$
$$20$$ −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 $$-0.557551\pi$$
0.941818 0.336124i $$-0.109116\pi$$
$$32$$ −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 $$-0.218745\pi$$
0.773021 + 0.634381i $$0.218745\pi$$
$$42$$ 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 0.950541 0.310599i $$-0.100530\pi$$
−0.744257 + 0.667893i $$0.767196\pi$$
$$48$$ 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 −0.908377 0.418153i $$-0.862678\pi$$
0.816319 + 0.577601i $$0.196011\pi$$
$$60$$ 2.00000 3.46410i 0.258199 0.447214i
$$61$$ 1.41421 + 2.44949i 0.181071 + 0.313625i 0.942246 0.334922i $$-0.108710\pi$$
−0.761174 + 0.648547i $$0.775377\pi$$
$$62$$ −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 −0.904435 0.426612i $$-0.859707\pi$$
0.821674 + 0.569958i $$0.193040\pi$$
$$74$$ −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 $$-0.682827\pi$$
−0.543305 + 0.839535i $$0.682827\pi$$
$$84$$ 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 0.615526 0.788116i $$-0.288944\pi$$
−0.990292 + 0.139003i $$0.955610\pi$$
$$90$$ 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 $$-0.667612\pi$$
−0.502571 + 0.864536i $$0.667612\pi$$
$$98$$ 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 −0.573992 0.818861i $$-0.694606\pi$$
0.996150 + 0.0876610i $$0.0279392\pi$$
$$102$$ −1.00000 + 1.73205i −0.0990148 + 0.171499i
$$103$$ 1.41421 + 2.44949i 0.139347 + 0.241355i 0.927249 0.374444i $$-0.122166\pi$$
−0.787903 + 0.615800i $$0.788833\pi$$
$$104$$ 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 $$0.0210063\pi$$
−0.441801 + 0.897113i $$0.645660\pi$$
$$132$$ −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 $$-0.637911\pi$$
−0.419832 + 0.907602i $$0.637911\pi$$
$$140$$ 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 −0.998477 0.0551630i $$-0.982432\pi$$
0.547011 + 0.837125i $$0.315765\pi$$
$$158$$ 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 $$-0.222221\pi$$
0.766046 + 0.642786i $$0.222221\pi$$
$$168$$ 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 $$-0.943472\pi$$
0.339149 0.940733i $$-0.389861\pi$$
$$174$$ 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 −0.675554 0.737311i $$-0.736095\pi$$
0.976307 + 0.216391i $$0.0694287\pi$$
$$200$$ −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 $$0.415264\pi$$
−0.967057 + 0.254561i $$0.918069\pi$$
$$228$$ −5.00000 + 8.66025i −0.331133 + 0.573539i
$$229$$ −8.48528 14.6969i −0.560723 0.971201i −0.997434 0.0715988i $$-0.977190\pi$$
0.436710 0.899602i $$-0.356143\pi$$
$$230$$ 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 $$0.406093\pi$$
−0.973989 + 0.226595i $$0.927241\pi$$
$$242$$ 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 $$-0.601141\pi$$
−0.312425 + 0.949942i $$0.601141\pi$$
$$252$$ 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 0.993351 0.115126i $$-0.0367273\pi$$
−0.596378 + 0.802704i $$0.703394\pi$$
$$258$$ 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 −0.985336 0.170623i $$-0.945422\pi$$
0.640432 + 0.768015i $$0.278755\pi$$
$$270$$ −8.00000 + 13.8564i −0.486864 + 0.843274i
$$271$$ 11.3137 + 19.5959i 0.687259 + 1.19037i 0.972721 + 0.231977i $$0.0745195\pi$$
−0.285462 + 0.958390i $$0.592147\pi$$
$$272$$ 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 −0.886277 0.463156i $$-0.846717\pi$$
0.844243 + 0.535960i $$0.180050\pi$$
$$284$$ 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 $$-0.303703\pi$$
0.578335 + 0.815800i $$0.303703\pi$$
$$294$$ 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 $$-0.408837\pi$$
0.282497 + 0.959268i $$0.408837\pi$$
$$308$$ 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 −0.980647 0.195783i $$-0.937275\pi$$
0.659877 + 0.751374i $$0.270609\pi$$
$$312$$ 0 0
$$313$$ 6.36396 + 11.0227i 0.359712 + 0.623040i 0.987913 0.155012i $$-0.0495415\pi$$
−0.628200 + 0.778052i $$0.716208\pi$$
$$314$$ 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 −0.884230 0.467052i $$-0.845316\pi$$
0.846594 + 0.532239i $$0.178649\pi$$
$$354$$ −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 $$-0.569003\pi$$
0.953299 0.302028i $$-0.0976636\pi$$
$$368$$ 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 $$-0.778033\pi$$
−0.172859 0.984947i $$-0.555300\pi$$
$$384$$ 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 $$0.0255459\pi$$
−0.428963 + 0.903322i $$0.641121\pi$$
$$398$$ −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 $$-0.440332\pi$$
0.757676 0.652631i $$-0.226335\pi$$
$$410$$ 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 $$-0.422259\pi$$
0.241811 + 0.970323i $$0.422259\pi$$
$$420$$ 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 $$-0.247059\pi$$
0.713609 + 0.700544i $$0.247059\pi$$
$$434$$ 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 0.589339 0.807886i $$-0.299388\pi$$
−0.994319 + 0.106439i $$0.966055\pi$$
$$440$$ 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 $$-0.873553\pi$$
−0.922131 + 0.386878i $$0.873553\pi$$
$$462$$ 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 $$0.104526\pi$$
−0.193984 + 0.981005i $$0.562141\pi$$
$$468$$ 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 $$0.418328\pi$$
−0.964562 + 0.263857i $$0.915005\pi$$
$$480$$ 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 $$-0.844340\pi$$
−0.882793 + 0.469762i $$0.844340\pi$$
$$504$$ 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 $$0.000541051\pi$$
−0.498527 + 0.866874i $$0.666126\pi$$
$$510$$ −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 −0.881099 0.472931i $$-0.843196\pi$$
0.850120 + 0.526589i $$0.176529\pi$$
$$522$$ 1.00000 1.73205i 0.0437688 0.0758098i
$$523$$ 6.36396 + 11.0227i 0.278277 + 0.481989i 0.970957 0.239256i $$-0.0769035\pi$$
−0.692680 + 0.721245i $$0.743570\pi$$
$$524$$ −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 −0.880541 0.473970i $$-0.842821\pi$$
0.850740 + 0.525586i $$0.176154\pi$$
$$564$$ 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 −0.997805 0.0662152i $$-0.978908\pi$$
0.556247 + 0.831017i $$0.312241\pi$$
$$578$$ 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 $$-0.290005\pi$$
0.612894 + 0.790165i $$0.290005\pi$$
$$588$$ 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 0.784256 0.620438i $$-0.213045\pi$$
−0.929443 + 0.368967i $$0.879712\pi$$
$$594$$ 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 $$-0.707112\pi$$
−0.605713 + 0.795683i $$0.707112\pi$$
$$602$$ 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 0.640839 0.767675i $$-0.278587\pi$$
−0.985246 + 0.171145i $$0.945253\pi$$
$$608$$ 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 −0.620010 0.784594i $$-0.712871\pi$$
0.989483 + 0.144647i $$0.0462048\pi$$
$$620$$ −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 $$-0.562535\pi$$
−0.195199 + 0.980764i $$0.562535\pi$$
$$644$$ 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 −0.770496 0.637445i $$-0.779991\pi$$
0.937291 + 0.348547i $$0.113325\pi$$
$$648$$ 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 −0.771643 0.636056i $$-0.780565\pi$$
0.936662 + 0.350234i $$0.113898\pi$$
$$662$$ −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 0.655622 0.755090i $$-0.272407\pi$$
−0.981738 + 0.190240i $$0.939073\pi$$
$$678$$ −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 0.961311 0.275464i $$-0.0888316\pi$$
−0.719215 + 0.694788i $$0.755498\pi$$
$$692$$ 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 0.891191 0.453629i $$-0.149871\pi$$
−0.838449 + 0.544979i $$0.816537\pi$$
$$720$$ 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 $$-0.380333\pi$$
0.367152 + 0.930161i $$0.380333\pi$$
$$728$$ 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 $$0.119915\pi$$
−0.146347 + 0.989233i $$0.546752\pi$$
$$734$$ −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 0.794802 0.606869i $$-0.207575\pi$$
−0.922965 + 0.384884i $$0.874241\pi$$
$$762$$ 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 $$-0.679868\pi$$
−0.535477 + 0.844550i $$0.679868\pi$$
$$770$$ 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 $$-0.500831\pi$$
0.867328 0.497738i $$-0.165836\pi$$
$$774$$ 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
$$786$$