# Properties

 Label 42.2.e.a.25.1 Level $42$ Weight $2$ Character 42.25 Analytic conductor $0.335$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$42 = 2 \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 42.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.335371688489$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 25.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 42.25 Dual form 42.2.e.a.37.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.00000 - 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-4.00000 - 6.92820i) q^{19} +1.00000 q^{20} +(2.50000 + 0.866025i) q^{21} +5.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} -1.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -5.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.50000 + 4.33013i) q^{33} -4.00000 q^{34} +(2.00000 - 1.73205i) q^{35} +1.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-4.00000 + 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 2.59808i) q^{42} +2.00000 q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{46} +(3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-2.00000 - 3.46410i) q^{51} +(4.50000 - 7.79423i) q^{53} +(0.500000 + 0.866025i) q^{54} +5.00000 q^{55} +(0.500000 + 2.59808i) q^{56} -8.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(5.50000 - 9.52628i) q^{59} +(0.500000 - 0.866025i) q^{60} +(3.00000 + 5.19615i) q^{61} +3.00000 q^{62} +(2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{68} +4.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +2.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-2.00000 - 3.46410i) q^{75} +8.00000 q^{76} +(-12.5000 - 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -7.00000 q^{83} +(-2.00000 + 1.73205i) q^{84} -4.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} -4.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(3.00000 - 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(5.50000 + 4.33013i) q^{98} +5.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} + 2q^{8} - q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{3} - q^{4} - q^{5} - 2q^{6} + q^{7} + 2q^{8} - q^{9} - q^{10} - 5q^{11} + q^{12} + 4q^{14} - 2q^{15} - q^{16} + 4q^{17} - q^{18} - 8q^{19} + 2q^{20} + 5q^{21} + 10q^{22} + 4q^{23} + q^{24} + 4q^{25} - 2q^{27} - 5q^{28} - 10q^{29} + q^{30} - 3q^{31} - q^{32} + 5q^{33} - 8q^{34} + 4q^{35} + 2q^{36} + 4q^{37} - 8q^{38} - q^{40} - q^{42} + 4q^{43} - 5q^{44} - q^{45} + 4q^{46} + 6q^{47} - 2q^{48} - 13q^{49} - 8q^{50} - 4q^{51} + 9q^{53} + q^{54} + 10q^{55} + q^{56} - 16q^{57} + 5q^{58} + 11q^{59} + q^{60} + 6q^{61} + 6q^{62} + 4q^{63} + 2q^{64} + 5q^{66} + 2q^{67} + 4q^{68} + 8q^{69} - 5q^{70} + 4q^{71} - q^{72} - 10q^{73} + 4q^{74} - 4q^{75} + 16q^{76} - 25q^{77} - 3q^{79} - q^{80} - q^{81} - 14q^{83} - 4q^{84} - 8q^{85} - 2q^{86} - 5q^{87} - 5q^{88} + 6q^{89} + 2q^{90} - 8q^{92} + 3q^{93} + 6q^{94} - 8q^{95} + q^{96} + 14q^{97} + 11q^{98} + 10q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$31$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i $$-0.238450\pi$$
−0.955901 + 0.293691i $$0.905116\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i $$0.438437\pi$$
−0.945979 + 0.324227i $$0.894896\pi$$
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 2.00000 1.73205i 0.534522 0.462910i
$$15$$ −1.00000 −0.258199
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.00000 3.46410i 0.485071 0.840168i −0.514782 0.857321i $$-0.672127\pi$$
0.999853 + 0.0171533i $$0.00546033\pi$$
$$18$$ −0.500000 + 0.866025i −0.117851 + 0.204124i
$$19$$ −4.00000 6.92820i −0.917663 1.58944i −0.802955 0.596040i $$-0.796740\pi$$
−0.114708 0.993399i $$-0.536593\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 2.50000 + 0.866025i 0.545545 + 0.188982i
$$22$$ 5.00000 1.06600
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ 2.00000 3.46410i 0.400000 0.692820i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ −2.50000 0.866025i −0.472456 0.163663i
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0.500000 + 0.866025i 0.0912871 + 0.158114i
$$31$$ −1.50000 + 2.59808i −0.269408 + 0.466628i −0.968709 0.248199i $$-0.920161\pi$$
0.699301 + 0.714827i $$0.253495\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 2.50000 + 4.33013i 0.435194 + 0.753778i
$$34$$ −4.00000 −0.685994
$$35$$ 2.00000 1.73205i 0.338062 0.292770i
$$36$$ 1.00000 0.166667
$$37$$ 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i $$-0.0600231\pi$$
−0.653476 + 0.756948i $$0.726690\pi$$
$$38$$ −4.00000 + 6.92820i −0.648886 + 1.12390i
$$39$$ 0 0
$$40$$ −0.500000 0.866025i −0.0790569 0.136931i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ −0.500000 2.59808i −0.0771517 0.400892i
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ −2.50000 4.33013i −0.376889 0.652791i
$$45$$ −0.500000 + 0.866025i −0.0745356 + 0.129099i
$$46$$ 2.00000 3.46410i 0.294884 0.510754i
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ −4.00000 −0.565685
$$51$$ −2.00000 3.46410i −0.280056 0.485071i
$$52$$ 0 0
$$53$$ 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i $$-0.621227\pi$$
0.989828 0.142269i $$-0.0454398\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 5.00000 0.674200
$$56$$ 0.500000 + 2.59808i 0.0668153 + 0.347183i
$$57$$ −8.00000 −1.05963
$$58$$ 2.50000 + 4.33013i 0.328266 + 0.568574i
$$59$$ 5.50000 9.52628i 0.716039 1.24022i −0.246518 0.969138i $$-0.579287\pi$$
0.962557 0.271078i $$-0.0873801\pi$$
$$60$$ 0.500000 0.866025i 0.0645497 0.111803i
$$61$$ 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i $$-0.0411748\pi$$
−0.607535 + 0.794293i $$0.707841\pi$$
$$62$$ 3.00000 0.381000
$$63$$ 2.00000 1.73205i 0.251976 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 2.50000 4.33013i 0.307729 0.533002i
$$67$$ 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i $$-0.794348\pi$$
0.920623 + 0.390453i $$0.127682\pi$$
$$68$$ 2.00000 + 3.46410i 0.242536 + 0.420084i
$$69$$ 4.00000 0.481543
$$70$$ −2.50000 0.866025i −0.298807 0.103510i
$$71$$ 2.00000 0.237356 0.118678 0.992933i $$-0.462134\pi$$
0.118678 + 0.992933i $$0.462134\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i $$0.365653\pi$$
−0.994850 + 0.101361i $$0.967680\pi$$
$$74$$ 2.00000 3.46410i 0.232495 0.402694i
$$75$$ −2.00000 3.46410i −0.230940 0.400000i
$$76$$ 8.00000 0.917663
$$77$$ −12.5000 4.33013i −1.42451 0.493464i
$$78$$ 0 0
$$79$$ −1.50000 2.59808i −0.168763 0.292306i 0.769222 0.638982i $$-0.220644\pi$$
−0.937985 + 0.346675i $$0.887311\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −7.00000 −0.768350 −0.384175 0.923260i $$-0.625514\pi$$
−0.384175 + 0.923260i $$0.625514\pi$$
$$84$$ −2.00000 + 1.73205i −0.218218 + 0.188982i
$$85$$ −4.00000 −0.433861
$$86$$ −1.00000 1.73205i −0.107833 0.186772i
$$87$$ −2.50000 + 4.33013i −0.268028 + 0.464238i
$$88$$ −2.50000 + 4.33013i −0.266501 + 0.461593i
$$89$$ 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i $$-0.0636557\pi$$
−0.662071 + 0.749441i $$0.730322\pi$$
$$90$$ 1.00000 0.105409
$$91$$ 0 0
$$92$$ −4.00000 −0.417029
$$93$$ 1.50000 + 2.59808i 0.155543 + 0.269408i
$$94$$ 3.00000 5.19615i 0.309426 0.535942i
$$95$$ −4.00000 + 6.92820i −0.410391 + 0.710819i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ 5.50000 + 4.33013i 0.555584 + 0.437409i
$$99$$ 5.00000 0.502519
$$100$$ 2.00000 + 3.46410i 0.200000 + 0.346410i
$$101$$ −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i $$-0.999089\pi$$
0.502477 + 0.864590i $$0.332422\pi$$
$$102$$ −2.00000 + 3.46410i −0.198030 + 0.342997i
$$103$$ −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i $$-0.295621\pi$$
−0.992990 + 0.118199i $$0.962288\pi$$
$$104$$ 0 0
$$105$$ −0.500000 2.59808i −0.0487950 0.253546i
$$106$$ −9.00000 −0.874157
$$107$$ −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i $$-0.212988\pi$$
−0.929377 + 0.369132i $$0.879655\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ −2.50000 4.33013i −0.238366 0.412861i
$$111$$ 4.00000 0.379663
$$112$$ 2.00000 1.73205i 0.188982 0.163663i
$$113$$ 16.0000 1.50515 0.752577 0.658505i $$-0.228811\pi$$
0.752577 + 0.658505i $$0.228811\pi$$
$$114$$ 4.00000 + 6.92820i 0.374634 + 0.648886i
$$115$$ 2.00000 3.46410i 0.186501 0.323029i
$$116$$ 2.50000 4.33013i 0.232119 0.402042i
$$117$$ 0 0
$$118$$ −11.0000 −1.01263
$$119$$ 10.0000 + 3.46410i 0.916698 + 0.317554i
$$120$$ −1.00000 −0.0912871
$$121$$ −7.00000 12.1244i −0.636364 1.10221i
$$122$$ 3.00000 5.19615i 0.271607 0.470438i
$$123$$ 0 0
$$124$$ −1.50000 2.59808i −0.134704 0.233314i
$$125$$ −9.00000 −0.804984
$$126$$ −2.50000 0.866025i −0.222718 0.0771517i
$$127$$ 9.00000 0.798621 0.399310 0.916816i $$-0.369250\pi$$
0.399310 + 0.916816i $$0.369250\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 1.00000 1.73205i 0.0880451 0.152499i
$$130$$ 0 0
$$131$$ −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i $$-0.180577\pi$$
−0.887041 + 0.461690i $$0.847243\pi$$
$$132$$ −5.00000 −0.435194
$$133$$ 16.0000 13.8564i 1.38738 1.20150i
$$134$$ −2.00000 −0.172774
$$135$$ 0.500000 + 0.866025i 0.0430331 + 0.0745356i
$$136$$ 2.00000 3.46410i 0.171499 0.297044i
$$137$$ 1.00000 1.73205i 0.0854358 0.147979i −0.820141 0.572161i $$-0.806105\pi$$
0.905577 + 0.424182i $$0.139438\pi$$
$$138$$ −2.00000 3.46410i −0.170251 0.294884i
$$139$$ −14.0000 −1.18746 −0.593732 0.804663i $$-0.702346\pi$$
−0.593732 + 0.804663i $$0.702346\pi$$
$$140$$ 0.500000 + 2.59808i 0.0422577 + 0.219578i
$$141$$ 6.00000 0.505291
$$142$$ −1.00000 1.73205i −0.0839181 0.145350i
$$143$$ 0 0
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ 2.50000 + 4.33013i 0.207614 + 0.359597i
$$146$$ 10.0000 0.827606
$$147$$ −1.00000 + 6.92820i −0.0824786 + 0.571429i
$$148$$ −4.00000 −0.328798
$$149$$ 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i $$0.0972370\pi$$
−0.216394 + 0.976306i $$0.569430\pi$$
$$150$$ −2.00000 + 3.46410i −0.163299 + 0.282843i
$$151$$ −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i $$0.447961\pi$$
−0.935857 + 0.352381i $$0.885372\pi$$
$$152$$ −4.00000 6.92820i −0.324443 0.561951i
$$153$$ −4.00000 −0.323381
$$154$$ 2.50000 + 12.9904i 0.201456 + 1.04679i
$$155$$ 3.00000 0.240966
$$156$$ 0 0
$$157$$ 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i $$-0.782307\pi$$
0.934731 + 0.355357i $$0.115641\pi$$
$$158$$ −1.50000 + 2.59808i −0.119334 + 0.206692i
$$159$$ −4.50000 7.79423i −0.356873 0.618123i
$$160$$ 1.00000 0.0790569
$$161$$ −8.00000 + 6.92820i −0.630488 + 0.546019i
$$162$$ 1.00000 0.0785674
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ 0 0
$$165$$ 2.50000 4.33013i 0.194625 0.337100i
$$166$$ 3.50000 + 6.06218i 0.271653 + 0.470516i
$$167$$ −14.0000 −1.08335 −0.541676 0.840587i $$-0.682210\pi$$
−0.541676 + 0.840587i $$0.682210\pi$$
$$168$$ 2.50000 + 0.866025i 0.192879 + 0.0668153i
$$169$$ −13.0000 −1.00000
$$170$$ 2.00000 + 3.46410i 0.153393 + 0.265684i
$$171$$ −4.00000 + 6.92820i −0.305888 + 0.529813i
$$172$$ −1.00000 + 1.73205i −0.0762493 + 0.132068i
$$173$$ −11.0000 19.0526i −0.836315 1.44854i −0.892956 0.450145i $$-0.851372\pi$$
0.0566411 0.998395i $$-0.481961\pi$$
$$174$$ 5.00000 0.379049
$$175$$ 10.0000 + 3.46410i 0.755929 + 0.261861i
$$176$$ 5.00000 0.376889
$$177$$ −5.50000 9.52628i −0.413405 0.716039i
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i $$-0.981361\pi$$
0.549825 + 0.835280i $$0.314694\pi$$
$$180$$ −0.500000 0.866025i −0.0372678 0.0645497i
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 6.00000 0.443533
$$184$$ 2.00000 + 3.46410i 0.147442 + 0.255377i
$$185$$ 2.00000 3.46410i 0.147043 0.254686i
$$186$$ 1.50000 2.59808i 0.109985 0.190500i
$$187$$ 10.0000 + 17.3205i 0.731272 + 1.26660i
$$188$$ −6.00000 −0.437595
$$189$$ −0.500000 2.59808i −0.0363696 0.188982i
$$190$$ 8.00000 0.580381
$$191$$ −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i $$-0.831886\pi$$
−0.00454614 0.999990i $$-0.501447\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i $$-0.890928\pi$$
0.761911 + 0.647682i $$0.224262\pi$$
$$194$$ −3.50000 6.06218i −0.251285 0.435239i
$$195$$ 0 0
$$196$$ 1.00000 6.92820i 0.0714286 0.494872i
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ −2.50000 4.33013i −0.177667 0.307729i
$$199$$ 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i $$-0.788052\pi$$
0.928166 + 0.372168i $$0.121385\pi$$
$$200$$ 2.00000 3.46410i 0.141421 0.244949i
$$201$$ −1.00000 1.73205i −0.0705346 0.122169i
$$202$$ 10.0000 0.703598
$$203$$ −2.50000 12.9904i −0.175466 0.911746i
$$204$$ 4.00000 0.280056
$$205$$ 0 0
$$206$$ −4.00000 + 6.92820i −0.278693 + 0.482711i
$$207$$ 2.00000 3.46410i 0.139010 0.240772i
$$208$$ 0 0
$$209$$ 40.0000 2.76686
$$210$$ −2.00000 + 1.73205i −0.138013 + 0.119523i
$$211$$ 2.00000 0.137686 0.0688428 0.997628i $$-0.478069\pi$$
0.0688428 + 0.997628i $$0.478069\pi$$
$$212$$ 4.50000 + 7.79423i 0.309061 + 0.535310i
$$213$$ 1.00000 1.73205i 0.0685189 0.118678i
$$214$$ −1.50000 + 2.59808i −0.102538 + 0.177601i
$$215$$ −1.00000 1.73205i −0.0681994 0.118125i
$$216$$ −1.00000 −0.0680414
$$217$$ −7.50000 2.59808i −0.509133 0.176369i
$$218$$ −2.00000 −0.135457
$$219$$ 5.00000 + 8.66025i 0.337869 + 0.585206i
$$220$$ −2.50000 + 4.33013i −0.168550 + 0.291937i
$$221$$ 0 0
$$222$$ −2.00000 3.46410i −0.134231 0.232495i
$$223$$ −7.00000 −0.468755 −0.234377 0.972146i $$-0.575305\pi$$
−0.234377 + 0.972146i $$0.575305\pi$$
$$224$$ −2.50000 0.866025i −0.167038 0.0578638i
$$225$$ −4.00000 −0.266667
$$226$$ −8.00000 13.8564i −0.532152 0.921714i
$$227$$ −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i $$-0.865076\pi$$
0.811943 + 0.583736i $$0.198410\pi$$
$$228$$ 4.00000 6.92820i 0.264906 0.458831i
$$229$$ 10.0000 + 17.3205i 0.660819 + 1.14457i 0.980401 + 0.197013i $$0.0631241\pi$$
−0.319582 + 0.947559i $$0.603543\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ −10.0000 + 8.66025i −0.657952 + 0.569803i
$$232$$ −5.00000 −0.328266
$$233$$ 2.00000 + 3.46410i 0.131024 + 0.226941i 0.924072 0.382219i $$-0.124840\pi$$
−0.793047 + 0.609160i $$0.791507\pi$$
$$234$$ 0 0
$$235$$ 3.00000 5.19615i 0.195698 0.338960i
$$236$$ 5.50000 + 9.52628i 0.358020 + 0.620108i
$$237$$ −3.00000 −0.194871
$$238$$ −2.00000 10.3923i −0.129641 0.673633i
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0.500000 + 0.866025i 0.0322749 + 0.0559017i
$$241$$ 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i $$-0.535394\pi$$
0.916159 0.400815i $$-0.131273\pi$$
$$242$$ −7.00000 + 12.1244i −0.449977 + 0.779383i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ −6.00000 −0.384111
$$245$$ 5.50000 + 4.33013i 0.351382 + 0.276642i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −1.50000 + 2.59808i −0.0952501 + 0.164978i
$$249$$ −3.50000 + 6.06218i −0.221803 + 0.384175i
$$250$$ 4.50000 + 7.79423i 0.284605 + 0.492950i
$$251$$ 21.0000 1.32551 0.662754 0.748837i $$-0.269387\pi$$
0.662754 + 0.748837i $$0.269387\pi$$
$$252$$ 0.500000 + 2.59808i 0.0314970 + 0.163663i
$$253$$ −20.0000 −1.25739
$$254$$ −4.50000 7.79423i −0.282355 0.489053i
$$255$$ −2.00000 + 3.46410i −0.125245 + 0.216930i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i $$-0.106747\pi$$
−0.757159 + 0.653231i $$0.773413\pi$$
$$258$$ −2.00000 −0.124515
$$259$$ −8.00000 + 6.92820i −0.497096 + 0.430498i
$$260$$ 0 0
$$261$$ 2.50000 + 4.33013i 0.154746 + 0.268028i
$$262$$ −0.500000 + 0.866025i −0.0308901 + 0.0535032i
$$263$$ 15.0000 25.9808i 0.924940 1.60204i 0.133281 0.991078i $$-0.457449\pi$$
0.791658 0.610964i $$-0.209218\pi$$
$$264$$ 2.50000 + 4.33013i 0.153864 + 0.266501i
$$265$$ −9.00000 −0.552866
$$266$$ −20.0000 6.92820i −1.22628 0.424795i
$$267$$ 6.00000 0.367194
$$268$$ 1.00000 + 1.73205i 0.0610847 + 0.105802i
$$269$$ −15.5000 + 26.8468i −0.945052 + 1.63688i −0.189404 + 0.981899i $$0.560656\pi$$
−0.755648 + 0.654978i $$0.772678\pi$$
$$270$$ 0.500000 0.866025i 0.0304290 0.0527046i
$$271$$ −7.50000 12.9904i −0.455593 0.789109i 0.543130 0.839649i $$-0.317239\pi$$
−0.998722 + 0.0505395i $$0.983906\pi$$
$$272$$ −4.00000 −0.242536
$$273$$ 0 0
$$274$$ −2.00000 −0.120824
$$275$$ 10.0000 + 17.3205i 0.603023 + 1.04447i
$$276$$ −2.00000 + 3.46410i −0.120386 + 0.208514i
$$277$$ 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i $$-0.673726\pi$$
0.999754 + 0.0221745i $$0.00705893\pi$$
$$278$$ 7.00000 + 12.1244i 0.419832 + 0.727171i
$$279$$ 3.00000 0.179605
$$280$$ 2.00000 1.73205i 0.119523 0.103510i
$$281$$ 2.00000 0.119310 0.0596550 0.998219i $$-0.481000\pi$$
0.0596550 + 0.998219i $$0.481000\pi$$
$$282$$ −3.00000 5.19615i −0.178647 0.309426i
$$283$$ −5.00000 + 8.66025i −0.297219 + 0.514799i −0.975499 0.220005i $$-0.929393\pi$$
0.678280 + 0.734804i $$0.262726\pi$$
$$284$$ −1.00000 + 1.73205i −0.0593391 + 0.102778i
$$285$$ 4.00000 + 6.92820i 0.236940 + 0.410391i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 2.50000 4.33013i 0.146805 0.254274i
$$291$$ 3.50000 6.06218i 0.205174 0.355371i
$$292$$ −5.00000 8.66025i −0.292603 0.506803i
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 6.50000 2.59808i 0.379088 0.151523i
$$295$$ −11.0000 −0.640445
$$296$$ 2.00000 + 3.46410i 0.116248 + 0.201347i
$$297$$ 2.50000 4.33013i 0.145065 0.251259i
$$298$$ 9.00000 15.5885i 0.521356 0.903015i
$$299$$ 0 0
$$300$$ 4.00000 0.230940
$$301$$ 1.00000 + 5.19615i 0.0576390 + 0.299501i
$$302$$ 19.0000 1.09333
$$303$$ 5.00000 + 8.66025i 0.287242 + 0.497519i
$$304$$ −4.00000 + 6.92820i −0.229416 + 0.397360i
$$305$$ 3.00000 5.19615i 0.171780 0.297531i
$$306$$ 2.00000 + 3.46410i 0.114332 + 0.198030i
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 10.0000 8.66025i 0.569803 0.493464i
$$309$$ −8.00000 −0.455104
$$310$$ −1.50000 2.59808i −0.0851943 0.147561i
$$311$$ 16.0000 27.7128i 0.907277 1.57145i 0.0894452 0.995992i $$-0.471491\pi$$
0.817832 0.575458i $$-0.195176\pi$$
$$312$$ 0 0
$$313$$ −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i $$-0.175664\pi$$
−0.879810 + 0.475325i $$0.842331\pi$$
$$314$$ −4.00000 −0.225733
$$315$$ −2.50000 0.866025i −0.140859 0.0487950i
$$316$$ 3.00000 0.168763
$$317$$ −1.50000 2.59808i −0.0842484 0.145922i 0.820822 0.571184i $$-0.193516\pi$$
−0.905071 + 0.425261i $$0.860182\pi$$
$$318$$ −4.50000 + 7.79423i −0.252347 + 0.437079i
$$319$$ 12.5000 21.6506i 0.699866 1.21220i
$$320$$ −0.500000 0.866025i −0.0279508 0.0484123i
$$321$$ −3.00000 −0.167444
$$322$$ 10.0000 + 3.46410i 0.557278 + 0.193047i
$$323$$ −32.0000 −1.78053
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 0 0
$$326$$ 2.00000 3.46410i 0.110770 0.191859i
$$327$$ −1.00000 1.73205i −0.0553001 0.0957826i
$$328$$ 0 0
$$329$$ −12.0000 + 10.3923i −0.661581 + 0.572946i
$$330$$ −5.00000 −0.275241
$$331$$ 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i $$-0.131604\pi$$
−0.805812 + 0.592172i $$0.798271\pi$$
$$332$$ 3.50000 6.06218i 0.192087 0.332705i
$$333$$ 2.00000 3.46410i 0.109599 0.189832i
$$334$$ 7.00000 + 12.1244i 0.383023 + 0.663415i
$$335$$ −2.00000 −0.109272
$$336$$ −0.500000 2.59808i −0.0272772 0.141737i
$$337$$ 9.00000 0.490261 0.245131 0.969490i $$-0.421169\pi$$
0.245131 + 0.969490i $$0.421169\pi$$
$$338$$ 6.50000 + 11.2583i 0.353553 + 0.612372i
$$339$$ 8.00000 13.8564i 0.434500 0.752577i
$$340$$ 2.00000 3.46410i 0.108465 0.187867i
$$341$$ −7.50000 12.9904i −0.406148 0.703469i
$$342$$ 8.00000 0.432590
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 2.00000 0.107833
$$345$$ −2.00000 3.46410i −0.107676 0.186501i
$$346$$ −11.0000 + 19.0526i −0.591364 + 1.02427i
$$347$$ −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i $$-0.937721\pi$$
0.658824 + 0.752297i $$0.271054\pi$$
$$348$$ −2.50000 4.33013i −0.134014 0.232119i
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ −2.00000 10.3923i −0.106904 0.555492i
$$351$$ 0 0
$$352$$ −2.50000 4.33013i −0.133250 0.230797i
$$353$$ −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i $$0.387192\pi$$
−0.985719 + 0.168397i $$0.946141\pi$$
$$354$$ −5.50000 + 9.52628i −0.292322 + 0.506316i
$$355$$ −1.00000 1.73205i −0.0530745 0.0919277i
$$356$$ −6.00000 −0.317999
$$357$$ 8.00000 6.92820i 0.423405 0.366679i
$$358$$ 12.0000 0.634220
$$359$$ −5.00000 8.66025i −0.263890 0.457071i 0.703382 0.710812i $$-0.251672\pi$$
−0.967272 + 0.253741i $$0.918339\pi$$
$$360$$ −0.500000 + 0.866025i −0.0263523 + 0.0456435i
$$361$$ −22.5000 + 38.9711i −1.18421 + 2.05111i
$$362$$ 0 0
$$363$$ −14.0000 −0.734809
$$364$$ 0 0
$$365$$ 10.0000 0.523424
$$366$$ −3.00000 5.19615i −0.156813 0.271607i
$$367$$ −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i $$-0.979666\pi$$
0.554264 + 0.832341i $$0.313000\pi$$
$$368$$ 2.00000 3.46410i 0.104257 0.180579i
$$369$$ 0 0
$$370$$ −4.00000 −0.207950
$$371$$ 22.5000 + 7.79423i 1.16814 + 0.404656i
$$372$$ −3.00000 −0.155543
$$373$$ 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i $$0.144109\pi$$
−0.0708063 + 0.997490i $$0.522557\pi$$
$$374$$ 10.0000 17.3205i 0.517088 0.895622i
$$375$$ −4.50000 + 7.79423i −0.232379 + 0.402492i
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ 0 0
$$378$$ −2.00000 + 1.73205i −0.102869 + 0.0890871i
$$379$$ 16.0000 0.821865 0.410932 0.911666i $$-0.365203\pi$$
0.410932 + 0.911666i $$0.365203\pi$$
$$380$$ −4.00000 6.92820i −0.205196 0.355409i
$$381$$ 4.50000 7.79423i 0.230542 0.399310i
$$382$$ −12.0000 + 20.7846i −0.613973 + 1.06343i
$$383$$ 17.0000 + 29.4449i 0.868659 + 1.50456i 0.863367 + 0.504576i $$0.168351\pi$$
0.00529229 + 0.999986i $$0.498315\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 2.50000 + 12.9904i 0.127412 + 0.662051i
$$386$$ 5.00000 0.254493
$$387$$ −1.00000 1.73205i −0.0508329 0.0880451i
$$388$$ −3.50000 + 6.06218i −0.177686 + 0.307760i
$$389$$ 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i $$-0.817187\pi$$
0.890263 + 0.455448i $$0.150521\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ −6.50000 + 2.59808i −0.328300 + 0.131223i
$$393$$ −1.00000 −0.0504433
$$394$$ −1.00000 1.73205i −0.0503793 0.0872595i
$$395$$ −1.50000 + 2.59808i −0.0754732 + 0.130723i
$$396$$ −2.50000 + 4.33013i −0.125630 + 0.217597i
$$397$$ −18.0000 31.1769i −0.903394 1.56472i −0.823058 0.567957i $$-0.807734\pi$$
−0.0803356 0.996768i $$-0.525599\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ −4.00000 20.7846i −0.200250 1.04053i
$$400$$ −4.00000 −0.200000
$$401$$ −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i $$-0.962132\pi$$
0.393680 0.919247i $$-0.371202\pi$$
$$402$$ −1.00000 + 1.73205i −0.0498755 + 0.0863868i
$$403$$ 0 0
$$404$$ −5.00000 8.66025i −0.248759 0.430864i
$$405$$ 1.00000 0.0496904
$$406$$ −10.0000 + 8.66025i −0.496292 + 0.429801i
$$407$$ −20.0000 −0.991363
$$408$$ −2.00000 3.46410i −0.0990148 0.171499i
$$409$$ 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i $$-0.621242\pi$$
0.989835 0.142222i $$-0.0454247\pi$$
$$410$$ 0 0
$$411$$ −1.00000 1.73205i −0.0493264 0.0854358i
$$412$$ 8.00000 0.394132
$$413$$ 27.5000 + 9.52628i 1.35319 + 0.468758i
$$414$$ −4.00000 −0.196589
$$415$$ 3.50000 + 6.06218i 0.171808 + 0.297581i
$$416$$ 0 0
$$417$$ −7.00000 + 12.1244i −0.342791 + 0.593732i
$$418$$ −20.0000 34.6410i −0.978232 1.69435i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 2.50000 + 0.866025i 0.121988 + 0.0422577i
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ −1.00000 1.73205i −0.0486792 0.0843149i
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ 4.50000 7.79423i 0.218539 0.378521i
$$425$$ −8.00000 13.8564i −0.388057 0.672134i
$$426$$ −2.00000 −0.0969003
$$427$$ −12.0000 + 10.3923i −0.580721 + 0.502919i
$$428$$ 3.00000 0.145010
$$429$$ 0 0
$$430$$ −1.00000 + 1.73205i −0.0482243 + 0.0835269i
$$431$$ −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i $$-0.926659\pi$$
0.684564 + 0.728953i $$0.259993\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 1.50000 + 7.79423i 0.0720023 + 0.374135i
$$435$$ 5.00000 0.239732
$$436$$ 1.00000 + 1.73205i 0.0478913 + 0.0829502i
$$437$$ 16.0000 27.7128i 0.765384 1.32568i
$$438$$ 5.00000 8.66025i 0.238909 0.413803i
$$439$$ −7.50000 12.9904i −0.357955 0.619997i 0.629664 0.776868i $$-0.283193\pi$$
−0.987619 + 0.156871i $$0.949859\pi$$
$$440$$ 5.00000 0.238366
$$441$$ 5.50000 + 4.33013i 0.261905 + 0.206197i
$$442$$ 0 0
$$443$$ −8.50000 14.7224i −0.403847 0.699484i 0.590339 0.807155i $$-0.298994\pi$$
−0.994187 + 0.107671i $$0.965661\pi$$
$$444$$ −2.00000 + 3.46410i −0.0949158 + 0.164399i
$$445$$ 3.00000 5.19615i 0.142214 0.246321i
$$446$$ 3.50000 + 6.06218i 0.165730 + 0.287052i
$$447$$ 18.0000 0.851371
$$448$$ 0.500000 + 2.59808i 0.0236228 + 0.122748i
$$449$$ 16.0000 0.755087 0.377543 0.925992i $$-0.376769\pi$$
0.377543 + 0.925992i $$0.376769\pi$$
$$450$$ 2.00000 + 3.46410i 0.0942809 + 0.163299i
$$451$$ 0 0
$$452$$ −8.00000 + 13.8564i −0.376288 + 0.651751i
$$453$$ 9.50000 + 16.4545i 0.446349 + 0.773099i
$$454$$ 3.00000 0.140797
$$455$$ 0 0
$$456$$ −8.00000 −0.374634
$$457$$ −15.5000 26.8468i −0.725059 1.25584i −0.958950 0.283577i $$-0.908479\pi$$
0.233890 0.972263i $$-0.424854\pi$$
$$458$$ 10.0000 17.3205i 0.467269 0.809334i
$$459$$ −2.00000 + 3.46410i −0.0933520 + 0.161690i
$$460$$ 2.00000 + 3.46410i 0.0932505 + 0.161515i
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 12.5000 + 4.33013i 0.581553 + 0.201456i
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 2.50000 + 4.33013i 0.116060 + 0.201021i
$$465$$ 1.50000 2.59808i 0.0695608 0.120483i
$$466$$ 2.00000 3.46410i 0.0926482 0.160471i
$$467$$ 10.0000 + 17.3205i 0.462745 + 0.801498i 0.999097 0.0424970i $$-0.0135313\pi$$
−0.536352 + 0.843995i $$0.680198\pi$$
$$468$$ 0 0
$$469$$ 5.00000 + 1.73205i 0.230879 + 0.0799787i
$$470$$ −6.00000 −0.276759
$$471$$ −2.00000 3.46410i −0.0921551 0.159617i
$$472$$ 5.50000 9.52628i 0.253158 0.438483i
$$473$$ −5.00000 + 8.66025i −0.229900 + 0.398199i
$$474$$ 1.50000 + 2.59808i 0.0688973 + 0.119334i
$$475$$ −32.0000 −1.46826
$$476$$ −8.00000 + 6.92820i −0.366679 + 0.317554i
$$477$$ −9.00000 −0.412082
$$478$$ 6.00000 + 10.3923i 0.274434 + 0.475333i
$$479$$ −19.0000 + 32.9090i −0.868132 + 1.50365i −0.00422900 + 0.999991i $$0.501346\pi$$
−0.863903 + 0.503658i $$0.831987\pi$$
$$480$$ 0.500000 0.866025i 0.0228218 0.0395285i
$$481$$ 0 0
$$482$$ −25.0000 −1.13872
$$483$$ 2.00000 + 10.3923i 0.0910032 + 0.472866i
$$484$$ 14.0000 0.636364
$$485$$ −3.50000 6.06218i −0.158927 0.275269i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −2.50000 + 4.33013i −0.113286 + 0.196217i −0.917093 0.398673i $$-0.869471\pi$$
0.803807 + 0.594890i $$0.202804\pi$$
$$488$$ 3.00000 + 5.19615i 0.135804 + 0.235219i
$$489$$ 4.00000 0.180886
$$490$$ 1.00000 6.92820i 0.0451754 0.312984i
$$491$$ 9.00000 0.406164 0.203082 0.979162i $$-0.434904\pi$$
0.203082 + 0.979162i $$0.434904\pi$$
$$492$$ 0 0
$$493$$ −10.0000 + 17.3205i −0.450377 + 0.780076i
$$494$$ 0 0
$$495$$ −2.50000 4.33013i −0.112367 0.194625i
$$496$$ 3.00000 0.134704
$$497$$ 1.00000 + 5.19615i 0.0448561 + 0.233079i
$$498$$ 7.00000 0.313678
$$499$$ −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i $$-0.238523\pi$$
−0.955968 + 0.293471i $$0.905190\pi$$
$$500$$ 4.50000 7.79423i 0.201246 0.348569i
$$501$$ −7.00000 + 12.1244i −0.312737 + 0.541676i
$$502$$ −10.5000 18.1865i −0.468638 0.811705i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 2.00000 1.73205i 0.0890871 0.0771517i
$$505$$ 10.0000 0.444994
$$506$$ 10.0000 + 17.3205i 0.444554 + 0.769991i
$$507$$ −6.50000 + 11.2583i −0.288675 + 0.500000i
$$508$$ −4.50000 + 7.79423i −0.199655 + 0.345813i
$$509$$ −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i $$-0.274536\pi$$
−0.982988 + 0.183669i $$0.941202\pi$$
$$510$$ 4.00000 0.177123
$$511$$ −25.0000 8.66025i −1.10593 0.383107i
$$512$$ 1.00000 0.0441942
$$513$$ 4.00000 + 6.92820i 0.176604 + 0.305888i
$$514$$ 3.00000 5.19615i 0.132324 0.229192i
$$515$$ −4.00000 + 6.92820i −0.176261 + 0.305293i
$$516$$ 1.00000 + 1.73205i 0.0440225 + 0.0762493i
$$517$$ −30.0000 −1.31940
$$518$$ 10.0000 + 3.46410i 0.439375 + 0.152204i
$$519$$ −22.0000 −0.965693
$$520$$ 0 0
$$521$$ 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i $$-0.704321\pi$$
0.993011 + 0.118020i $$0.0376547\pi$$
$$522$$ 2.50000 4.33013i 0.109422 0.189525i
$$523$$ −4.00000 6.92820i −0.174908 0.302949i 0.765222 0.643767i $$-0.222629\pi$$
−0.940129 + 0.340818i $$0.889296\pi$$
$$524$$ 1.00000 0.0436852
$$525$$ 8.00000 6.92820i 0.349149 0.302372i
$$526$$ −30.0000 −1.30806
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ 2.50000 4.33013i 0.108799 0.188445i
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 4.50000 + 7.79423i 0.195468 + 0.338560i
$$531$$ −11.0000 −0.477359
$$532$$ 4.00000 + 20.7846i 0.173422 + 0.901127i
$$533$$ 0 0
$$534$$ −3.00000 5.19615i −0.129823 0.224860i
$$535$$ −1.50000 + 2.59808i −0.0648507 + 0.112325i
$$536$$ 1.00000 1.73205i 0.0431934 0.0748132i
$$537$$ 6.00000 + 10.3923i 0.258919 + 0.448461i
$$538$$ 31.0000 1.33650
$$539$$ 5.00000 34.6410i 0.215365 1.49209i
$$540$$ −1.00000 −0.0430331
$$541$$ 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i $$-0.0401986\pi$$
−0.605096 + 0.796152i $$0.706865\pi$$
$$542$$ −7.50000 + 12.9904i −0.322153 + 0.557985i
$$543$$ 0 0
$$544$$ 2.00000 + 3.46410i 0.0857493 + 0.148522i
$$545$$ −2.00000 −0.0856706
$$546$$ 0 0
$$547$$ −12.0000 −0.513083 −0.256541 0.966533i $$-0.582583\pi$$
−0.256541 + 0.966533i $$0.582583\pi$$
$$548$$ 1.00000 + 1.73205i 0.0427179 + 0.0739895i
$$549$$ 3.00000 5.19615i 0.128037 0.221766i
$$550$$ 10.0000 17.3205i 0.426401 0.738549i
$$551$$ 20.0000 + 34.6410i 0.852029 + 1.47576i
$$552$$ 4.00000 0.170251
$$553$$ 6.00000 5.19615i 0.255146 0.220963i
$$554$$ −16.0000 −0.679775
$$555$$ −2.00000 3.46410i −0.0848953 0.147043i
$$556$$ 7.00000 12.1244i 0.296866 0.514187i
$$557$$ 11.5000 19.9186i 0.487271 0.843978i −0.512622 0.858614i $$-0.671326\pi$$
0.999893 + 0.0146368i $$0.00465919\pi$$
$$558$$ −1.50000 2.59808i −0.0635001 0.109985i
$$559$$ 0 0
$$560$$ −2.50000 0.866025i −0.105644 0.0365963i
$$561$$ 20.0000 0.844401
$$562$$ −1.00000 1.73205i −0.0421825 0.0730622i
$$563$$ −8.50000 + 14.7224i −0.358232 + 0.620477i −0.987666 0.156578i $$-0.949954\pi$$
0.629433 + 0.777055i $$0.283287\pi$$
$$564$$ −3.00000 + 5.19615i −0.126323 + 0.218797i
$$565$$ −8.00000 13.8564i −0.336563 0.582943i
$$566$$ 10.0000 0.420331
$$567$$ −2.50000 0.866025i −0.104990 0.0363696i
$$568$$ 2.00000 0.0839181
$$569$$ −12.0000 20.7846i −0.503066 0.871336i −0.999994 0.00354413i $$-0.998872\pi$$
0.496928 0.867792i $$-0.334461\pi$$
$$570$$ 4.00000 6.92820i 0.167542 0.290191i
$$571$$ 15.0000 25.9808i 0.627730 1.08726i −0.360276 0.932846i $$-0.617317\pi$$
0.988006 0.154415i $$-0.0493493\pi$$
$$572$$ 0 0
$$573$$ −24.0000 −1.00261
$$574$$ 0 0
$$575$$ 16.0000 0.667246
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i $$0.389923\pi$$
−0.984238 + 0.176847i $$0.943410\pi$$
$$578$$ 0.500000 0.866025i 0.0207973 0.0360219i
$$579$$ 2.50000 + 4.33013i 0.103896 + 0.179954i
$$580$$ −5.00000 −0.207614
$$581$$ −3.50000 18.1865i −0.145204 0.754505i
$$582$$ −7.00000 −0.290159
$$583$$ 22.5000 + 38.9711i 0.931855 + 1.61402i
$$584$$ −5.00000 + 8.66025i −0.206901 + 0.358364i
$$585$$ 0 0
$$586$$ 10.5000 + 18.1865i 0.433751 + 0.751279i
$$587$$ 35.0000 1.44460 0.722302 0.691577i $$-0.243084\pi$$
0.722302 + 0.691577i $$0.243084\pi$$
$$588$$ −5.50000 4.33013i −0.226816 0.178571i
$$589$$ 24.0000 0.988903
$$590$$ 5.50000 + 9.52628i 0.226431 + 0.392191i
$$591$$ 1.00000 1.73205i 0.0411345 0.0712470i
$$592$$ 2.00000 3.46410i 0.0821995 0.142374i
$$593$$ −18.0000 31.1769i −0.739171 1.28028i −0.952869 0.303383i $$-0.901884\pi$$
0.213697 0.976900i $$-0.431449\pi$$
$$594$$ −5.00000 −0.205152
$$595$$ −2.00000 10.3923i −0.0819920 0.426043i
$$596$$ −18.0000 −0.737309
$$597$$ −2.00000 3.46410i −0.0818546 0.141776i
$$598$$ 0 0
$$599$$ 15.0000 25.9808i 0.612883 1.06155i −0.377869 0.925859i $$-0.623343\pi$$
0.990752 0.135686i $$-0.0433238\pi$$
$$600$$ −2.00000 3.46410i −0.0816497 0.141421i
$$601$$ 35.0000 1.42768 0.713840 0.700309i $$-0.246954\pi$$
0.713840 + 0.700309i $$0.246954\pi$$
$$602$$ 4.00000 3.46410i 0.163028 0.141186i
$$603$$ −2.00000 −0.0814463
$$604$$ −9.50000 16.4545i −0.386550 0.669523i
$$605$$ −7.00000 + 12.1244i −0.284590 + 0.492925i
$$606$$ 5.00000 8.66025i 0.203111 0.351799i
$$607$$ 13.5000 + 23.3827i 0.547948 + 0.949074i 0.998415 + 0.0562808i $$0.0179242\pi$$
−0.450467 + 0.892793i $$0.648742\pi$$
$$608$$ 8.00000 0.324443
$$609$$ −12.5000 4.33013i −0.506526 0.175466i
$$610$$ −6.00000 −0.242933
$$611$$ 0 0
$$612$$ 2.00000 3.46410i 0.0808452 0.140028i
$$613$$ −6.00000 + 10.3923i −0.242338 + 0.419741i −0.961380 0.275225i $$-0.911248\pi$$
0.719042 + 0.694967i $$0.244581\pi$$
$$614$$ −14.0000 24.2487i −0.564994 0.978598i
$$615$$ 0 0
$$616$$ −12.5000 4.33013i −0.503639 0.174466i
$$617$$ 2.00000 0.0805170 0.0402585 0.999189i $$-0.487182\pi$$
0.0402585 + 0.999189i $$0.487182\pi$$
$$618$$ 4.00000 + 6.92820i 0.160904 + 0.278693i
$$619$$ −5.00000 + 8.66025i −0.200967 + 0.348085i −0.948840 0.315757i $$-0.897742\pi$$
0.747873 + 0.663842i $$0.231075\pi$$
$$620$$ −1.50000 + 2.59808i −0.0602414 + 0.104341i
$$621$$ −2.00000 3.46410i −0.0802572 0.139010i
$$622$$ −32.0000 −1.28308
$$623$$ −12.0000 + 10.3923i −0.480770 + 0.416359i
$$624$$ 0 0
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ −0.500000 + 0.866025i −0.0199840 + 0.0346133i
$$627$$ 20.0000 34.6410i 0.798723 1.38343i
$$628$$ 2.00000 + 3.46410i 0.0798087 + 0.138233i
$$629$$ 16.0000 0.637962
$$630$$ 0.500000 + 2.59808i 0.0199205 + 0.103510i
$$631$$ −19.0000 −0.756378 −0.378189 0.925728i $$-0.623453\pi$$
−0.378189 + 0.925728i $$0.623453\pi$$
$$632$$ −1.50000 2.59808i −0.0596668 0.103346i
$$633$$ 1.00000 1.73205i 0.0397464 0.0688428i
$$634$$ −1.50000 + 2.59808i −0.0595726 + 0.103183i
$$635$$ −4.50000 7.79423i −0.178577 0.309305i
$$636$$ 9.00000 0.356873
$$637$$ 0 0
$$638$$ −25.0000 −0.989759
$$639$$ −1.00000 1.73205i −0.0395594 0.0685189i
$$640$$ −0.500000 + 0.866025i −0.0197642 + 0.0342327i
$$641$$ −13.0000 + 22.5167i −0.513469 + 0.889355i 0.486409 + 0.873731i $$0.338307\pi$$
−0.999878 + 0.0156233i $$0.995027\pi$$
$$642$$ 1.50000 + 2.59808i 0.0592003 + 0.102538i
$$643$$ 14.0000 0.552106 0.276053 0.961142i $$-0.410973\pi$$
0.276053 + 0.961142i $$0.410973\pi$$
$$644$$ −2.00000 10.3923i −0.0788110 0.409514i
$$645$$ −2.00000 −0.0787499
$$646$$ 16.0000 + 27.7128i 0.629512 + 1.09035i
$$647$$ 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i $$-0.718214\pi$$
0.986916 + 0.161233i $$0.0515470\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ 27.5000 + 47.6314i 1.07947 + 1.86970i
$$650$$ 0 0
$$651$$ −6.00000 + 5.19615i −0.235159 + 0.203653i
$$652$$ −4.00000 −0.156652
$$653$$ 19.5000 + 33.7750i 0.763094 + 1.32172i 0.941248 + 0.337715i $$0.109654\pi$$
−0.178154 + 0.984003i $$0.557013\pi$$
$$654$$ −1.00000 + 1.73205i −0.0391031 + 0.0677285i
$$655$$ −0.500000 + 0.866025i −0.0195366 + 0.0338384i
$$656$$ 0 0
$$657$$ 10.0000 0.390137
$$658$$ 15.0000 + 5.19615i 0.584761 + 0.202567i
$$659$$ −40.0000 −1.55818 −0.779089 0.626913i $$-0.784318\pi$$
−0.779089 + 0.626913i $$0.784318\pi$$
$$660$$ 2.50000 + 4.33013i 0.0973124 + 0.168550i
$$661$$ −5.00000 + 8.66025i −0.194477 + 0.336845i −0.946729 0.322031i $$-0.895634\pi$$
0.752252 + 0.658876i $$0.228968\pi$$
$$662$$ 2.00000 3.46410i 0.0777322 0.134636i
$$663$$ 0 0
$$664$$ −7.00000 −0.271653
$$665$$ −20.0000 6.92820i −0.775567 0.268664i
$$666$$ −4.00000 −0.154997
$$667$$ −10.0000 17.3205i −0.387202 0.670653i
$$668$$ 7.00000 12.1244i 0.270838 0.469105i
$$669$$ −3.50000 + 6.06218i −0.135318 + 0.234377i
$$670$$ 1.00000 + 1.73205i 0.0386334 + 0.0669150i
$$671$$ −30.0000 −1.15814
$$672$$ −2.00000 + 1.73205i −0.0771517 + 0.0668153i
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ −4.50000 7.79423i −0.173334 0.300222i
$$675$$ −2.00000 + 3.46410i −0.0769800 + 0.133333i
$$676$$ 6.50000 11.2583i 0.250000 0.433013i
$$677$$ 13.5000 + 23.3827i 0.518847 + 0.898670i 0.999760 + 0.0219013i $$0.00697196\pi$$
−0.480913 + 0.876768i $$0.659695\pi$$
$$678$$ −16.0000 −0.614476
$$679$$ 3.50000 + 18.1865i 0.134318 + 0.697935i
$$680$$ −4.00000 −0.153393
$$681$$ 1.50000 + 2.59808i 0.0574801 + 0.0995585i
$$682$$ −7.50000 + 12.9904i −0.287190 + 0.497427i
$$683$$ 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i $$-0.778250\pi$$
0.939184 + 0.343413i $$0.111583\pi$$
$$684$$ −4.00000 6.92820i −0.152944 0.264906i
$$685$$ −2.00000 −0.0764161
$$686$$ −8.50000 + 16.4545i −0.324532 + 0.628235i
$$687$$ 20.0000 0.763048
$$688$$ −1.00000 1.73205i −0.0381246 0.0660338i
$$689$$ 0 0
$$690$$ −2.00000 + 3.46410i −0.0761387 + 0.131876i
$$691$$ −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i $$-0.215292\pi$$
−0.932024 + 0.362397i $$0.881959\pi$$
$$692$$ 22.0000 0.836315
$$693$$ 2.50000 + 12.9904i 0.0949671 + 0.493464i
$$694$$ 12.0000 0.455514
$$695$$ 7.00000 + 12.1244i 0.265525 + 0.459903i
$$696$$ −2.50000 + 4.33013i −0.0947623 + 0.164133i
$$697$$ 0 0
$$698$$ 7.00000 + 12.1244i 0.264954 + 0.458914i
$$699$$ 4.00000 0.151294
$$700$$ −8.00000 + 6.92820i −0.302372 + 0.261861i
$$701$$ −5.00000 −0.188847 −0.0944237 0.995532i $$-0.530101\pi$$
−0.0944237 + 0.995532i $$0.530101\pi$$
$$702$$ 0 0
$$703$$ 16.0000 27.7128i 0.603451 1.04521i
$$704$$ −2.50000 + 4.33013i −0.0942223 + 0.163198i
$$705$$ −3.00000 5.19615i −0.112987 0.195698i
$$706$$ 24.0000 0.903252
$$707$$ −25.0000 8.66025i −0.940222 0.325702i
$$708$$ 11.0000 0.413405
$$709$$ −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i $$-0.913748\pi$$
0.249952 0.968258i $$-0.419585\pi$$
$$710$$ −1.00000 + 1.73205i −0.0375293 + 0.0650027i
$$711$$ −1.50000 + 2.59808i −0.0562544 + 0.0974355i
$$712$$ 3.00000 + 5.19615i 0.112430 + 0.194734i
$$713$$ −12.0000 −0.449404
$$714$$ −10.0000 3.46410i −0.374241 0.129641i
$$715$$ 0 0
$$716$$ −6.00000 10.3923i −0.224231 0.388379i
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ −5.00000 + 8.66025i −0.186598 + 0.323198i
$$719$$ 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i $$-0.130979\pi$$
−0.804648 + 0.593753i $$0.797646\pi$$
$$720$$ 1.00000 0.0372678
$$721$$ 16.0000 13.8564i 0.595871 0.516040i
$$722$$ 45.0000 1.67473
$$723$$ −12.5000 21.6506i −0.464880 0.805196i
$$724$$ 0 0
$$725$$ −10.0000 + 17.3205i −0.371391 + 0.643268i
$$726$$ 7.00000 + 12.1244i 0.259794 + 0.449977i
$$727$$ 7.00000 0.259616 0.129808 0.991539i $$-0.458564\pi$$
0.129808 + 0.991539i $$0.458564\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ −5.00000 8.66025i −0.185058 0.320530i
$$731$$ 4.00000 6.92820i 0.147945 0.256249i
$$732$$ −3.00000 + 5.19615i −0.110883 + 0.192055i
$$733$$ 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i $$-0.131323\pi$$
−0.805289 + 0.592883i $$0.797990\pi$$
$$734$$ 17.0000 0.627481
$$735$$ 6.50000 2.59808i 0.239756 0.0958315i
$$736$$ −4.00000 −0.147442
$$737$$ 5.00000 + 8.66025i 0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i $$-0.647281\pi$$
0.998146 0.0608653i $$-0.0193860\pi$$
$$740$$ 2.00000 + 3.46410i 0.0735215 + 0.127343i
$$741$$ 0 0
$$742$$ −4.50000 23.3827i −0.165200 0.858405i
$$743$$ 30.0000 1.10059 0.550297 0.834969i $$-0.314515\pi$$
0.550297 + 0.834969i $$0.314515\pi$$
$$744$$ 1.50000 + 2.59808i 0.0549927 + 0.0952501i
$$745$$ 9.00000 15.5885i 0.329734 0.571117i
$$746$$ 16.0000 27.7128i 0.585802 1.01464i
$$747$$ 3.50000 + 6.06218i 0.128058 + 0.221803i
$$748$$ −20.0000 −0.731272
$$749$$ 6.00000 5.19615i 0.219235 0.189863i
$$750$$ 9.00000 0.328634
$$751$$ −22.5000 38.9711i −0.821037 1.42208i −0.904911 0.425601i $$-0.860063\pi$$
0.0838743 0.996476i $$-0.473271\pi$$
$$752$$ 3.00000 5.19615i 0.109399 0.189484i
$$753$$ 10.5000 18.1865i 0.382641 0.662754i
$$754$$ 0 0
$$755$$ 19.0000 0.691481
$$756$$ 2.50000 + 0.866025i 0.0909241 + 0.0314970i
$$757$$ −54.0000 −1.96266 −0.981332 0.192323i $$-0.938398\pi$$
−0.981332 + 0.192323i $$0.938398\pi$$
$$758$$ −8.00000 13.8564i −0.290573 0.503287i
$$759$$ −10.0000 + 17.3205i −0.362977 + 0.628695i
$$760$$ −4.00000 + 6.92820i −0.145095 + 0.251312i
$$761$$ −4.00000 6.92820i −0.145000 0.251147i 0.784373 0.620289i $$-0.212985\pi$$
−0.929373 + 0.369142i $$0.879652\pi$$
$$762$$ −9.00000 −0.326036
$$763$$ 5.00000 + 1.73205i 0.181012 + 0.0627044i
$$764$$ 24.0000 0.868290
$$765$$ 2.00000 + 3.46410i 0.0723102 + 0.125245i
$$766$$ 17.0000 29.4449i 0.614235 1.06389i
$$767$$ 0 0
$$768$$ 0.500000 + 0.866025i 0.0180422 + 0.0312500i
$$769$$ −35.0000 −1.26213 −0.631066 0.775729i $$-0.717382\pi$$
−0.631066 + 0.775729i $$0.717382\pi$$
$$770$$ 10.0000 8.66025i 0.360375 0.312094i
$$771$$ 6.00000 0.216085
$$772$$ −2.50000 4.33013i −0.0899770 0.155845i
$$773$$ −5.00000 + 8.66025i −0.179838 + 0.311488i −0.941825 0.336104i $$-0.890891\pi$$
0.761987 + 0.647592i $$0.224224\pi$$
$$774$$ −1.00000 + 1.73205i −0.0359443 + 0.0622573i
$$775$$ 6.00000 + 10.3923i 0.215526 + 0.373303i
$$776$$ 7.00000 0.251285
$$777$$ 2.00000 + 10.3923i 0.0717496 + 0.372822i
$$778$$ −2.00000 −0.0717035
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −5.00000 + 8.66025i −0.178914 + 0.30