# Properties

 Label 1950.2.y.b.49.1 Level $1950$ Weight $2$ Character 1950.49 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.y (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 78) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.49 Dual form 1950.2.y.b.199.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.09808 - 0.633975i) q^{11} -1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96410 - 2.86603i) q^{17} -1.00000 q^{18} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-1.09808 - 0.633975i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000i q^{27} +(-1.36603 - 2.36603i) q^{28} +(-2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.633975 + 1.09808i) q^{33} +5.73205i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.76795 + 3.06218i) q^{37} +4.73205i q^{38} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(8.36603 + 4.83013i) q^{43} +1.26795i q^{44} +(-3.63397 - 2.09808i) q^{46} -2.19615 q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(-1.00000 - 3.46410i) q^{52} +6.46410i q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(-2.23205 + 3.86603i) q^{58} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(-1.26795 + 0.732051i) q^{62} +(1.36603 + 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 - 11.3660i) q^{67} +(4.96410 - 2.86603i) q^{68} +(-2.09808 + 3.63397i) q^{69} +(4.09808 + 2.36603i) q^{71} +(0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(1.76795 - 3.06218i) q^{74} +(4.09808 - 2.36603i) q^{76} +3.46410i q^{77} +(-3.46410 + 1.00000i) q^{78} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.13397 - 4.69615i) q^{82} +0.196152 q^{83} +(2.36603 + 1.36603i) q^{84} -9.66025i q^{86} +(3.86603 + 2.23205i) q^{87} +(1.09808 - 0.633975i) q^{88} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +4.19615i q^{92} +(0.732051 + 1.26795i) q^{93} +(1.09808 + 1.90192i) q^{94} -1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.232051 + 0.401924i) q^{98} -1.26795i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ 0 0
$$6$$ 0.866025 + 0.500000i 0.353553 + 0.204124i
$$7$$ −1.36603 + 2.36603i −0.516309 + 0.894274i 0.483512 + 0.875338i $$0.339361\pi$$
−0.999821 + 0.0189356i $$0.993972\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 0 0
$$11$$ 1.09808 0.633975i 0.331082 0.191151i −0.325239 0.945632i $$-0.605445\pi$$
0.656322 + 0.754481i $$0.272111\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −2.50000 + 2.59808i −0.693375 + 0.720577i
$$14$$ 2.73205 0.730171
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −4.96410 2.86603i −1.20397 0.695113i −0.242536 0.970143i $$-0.577979\pi$$
−0.961436 + 0.275029i $$0.911312\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −4.09808 2.36603i −0.940163 0.542803i −0.0501517 0.998742i $$-0.515970\pi$$
−0.890011 + 0.455938i $$0.849304\pi$$
$$20$$ 0 0
$$21$$ 2.73205i 0.596182i
$$22$$ −1.09808 0.633975i −0.234111 0.135164i
$$23$$ 3.63397 2.09808i 0.757736 0.437479i −0.0707462 0.997494i $$-0.522538\pi$$
0.828482 + 0.560015i $$0.189205\pi$$
$$24$$ −0.866025 + 0.500000i −0.176777 + 0.102062i
$$25$$ 0 0
$$26$$ 3.50000 + 0.866025i 0.686406 + 0.169842i
$$27$$ 1.00000i 0.192450i
$$28$$ −1.36603 2.36603i −0.258155 0.447137i
$$29$$ −2.23205 3.86603i −0.414481 0.717903i 0.580892 0.813980i $$-0.302704\pi$$
−0.995374 + 0.0960774i $$0.969370\pi$$
$$30$$ 0 0
$$31$$ 1.46410i 0.262960i −0.991319 0.131480i $$-0.958027\pi$$
0.991319 0.131480i $$-0.0419730\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −0.633975 + 1.09808i −0.110361 + 0.191151i
$$34$$ 5.73205i 0.983039i
$$35$$ 0 0
$$36$$ 0.500000 + 0.866025i 0.0833333 + 0.144338i
$$37$$ 1.76795 + 3.06218i 0.290649 + 0.503419i 0.973963 0.226705i $$-0.0727955\pi$$
−0.683314 + 0.730124i $$0.739462\pi$$
$$38$$ 4.73205i 0.767640i
$$39$$ 0.866025 3.50000i 0.138675 0.560449i
$$40$$ 0 0
$$41$$ 8.13397 4.69615i 1.27031 0.733416i 0.295267 0.955415i $$-0.404592\pi$$
0.975047 + 0.221999i $$0.0712582\pi$$
$$42$$ −2.36603 + 1.36603i −0.365086 + 0.210782i
$$43$$ 8.36603 + 4.83013i 1.27581 + 0.736587i 0.976075 0.217436i $$-0.0697693\pi$$
0.299732 + 0.954023i $$0.403103\pi$$
$$44$$ 1.26795i 0.191151i
$$45$$ 0 0
$$46$$ −3.63397 2.09808i −0.535800 0.309344i
$$47$$ −2.19615 −0.320342 −0.160171 0.987089i $$-0.551205\pi$$
−0.160171 + 0.987089i $$0.551205\pi$$
$$48$$ 0.866025 + 0.500000i 0.125000 + 0.0721688i
$$49$$ −0.232051 0.401924i −0.0331501 0.0574177i
$$50$$ 0 0
$$51$$ 5.73205 0.802648
$$52$$ −1.00000 3.46410i −0.138675 0.480384i
$$53$$ 6.46410i 0.887913i 0.896048 + 0.443956i $$0.146425\pi$$
−0.896048 + 0.443956i $$0.853575\pi$$
$$54$$ 0.866025 0.500000i 0.117851 0.0680414i
$$55$$ 0 0
$$56$$ −1.36603 + 2.36603i −0.182543 + 0.316173i
$$57$$ 4.73205 0.626775
$$58$$ −2.23205 + 3.86603i −0.293083 + 0.507634i
$$59$$ 6.92820 + 4.00000i 0.901975 + 0.520756i 0.877841 0.478953i $$-0.158984\pi$$
0.0241347 + 0.999709i $$0.492317\pi$$
$$60$$ 0 0
$$61$$ 4.59808 7.96410i 0.588723 1.01970i −0.405677 0.914017i $$-0.632964\pi$$
0.994400 0.105682i $$-0.0337026\pi$$
$$62$$ −1.26795 + 0.732051i −0.161030 + 0.0929705i
$$63$$ 1.36603 + 2.36603i 0.172103 + 0.298091i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 1.26795 0.156074
$$67$$ −6.56218 11.3660i −0.801698 1.38858i −0.918498 0.395426i $$-0.870597\pi$$
0.116800 0.993155i $$-0.462736\pi$$
$$68$$ 4.96410 2.86603i 0.601986 0.347557i
$$69$$ −2.09808 + 3.63397i −0.252579 + 0.437479i
$$70$$ 0 0
$$71$$ 4.09808 + 2.36603i 0.486352 + 0.280796i 0.723060 0.690785i $$-0.242735\pi$$
−0.236708 + 0.971581i $$0.576068\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −6.26795 −0.733608 −0.366804 0.930298i $$-0.619548\pi$$
−0.366804 + 0.930298i $$0.619548\pi$$
$$74$$ 1.76795 3.06218i 0.205520 0.355971i
$$75$$ 0 0
$$76$$ 4.09808 2.36603i 0.470082 0.271402i
$$77$$ 3.46410i 0.394771i
$$78$$ −3.46410 + 1.00000i −0.392232 + 0.113228i
$$79$$ 2.53590 0.285311 0.142655 0.989772i $$-0.454436\pi$$
0.142655 + 0.989772i $$0.454436\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −8.13397 4.69615i −0.898247 0.518603i
$$83$$ 0.196152 0.0215305 0.0107653 0.999942i $$-0.496573\pi$$
0.0107653 + 0.999942i $$0.496573\pi$$
$$84$$ 2.36603 + 1.36603i 0.258155 + 0.149046i
$$85$$ 0 0
$$86$$ 9.66025i 1.04169i
$$87$$ 3.86603 + 2.23205i 0.414481 + 0.239301i
$$88$$ 1.09808 0.633975i 0.117055 0.0675819i
$$89$$ 8.19615 4.73205i 0.868790 0.501596i 0.00184433 0.999998i $$-0.499413\pi$$
0.866946 + 0.498402i $$0.166080\pi$$
$$90$$ 0 0
$$91$$ −2.73205 9.46410i −0.286397 0.992107i
$$92$$ 4.19615i 0.437479i
$$93$$ 0.732051 + 1.26795i 0.0759101 + 0.131480i
$$94$$ 1.09808 + 1.90192i 0.113258 + 0.196168i
$$95$$ 0 0
$$96$$ 1.00000i 0.102062i
$$97$$ 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i $$-0.734809\pi$$
0.977173 + 0.212445i $$0.0681426\pi$$
$$98$$ −0.232051 + 0.401924i −0.0234407 + 0.0406004i
$$99$$ 1.26795i 0.127434i
$$100$$ 0 0
$$101$$ 0.964102 + 1.66987i 0.0959317 + 0.166159i 0.909997 0.414615i $$-0.136084\pi$$
−0.814065 + 0.580773i $$0.802750\pi$$
$$102$$ −2.86603 4.96410i −0.283779 0.491519i
$$103$$ 15.2679i 1.50440i −0.658937 0.752198i $$-0.728994\pi$$
0.658937 0.752198i $$-0.271006\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 0 0
$$106$$ 5.59808 3.23205i 0.543733 0.313925i
$$107$$ 8.83013 5.09808i 0.853641 0.492850i −0.00823695 0.999966i $$-0.502622\pi$$
0.861878 + 0.507116i $$0.169289\pi$$
$$108$$ −0.866025 0.500000i −0.0833333 0.0481125i
$$109$$ 1.46410i 0.140236i 0.997539 + 0.0701178i $$0.0223375\pi$$
−0.997539 + 0.0701178i $$0.977662\pi$$
$$110$$ 0 0
$$111$$ −3.06218 1.76795i −0.290649 0.167806i
$$112$$ 2.73205 0.258155
$$113$$ −1.16025 0.669873i −0.109148 0.0630163i 0.444432 0.895812i $$-0.353405\pi$$
−0.553580 + 0.832796i $$0.686739\pi$$
$$114$$ −2.36603 4.09808i −0.221599 0.383820i
$$115$$ 0 0
$$116$$ 4.46410 0.414481
$$117$$ 1.00000 + 3.46410i 0.0924500 + 0.320256i
$$118$$ 8.00000i 0.736460i
$$119$$ 13.5622 7.83013i 1.24324 0.717787i
$$120$$ 0 0
$$121$$ −4.69615 + 8.13397i −0.426923 + 0.739452i
$$122$$ −9.19615 −0.832581
$$123$$ −4.69615 + 8.13397i −0.423438 + 0.733416i
$$124$$ 1.26795 + 0.732051i 0.113865 + 0.0657401i
$$125$$ 0 0
$$126$$ 1.36603 2.36603i 0.121695 0.210782i
$$127$$ 8.53590 4.92820i 0.757438 0.437307i −0.0709368 0.997481i $$-0.522599\pi$$
0.828375 + 0.560173i $$0.189266\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ −9.66025 −0.850538
$$130$$ 0 0
$$131$$ 6.53590 0.571044 0.285522 0.958372i $$-0.407833\pi$$
0.285522 + 0.958372i $$0.407833\pi$$
$$132$$ −0.633975 1.09808i −0.0551804 0.0955753i
$$133$$ 11.1962 6.46410i 0.970830 0.560509i
$$134$$ −6.56218 + 11.3660i −0.566886 + 0.981875i
$$135$$ 0 0
$$136$$ −4.96410 2.86603i −0.425668 0.245760i
$$137$$ 5.96410 10.3301i 0.509548 0.882562i −0.490391 0.871502i $$-0.663146\pi$$
0.999939 0.0110599i $$-0.00352055\pi$$
$$138$$ 4.19615 0.357200
$$139$$ 8.92820 15.4641i 0.757280 1.31165i −0.186952 0.982369i $$-0.559861\pi$$
0.944233 0.329279i $$-0.106806\pi$$
$$140$$ 0 0
$$141$$ 1.90192 1.09808i 0.160171 0.0924747i
$$142$$ 4.73205i 0.397105i
$$143$$ −1.09808 + 4.43782i −0.0918257 + 0.371109i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 3.13397 + 5.42820i 0.259370 + 0.449241i
$$147$$ 0.401924 + 0.232051i 0.0331501 + 0.0191392i
$$148$$ −3.53590 −0.290649
$$149$$ −11.4282 6.59808i −0.936235 0.540535i −0.0474568 0.998873i $$-0.515112\pi$$
−0.888778 + 0.458338i $$0.848445\pi$$
$$150$$ 0 0
$$151$$ 6.73205i 0.547847i 0.961752 + 0.273923i $$0.0883214\pi$$
−0.961752 + 0.273923i $$0.911679\pi$$
$$152$$ −4.09808 2.36603i −0.332398 0.191910i
$$153$$ −4.96410 + 2.86603i −0.401324 + 0.231704i
$$154$$ 3.00000 1.73205i 0.241747 0.139573i
$$155$$ 0 0
$$156$$ 2.59808 + 2.50000i 0.208013 + 0.200160i
$$157$$ 7.58846i 0.605625i 0.953050 + 0.302812i $$0.0979256\pi$$
−0.953050 + 0.302812i $$0.902074\pi$$
$$158$$ −1.26795 2.19615i −0.100873 0.174717i
$$159$$ −3.23205 5.59808i −0.256318 0.443956i
$$160$$ 0 0
$$161$$ 11.4641i 0.903498i
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ 6.73205 11.6603i 0.527295 0.913302i −0.472199 0.881492i $$-0.656540\pi$$
0.999494 0.0318096i $$-0.0101270\pi$$
$$164$$ 9.39230i 0.733416i
$$165$$ 0 0
$$166$$ −0.0980762 0.169873i −0.00761219 0.0131847i
$$167$$ −4.73205 8.19615i −0.366177 0.634237i 0.622787 0.782391i $$-0.286000\pi$$
−0.988964 + 0.148154i $$0.952667\pi$$
$$168$$ 2.73205i 0.210782i
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 0 0
$$171$$ −4.09808 + 2.36603i −0.313388 + 0.180934i
$$172$$ −8.36603 + 4.83013i −0.637903 + 0.368294i
$$173$$ −3.80385 2.19615i −0.289201 0.166970i 0.348380 0.937353i $$-0.386732\pi$$
−0.637582 + 0.770383i $$0.720065\pi$$
$$174$$ 4.46410i 0.338423i
$$175$$ 0 0
$$176$$ −1.09808 0.633975i −0.0827706 0.0477876i
$$177$$ −8.00000 −0.601317
$$178$$ −8.19615 4.73205i −0.614328 0.354682i
$$179$$ 8.02628 + 13.9019i 0.599912 + 1.03908i 0.992833 + 0.119506i $$0.0381312\pi$$
−0.392921 + 0.919572i $$0.628535\pi$$
$$180$$ 0 0
$$181$$ −19.1962 −1.42684 −0.713419 0.700737i $$-0.752855\pi$$
−0.713419 + 0.700737i $$0.752855\pi$$
$$182$$ −6.83013 + 7.09808i −0.506283 + 0.526144i
$$183$$ 9.19615i 0.679799i
$$184$$ 3.63397 2.09808i 0.267900 0.154672i
$$185$$ 0 0
$$186$$ 0.732051 1.26795i 0.0536766 0.0929705i
$$187$$ −7.26795 −0.531485
$$188$$ 1.09808 1.90192i 0.0800854 0.138712i
$$189$$ −2.36603 1.36603i −0.172103 0.0993637i
$$190$$ 0 0
$$191$$ 3.46410 6.00000i 0.250654 0.434145i −0.713052 0.701111i $$-0.752688\pi$$
0.963706 + 0.266966i $$0.0860212\pi$$
$$192$$ −0.866025 + 0.500000i −0.0625000 + 0.0360844i
$$193$$ 5.86603 + 10.1603i 0.422246 + 0.731351i 0.996159 0.0875652i $$-0.0279086\pi$$
−0.573913 + 0.818916i $$0.694575\pi$$
$$194$$ −6.00000 −0.430775
$$195$$ 0 0
$$196$$ 0.464102 0.0331501
$$197$$ 8.92820 + 15.4641i 0.636108 + 1.10177i 0.986279 + 0.165086i $$0.0527901\pi$$
−0.350171 + 0.936686i $$0.613877\pi$$
$$198$$ −1.09808 + 0.633975i −0.0780369 + 0.0450546i
$$199$$ 7.09808 12.2942i 0.503169 0.871515i −0.496824 0.867851i $$-0.665501\pi$$
0.999993 0.00366345i $$-0.00116611\pi$$
$$200$$ 0 0
$$201$$ 11.3660 + 6.56218i 0.801698 + 0.462860i
$$202$$ 0.964102 1.66987i 0.0678340 0.117492i
$$203$$ 12.1962 0.856002
$$204$$ −2.86603 + 4.96410i −0.200662 + 0.347557i
$$205$$ 0 0
$$206$$ −13.2224 + 7.63397i −0.921250 + 0.531884i
$$207$$ 4.19615i 0.291653i
$$208$$ 3.50000 + 0.866025i 0.242681 + 0.0600481i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −8.19615 14.1962i −0.564246 0.977303i −0.997119 0.0758485i $$-0.975833\pi$$
0.432873 0.901455i $$-0.357500\pi$$
$$212$$ −5.59808 3.23205i −0.384477 0.221978i
$$213$$ −4.73205 −0.324235
$$214$$ −8.83013 5.09808i −0.603615 0.348497i
$$215$$ 0 0
$$216$$ 1.00000i 0.0680414i
$$217$$ 3.46410 + 2.00000i 0.235159 + 0.135769i
$$218$$ 1.26795 0.732051i 0.0858764 0.0495807i
$$219$$ 5.42820 3.13397i 0.366804 0.211774i
$$220$$ 0 0
$$221$$ 19.8564 5.73205i 1.33569 0.385579i
$$222$$ 3.53590i 0.237314i
$$223$$ −13.4641 23.3205i −0.901623 1.56166i −0.825387 0.564567i $$-0.809043\pi$$
−0.0762356 0.997090i $$-0.524290\pi$$
$$224$$ −1.36603 2.36603i −0.0912714 0.158087i
$$225$$ 0 0
$$226$$ 1.33975i 0.0891186i
$$227$$ 6.09808 10.5622i 0.404744 0.701036i −0.589548 0.807733i $$-0.700694\pi$$
0.994292 + 0.106697i $$0.0340275\pi$$
$$228$$ −2.36603 + 4.09808i −0.156694 + 0.271402i
$$229$$ 11.8564i 0.783493i 0.920073 + 0.391747i $$0.128129\pi$$
−0.920073 + 0.391747i $$0.871871\pi$$
$$230$$ 0 0
$$231$$ −1.73205 3.00000i −0.113961 0.197386i
$$232$$ −2.23205 3.86603i −0.146541 0.253817i
$$233$$ 7.85641i 0.514690i −0.966320 0.257345i $$-0.917152\pi$$
0.966320 0.257345i $$-0.0828477\pi$$
$$234$$ 2.50000 2.59808i 0.163430 0.169842i
$$235$$ 0 0
$$236$$ −6.92820 + 4.00000i −0.450988 + 0.260378i
$$237$$ −2.19615 + 1.26795i −0.142655 + 0.0823622i
$$238$$ −13.5622 7.83013i −0.879105 0.507552i
$$239$$ 7.66025i 0.495501i 0.968824 + 0.247750i $$0.0796913\pi$$
−0.968824 + 0.247750i $$0.920309\pi$$
$$240$$ 0 0
$$241$$ −11.7679 6.79423i −0.758040 0.437655i 0.0705514 0.997508i $$-0.477524\pi$$
−0.828592 + 0.559853i $$0.810857\pi$$
$$242$$ 9.39230 0.603760
$$243$$ 0.866025 + 0.500000i 0.0555556 + 0.0320750i
$$244$$ 4.59808 + 7.96410i 0.294362 + 0.509849i
$$245$$ 0 0
$$246$$ 9.39230 0.598831
$$247$$ 16.3923 4.73205i 1.04302 0.301093i
$$248$$ 1.46410i 0.0929705i
$$249$$ −0.169873 + 0.0980762i −0.0107653 + 0.00621533i
$$250$$ 0 0
$$251$$ 6.73205 11.6603i 0.424923 0.735989i −0.571490 0.820609i $$-0.693634\pi$$
0.996413 + 0.0846203i $$0.0269677\pi$$
$$252$$ −2.73205 −0.172103
$$253$$ 2.66025 4.60770i 0.167249 0.289683i
$$254$$ −8.53590 4.92820i −0.535590 0.309223i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −8.08846 + 4.66987i −0.504544 + 0.291299i −0.730588 0.682818i $$-0.760754\pi$$
0.226044 + 0.974117i $$0.427421\pi$$
$$258$$ 4.83013 + 8.36603i 0.300711 + 0.520846i
$$259$$ −9.66025 −0.600259
$$260$$ 0 0
$$261$$ −4.46410 −0.276321
$$262$$ −3.26795 5.66025i −0.201895 0.349692i
$$263$$ 8.70577 5.02628i 0.536821 0.309934i −0.206969 0.978348i $$-0.566360\pi$$
0.743790 + 0.668414i $$0.233026\pi$$
$$264$$ −0.633975 + 1.09808i −0.0390184 + 0.0675819i
$$265$$ 0 0
$$266$$ −11.1962 6.46410i −0.686480 0.396339i
$$267$$ −4.73205 + 8.19615i −0.289597 + 0.501596i
$$268$$ 13.1244 0.801698
$$269$$ 2.73205 4.73205i 0.166576 0.288518i −0.770638 0.637273i $$-0.780062\pi$$
0.937214 + 0.348755i $$0.113396\pi$$
$$270$$ 0 0
$$271$$ −18.9282 + 10.9282i −1.14981 + 0.663841i −0.948840 0.315757i $$-0.897742\pi$$
−0.200966 + 0.979598i $$0.564408\pi$$
$$272$$ 5.73205i 0.347557i
$$273$$ 7.09808 + 6.83013i 0.429595 + 0.413378i
$$274$$ −11.9282 −0.720609
$$275$$ 0 0
$$276$$ −2.09808 3.63397i −0.126289 0.218740i
$$277$$ −4.96410 2.86603i −0.298264 0.172203i 0.343399 0.939190i $$-0.388422\pi$$
−0.641663 + 0.766987i $$0.721755\pi$$
$$278$$ −17.8564 −1.07096
$$279$$ −1.26795 0.732051i −0.0759101 0.0438267i
$$280$$ 0 0
$$281$$ 12.3205i 0.734980i 0.930027 + 0.367490i $$0.119783\pi$$
−0.930027 + 0.367490i $$0.880217\pi$$
$$282$$ −1.90192 1.09808i −0.113258 0.0653895i
$$283$$ 22.2224 12.8301i 1.32099 0.762672i 0.337100 0.941469i $$-0.390554\pi$$
0.983886 + 0.178797i $$0.0572205\pi$$
$$284$$ −4.09808 + 2.36603i −0.243176 + 0.140398i
$$285$$ 0 0
$$286$$ 4.39230 1.26795i 0.259722 0.0749754i
$$287$$ 25.6603i 1.51468i
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ 7.92820 + 13.7321i 0.466365 + 0.807768i
$$290$$ 0 0
$$291$$ 6.00000i 0.351726i
$$292$$ 3.13397 5.42820i 0.183402 0.317662i
$$293$$ −15.2583 + 26.4282i −0.891401 + 1.54395i −0.0532048 + 0.998584i $$0.516944\pi$$
−0.838196 + 0.545368i $$0.816390\pi$$
$$294$$ 0.464102i 0.0270670i
$$295$$ 0 0
$$296$$ 1.76795 + 3.06218i 0.102760 + 0.177985i
$$297$$ 0.633975 + 1.09808i 0.0367869 + 0.0637168i
$$298$$ 13.1962i 0.764433i
$$299$$ −3.63397 + 14.6865i −0.210158 + 0.849344i
$$300$$ 0 0
$$301$$ −22.8564 + 13.1962i −1.31742 + 0.760614i
$$302$$ 5.83013 3.36603i 0.335486 0.193693i
$$303$$ −1.66987 0.964102i −0.0959317 0.0553862i
$$304$$ 4.73205i 0.271402i
$$305$$ 0 0
$$306$$ 4.96410 + 2.86603i 0.283779 + 0.163840i
$$307$$ 22.5885 1.28919 0.644596 0.764524i $$-0.277026\pi$$
0.644596 + 0.764524i $$0.277026\pi$$
$$308$$ −3.00000 1.73205i −0.170941 0.0986928i
$$309$$ 7.63397 + 13.2224i 0.434282 + 0.752198i
$$310$$ 0 0
$$311$$ 1.66025 0.0941444 0.0470722 0.998891i $$-0.485011\pi$$
0.0470722 + 0.998891i $$0.485011\pi$$
$$312$$ 0.866025 3.50000i 0.0490290 0.198148i
$$313$$ 6.53590i 0.369431i −0.982792 0.184715i $$-0.940864\pi$$
0.982792 0.184715i $$-0.0591363\pi$$
$$314$$ 6.57180 3.79423i 0.370868 0.214121i
$$315$$ 0 0
$$316$$ −1.26795 + 2.19615i −0.0713277 + 0.123543i
$$317$$ 20.6603 1.16040 0.580198 0.814476i $$-0.302975\pi$$
0.580198 + 0.814476i $$0.302975\pi$$
$$318$$ −3.23205 + 5.59808i −0.181244 + 0.313925i
$$319$$ −4.90192 2.83013i −0.274455 0.158457i
$$320$$ 0 0
$$321$$ −5.09808 + 8.83013i −0.284547 + 0.492850i
$$322$$ 9.92820 5.73205i 0.553277 0.319435i
$$323$$ 13.5622 + 23.4904i 0.754620 + 1.30704i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ −13.4641 −0.745708
$$327$$ −0.732051 1.26795i −0.0404825 0.0701178i
$$328$$ 8.13397 4.69615i 0.449124 0.259302i
$$329$$ 3.00000 5.19615i 0.165395 0.286473i
$$330$$ 0 0
$$331$$ 17.3205 + 10.0000i 0.952021 + 0.549650i 0.893708 0.448649i $$-0.148095\pi$$
0.0583130 + 0.998298i $$0.481428\pi$$
$$332$$ −0.0980762 + 0.169873i −0.00538263 + 0.00932299i
$$333$$ 3.53590 0.193766
$$334$$ −4.73205 + 8.19615i −0.258926 + 0.448474i
$$335$$ 0 0
$$336$$ −2.36603 + 1.36603i −0.129077 + 0.0745228i
$$337$$ 20.8564i 1.13612i 0.822987 + 0.568060i $$0.192306\pi$$
−0.822987 + 0.568060i $$0.807694\pi$$
$$338$$ −11.0000 + 6.92820i −0.598321 + 0.376845i
$$339$$ 1.33975 0.0727650
$$340$$ 0 0
$$341$$ −0.928203 1.60770i −0.0502650 0.0870616i
$$342$$ 4.09808 + 2.36603i 0.221599 + 0.127940i
$$343$$ −17.8564 −0.964155
$$344$$ 8.36603 + 4.83013i 0.451066 + 0.260423i
$$345$$ 0 0
$$346$$ 4.39230i 0.236132i
$$347$$ −28.6865 16.5622i −1.53997 0.889104i −0.998839 0.0481683i $$-0.984662\pi$$
−0.541135 0.840936i $$-0.682005\pi$$
$$348$$ −3.86603 + 2.23205i −0.207241 + 0.119650i
$$349$$ −13.2679 + 7.66025i −0.710217 + 0.410044i −0.811141 0.584850i $$-0.801153\pi$$
0.100924 + 0.994894i $$0.467820\pi$$
$$350$$ 0 0
$$351$$ −2.59808 2.50000i −0.138675 0.133440i
$$352$$ 1.26795i 0.0675819i
$$353$$ −10.8923 18.8660i −0.579739 1.00414i −0.995509 0.0946674i $$-0.969821\pi$$
0.415770 0.909470i $$-0.363512\pi$$
$$354$$ 4.00000 + 6.92820i 0.212598 + 0.368230i
$$355$$ 0 0
$$356$$ 9.46410i 0.501596i
$$357$$ −7.83013 + 13.5622i −0.414414 + 0.717787i
$$358$$ 8.02628 13.9019i 0.424202 0.734740i
$$359$$ 1.12436i 0.0593412i 0.999560 + 0.0296706i $$0.00944584\pi$$
−0.999560 + 0.0296706i $$0.990554\pi$$
$$360$$ 0 0
$$361$$ 1.69615 + 2.93782i 0.0892712 + 0.154622i
$$362$$ 9.59808 + 16.6244i 0.504464 + 0.873757i
$$363$$ 9.39230i 0.492968i
$$364$$ 9.56218 + 2.36603i 0.501194 + 0.124013i
$$365$$ 0 0
$$366$$ 7.96410 4.59808i 0.416290 0.240345i
$$367$$ −9.75833 + 5.63397i −0.509381 + 0.294091i −0.732579 0.680682i $$-0.761684\pi$$
0.223198 + 0.974773i $$0.428350\pi$$
$$368$$ −3.63397 2.09808i −0.189434 0.109370i
$$369$$ 9.39230i 0.488944i
$$370$$ 0 0
$$371$$ −15.2942 8.83013i −0.794037 0.458437i
$$372$$ −1.46410 −0.0759101
$$373$$ −11.8923 6.86603i −0.615760 0.355509i 0.159456 0.987205i $$-0.449026\pi$$
−0.775216 + 0.631696i $$0.782359\pi$$
$$374$$ 3.63397 + 6.29423i 0.187908 + 0.325467i
$$375$$ 0 0
$$376$$ −2.19615 −0.113258
$$377$$ 15.6244 + 3.86603i 0.804695 + 0.199110i
$$378$$ 2.73205i 0.140522i
$$379$$ −4.73205 + 2.73205i −0.243069 + 0.140336i −0.616587 0.787287i $$-0.711485\pi$$
0.373517 + 0.927623i $$0.378152\pi$$
$$380$$ 0 0
$$381$$ −4.92820 + 8.53590i −0.252479 + 0.437307i
$$382$$ −6.92820 −0.354478
$$383$$ −0.732051 + 1.26795i −0.0374060 + 0.0647892i −0.884122 0.467255i $$-0.845243\pi$$
0.846716 + 0.532045i $$0.178576\pi$$
$$384$$ 0.866025 + 0.500000i 0.0441942 + 0.0255155i
$$385$$ 0 0
$$386$$ 5.86603 10.1603i 0.298573 0.517143i
$$387$$ 8.36603 4.83013i 0.425269 0.245529i
$$388$$ 3.00000 + 5.19615i 0.152302 + 0.263795i
$$389$$ 11.7846 0.597503 0.298752 0.954331i $$-0.403430\pi$$
0.298752 + 0.954331i $$0.403430\pi$$
$$390$$ 0 0
$$391$$ −24.0526 −1.21639
$$392$$ −0.232051 0.401924i −0.0117203 0.0203002i
$$393$$ −5.66025 + 3.26795i −0.285522 + 0.164846i
$$394$$ 8.92820 15.4641i 0.449796 0.779070i
$$395$$ 0 0
$$396$$ 1.09808 + 0.633975i 0.0551804 + 0.0318584i
$$397$$ 10.1962 17.6603i 0.511730 0.886343i −0.488177 0.872744i $$-0.662338\pi$$
0.999908 0.0135983i $$-0.00432860\pi$$
$$398$$ −14.1962 −0.711589
$$399$$ −6.46410 + 11.1962i −0.323610 + 0.560509i
$$400$$ 0 0
$$401$$ 6.99038 4.03590i 0.349083 0.201543i −0.315198 0.949026i $$-0.602071\pi$$
0.664281 + 0.747483i $$0.268738\pi$$
$$402$$ 13.1244i 0.654583i
$$403$$ 3.80385 + 3.66025i 0.189483 + 0.182330i
$$404$$ −1.92820 −0.0959317
$$405$$ 0 0
$$406$$ −6.09808 10.5622i −0.302642 0.524192i
$$407$$ 3.88269 + 2.24167i 0.192458 + 0.111115i
$$408$$ 5.73205 0.283779
$$409$$ −15.3564 8.86603i −0.759325 0.438397i 0.0697281 0.997566i $$-0.477787\pi$$
−0.829053 + 0.559169i $$0.811120\pi$$
$$410$$ 0 0
$$411$$ 11.9282i 0.588375i
$$412$$ 13.2224 + 7.63397i 0.651422 + 0.376099i
$$413$$ −18.9282 + 10.9282i −0.931396 + 0.537742i
$$414$$ −3.63397 + 2.09808i −0.178600 + 0.103115i
$$415$$ 0 0
$$416$$ −1.00000 3.46410i −0.0490290 0.169842i
$$417$$ 17.8564i 0.874432i
$$418$$ 3.00000 + 5.19615i 0.146735 + 0.254152i
$$419$$ −8.73205 15.1244i −0.426589 0.738873i 0.569979 0.821659i $$-0.306951\pi$$
−0.996567 + 0.0827863i $$0.973618\pi$$
$$420$$ 0 0
$$421$$ 22.7128i 1.10695i 0.832864 + 0.553477i $$0.186699\pi$$
−0.832864 + 0.553477i $$0.813301\pi$$
$$422$$ −8.19615 + 14.1962i −0.398982 + 0.691058i
$$423$$ −1.09808 + 1.90192i −0.0533903 + 0.0924747i
$$424$$ 6.46410i 0.313925i
$$425$$ 0 0
$$426$$ 2.36603 + 4.09808i 0.114634 + 0.198552i
$$427$$ 12.5622 + 21.7583i 0.607926 + 1.05296i
$$428$$ 10.1962i 0.492850i
$$429$$ −1.26795 4.39230i −0.0612172 0.212062i
$$430$$ 0 0
$$431$$ −11.3660 + 6.56218i −0.547482 + 0.316089i −0.748106 0.663579i $$-0.769036\pi$$
0.200624 + 0.979668i $$0.435703\pi$$
$$432$$ 0.866025 0.500000i 0.0416667 0.0240563i
$$433$$ −11.1340 6.42820i −0.535065 0.308920i 0.208012 0.978126i $$-0.433301\pi$$
−0.743076 + 0.669207i $$0.766634\pi$$
$$434$$ 4.00000i 0.192006i
$$435$$ 0 0
$$436$$ −1.26795 0.732051i −0.0607238 0.0350589i
$$437$$ −19.8564 −0.949861
$$438$$ −5.42820 3.13397i −0.259370 0.149747i
$$439$$ 0.169873 + 0.294229i 0.00810760 + 0.0140428i 0.870051 0.492962i $$-0.164086\pi$$
−0.861943 + 0.507005i $$0.830753\pi$$
$$440$$ 0 0
$$441$$ −0.464102 −0.0221001
$$442$$ −14.8923 14.3301i −0.708355 0.681615i
$$443$$ 15.6077i 0.741544i −0.928724 0.370772i $$-0.879093\pi$$
0.928724 0.370772i $$-0.120907\pi$$
$$444$$ 3.06218 1.76795i 0.145325 0.0839032i
$$445$$ 0 0
$$446$$ −13.4641 + 23.3205i −0.637544 + 1.10426i
$$447$$ 13.1962 0.624157
$$448$$ −1.36603 + 2.36603i −0.0645386 + 0.111784i
$$449$$ 9.80385 + 5.66025i 0.462672 + 0.267124i 0.713167 0.700994i $$-0.247260\pi$$
−0.250495 + 0.968118i $$0.580593\pi$$
$$450$$ 0 0
$$451$$ 5.95448 10.3135i 0.280386 0.485642i
$$452$$ 1.16025 0.669873i 0.0545738 0.0315082i
$$453$$ −3.36603 5.83013i −0.158150 0.273923i
$$454$$ −12.1962 −0.572394
$$455$$ 0 0
$$456$$ 4.73205 0.221599
$$457$$ −0.669873 1.16025i −0.0313353 0.0542744i 0.849932 0.526892i $$-0.176643\pi$$
−0.881268 + 0.472617i $$0.843309\pi$$
$$458$$ 10.2679 5.92820i 0.479790 0.277007i
$$459$$ 2.86603 4.96410i 0.133775 0.231704i
$$460$$ 0 0
$$461$$ 19.2846 + 11.1340i 0.898174 + 0.518561i 0.876607 0.481207i $$-0.159801\pi$$
0.0215666 + 0.999767i $$0.493135\pi$$
$$462$$ −1.73205 + 3.00000i −0.0805823 + 0.139573i
$$463$$ 10.0526 0.467182 0.233591 0.972335i $$-0.424952\pi$$
0.233591 + 0.972335i $$0.424952\pi$$
$$464$$ −2.23205 + 3.86603i −0.103620 + 0.179476i
$$465$$ 0 0
$$466$$ −6.80385 + 3.92820i −0.315182 + 0.181971i
$$467$$ 18.5885i 0.860171i −0.902788 0.430086i $$-0.858483\pi$$
0.902788 0.430086i $$-0.141517\pi$$
$$468$$ −3.50000 0.866025i −0.161788 0.0400320i
$$469$$ 35.8564 1.65570
$$470$$ 0 0
$$471$$ −3.79423 6.57180i −0.174829 0.302812i
$$472$$ 6.92820 + 4.00000i 0.318896 + 0.184115i
$$473$$ 12.2487 0.563196
$$474$$ 2.19615 + 1.26795i 0.100873 + 0.0582388i
$$475$$ 0 0
$$476$$ 15.6603i 0.717787i
$$477$$ 5.59808 + 3.23205i 0.256318 + 0.147985i
$$478$$ 6.63397 3.83013i 0.303431 0.175186i
$$479$$ −28.9808 + 16.7321i −1.32416 + 0.764507i −0.984390 0.176000i $$-0.943684\pi$$
−0.339775 + 0.940507i $$0.610351\pi$$
$$480$$ 0 0
$$481$$ −12.3756 3.06218i −0.564281 0.139623i
$$482$$ 13.5885i 0.618937i
$$483$$ −5.73205 9.92820i −0.260817 0.451749i
$$484$$ −4.69615 8.13397i −0.213461 0.369726i
$$485$$ 0 0
$$486$$ 1.00000i 0.0453609i
$$487$$ 1.56218 2.70577i 0.0707890 0.122610i −0.828458 0.560051i $$-0.810782\pi$$
0.899247 + 0.437441i $$0.144115\pi$$
$$488$$ 4.59808 7.96410i 0.208145 0.360518i
$$489$$ 13.4641i 0.608868i
$$490$$ 0 0
$$491$$ 4.36603 + 7.56218i 0.197036 + 0.341276i 0.947566 0.319560i $$-0.103535\pi$$
−0.750530 + 0.660836i $$0.770202\pi$$
$$492$$ −4.69615 8.13397i −0.211719 0.366708i
$$493$$ 25.5885i 1.15245i
$$494$$ −12.2942 11.8301i −0.553143 0.532263i
$$495$$ 0 0
$$496$$ −1.26795 + 0.732051i −0.0569326 + 0.0328701i
$$497$$ −11.1962 + 6.46410i −0.502216 + 0.289955i
$$498$$ 0.169873 + 0.0980762i 0.00761219 + 0.00439490i
$$499$$ 32.0000i 1.43252i 0.697835 + 0.716258i $$0.254147\pi$$
−0.697835 + 0.716258i $$0.745853\pi$$
$$500$$ 0 0
$$501$$ 8.19615 + 4.73205i 0.366177 + 0.211412i
$$502$$ −13.4641 −0.600932
$$503$$ 35.4904 + 20.4904i 1.58244 + 0.913621i 0.994502 + 0.104713i $$0.0333924\pi$$
0.587935 + 0.808908i $$0.299941\pi$$
$$504$$ 1.36603 + 2.36603i 0.0608476 + 0.105391i
$$505$$ 0 0
$$506$$ −5.32051 −0.236525
$$507$$ 6.92820 + 11.0000i 0.307692 + 0.488527i
$$508$$ 9.85641i 0.437307i
$$509$$ 11.8923 6.86603i 0.527117 0.304331i −0.212725 0.977112i $$-0.568234\pi$$
0.739842 + 0.672781i $$0.234900\pi$$
$$510$$ 0 0
$$511$$ 8.56218 14.8301i 0.378768 0.656046i
$$512$$ 1.00000 0.0441942
$$513$$ 2.36603 4.09808i 0.104463 0.180934i
$$514$$ 8.08846 + 4.66987i 0.356767 + 0.205979i
$$515$$ 0 0
$$516$$ 4.83013 8.36603i 0.212634 0.368294i
$$517$$ −2.41154 + 1.39230i −0.106060 + 0.0612335i
$$518$$ 4.83013 + 8.36603i 0.212224 + 0.367582i
$$519$$ 4.39230 0.192801
$$520$$ 0 0
$$521$$ 41.4449 1.81573 0.907866 0.419260i $$-0.137710\pi$$
0.907866 + 0.419260i $$0.137710\pi$$
$$522$$ 2.23205 + 3.86603i 0.0976942 + 0.169211i
$$523$$ 19.4378 11.2224i 0.849957 0.490723i −0.0106796 0.999943i $$-0.503399\pi$$
0.860636 + 0.509220i $$0.170066\pi$$
$$524$$ −3.26795 + 5.66025i −0.142761 + 0.247269i
$$525$$ 0 0
$$526$$ −8.70577 5.02628i −0.379590 0.219156i
$$527$$ −4.19615 + 7.26795i −0.182787 + 0.316597i
$$528$$ 1.26795 0.0551804
$$529$$ −2.69615 + 4.66987i −0.117224 + 0.203038i
$$530$$ 0 0
$$531$$ 6.92820 4.00000i 0.300658 0.173585i
$$532$$ 12.9282i 0.560509i
$$533$$ −8.13397 + 32.8731i −0.352322 + 1.42389i
$$534$$ 9.46410 0.409552
$$535$$ 0 0
$$536$$ −6.56218 11.3660i −0.283443 0.490938i
$$537$$ −13.9019 8.02628i −0.599912 0.346360i
$$538$$ −5.46410 −0.235574
$$539$$ −0.509619 0.294229i −0.0219508 0.0126733i
$$540$$ 0 0
$$541$$ 5.67949i 0.244180i 0.992519 + 0.122090i $$0.0389597\pi$$
−0.992519 + 0.122090i $$0.961040\pi$$
$$542$$ 18.9282 + 10.9282i 0.813036 + 0.469407i
$$543$$ 16.6244 9.59808i 0.713419 0.411893i
$$544$$ 4.96410 2.86603i 0.212834 0.122880i
$$545$$ 0 0
$$546$$ 2.36603 9.56218i 0.101257 0.409223i
$$547$$ 4.19615i 0.179415i −0.995968 0.0897073i $$-0.971407\pi$$
0.995968 0.0897073i $$-0.0285931\pi$$
$$548$$ 5.96410 + 10.3301i 0.254774 + 0.441281i
$$549$$ −4.59808 7.96410i −0.196241 0.339900i
$$550$$ 0 0
$$551$$ 21.1244i 0.899928i
$$552$$ −2.09808 + 3.63397i −0.0893001 + 0.154672i
$$553$$ −3.46410 + 6.00000i −0.147309 + 0.255146i
$$554$$ 5.73205i 0.243532i
$$555$$ 0 0
$$556$$ 8.92820 + 15.4641i 0.378640 + 0.655824i
$$557$$ 21.1865 + 36.6962i 0.897702 + 1.55487i 0.830424 + 0.557132i $$0.188098\pi$$
0.0672780 + 0.997734i $$0.478569\pi$$
$$558$$ 1.46410i 0.0619804i
$$559$$ −33.4641 + 9.66025i −1.41538 + 0.408585i
$$560$$ 0 0
$$561$$ 6.29423 3.63397i 0.265743 0.153427i
$$562$$ 10.6699 6.16025i 0.450081 0.259855i
$$563$$ −30.2487 17.4641i −1.27483 0.736024i −0.298938 0.954273i $$-0.596632\pi$$
−0.975893 + 0.218248i $$0.929966\pi$$
$$564$$ 2.19615i 0.0924747i
$$565$$ 0 0
$$566$$ −22.2224 12.8301i −0.934078 0.539290i
$$567$$ 2.73205 0.114735
$$568$$ 4.09808 + 2.36603i 0.171951 + 0.0992762i
$$569$$ −15.3205 26.5359i −0.642269 1.11244i −0.984925 0.172982i $$-0.944660\pi$$
0.342656 0.939461i $$-0.388674\pi$$
$$570$$ 0 0
$$571$$ −14.0526 −0.588081 −0.294041 0.955793i $$-0.595000\pi$$
−0.294041 + 0.955793i $$0.595000\pi$$
$$572$$ −3.29423 3.16987i −0.137739 0.132539i
$$573$$ 6.92820i 0.289430i
$$574$$ 22.2224 12.8301i 0.927546 0.535519i
$$575$$ 0 0
$$576$$ 0.500000 0.866025i 0.0208333 0.0360844i
$$577$$ 3.73205 0.155367 0.0776837 0.996978i $$-0.475248\pi$$
0.0776837 + 0.996978i $$0.475248\pi$$
$$578$$ 7.92820 13.7321i 0.329770 0.571178i
$$579$$ −10.1603 5.86603i −0.422246 0.243784i
$$580$$ 0 0
$$581$$ −0.267949 + 0.464102i −0.0111164 + 0.0192542i
$$582$$ 5.19615 3.00000i 0.215387 0.124354i
$$583$$ 4.09808 + 7.09808i 0.169725 + 0.293972i
$$584$$ −6.26795 −0.259370
$$585$$ 0 0
$$586$$ 30.5167 1.26063
$$587$$ −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i $$-0.273781\pi$$
−0.982550 + 0.185999i $$0.940448\pi$$
$$588$$ −0.401924 + 0.232051i −0.0165751 + 0.00956961i
$$589$$ −3.46410 + 6.00000i −0.142736 + 0.247226i
$$590$$ 0 0
$$591$$ −15.4641 8.92820i −0.636108 0.367257i
$$592$$ 1.76795 3.06218i 0.0726623 0.125855i
$$593$$ −9.14359 −0.375482 −0.187741 0.982219i $$-0.560117\pi$$
−0.187741 + 0.982219i $$0.560117\pi$$
$$594$$ 0.633975 1.09808i 0.0260123 0.0450546i
$$595$$ 0 0
$$596$$ 11.4282 6.59808i 0.468117 0.270268i
$$597$$ 14.1962i 0.581010i
$$598$$ 14.5359 4.19615i 0.594417 0.171593i
$$599$$ 2.53590 0.103614 0.0518070 0.998657i $$-0.483502\pi$$
0.0518070 + 0.998657i $$0.483502\pi$$
$$600$$ 0 0
$$601$$ −3.96410 6.86603i −0.161699 0.280071i 0.773779 0.633456i $$-0.218364\pi$$
−0.935478 + 0.353385i $$0.885031\pi$$
$$602$$ 22.8564 + 13.1962i 0.931558 + 0.537835i
$$603$$ −13.1244 −0.534465
$$604$$ −5.83013 3.36603i −0.237225 0.136962i
$$605$$ 0 0
$$606$$ 1.92820i 0.0783279i
$$607$$ 35.3205 + 20.3923i 1.43362 + 0.827698i 0.997394 0.0721415i $$-0.0229833\pi$$
0.436221 + 0.899840i $$0.356317\pi$$
$$608$$ 4.09808 2.36603i 0.166199 0.0959550i
$$609$$ −10.5622 + 6.09808i −0.428001 + 0.247107i
$$610$$ 0 0
$$611$$ 5.49038 5.70577i 0.222117 0.230831i
$$612$$ 5.73205i 0.231704i
$$613$$ −4.69615 8.13397i −0.189676 0.328528i 0.755466 0.655187i $$-0.227410\pi$$
−0.945142 + 0.326659i $$0.894077\pi$$
$$614$$ −11.2942 19.5622i −0.455798 0.789465i
$$615$$ 0 0
$$616$$ 3.46410i 0.139573i
$$617$$ 6.62436 11.4737i 0.266687 0.461915i −0.701318 0.712849i $$-0.747404\pi$$
0.968004 + 0.250934i $$0.0807378\pi$$
$$618$$ 7.63397 13.2224i 0.307083 0.531884i
$$619$$ 17.4641i 0.701942i −0.936386 0.350971i $$-0.885852\pi$$
0.936386 0.350971i $$-0.114148\pi$$
$$620$$ 0 0
$$621$$ 2.09808 + 3.63397i 0.0841929 + 0.145826i
$$622$$ −0.830127 1.43782i −0.0332851 0.0576514i
$$623$$ 25.8564i 1.03592i
$$624$$ −3.46410 + 1.00000i −0.138675 + 0.0400320i
$$625$$ 0 0
$$626$$ −5.66025 + 3.26795i −0.226229 + 0.130614i
$$627$$ 5.19615 3.00000i 0.207514 0.119808i
$$628$$ −6.57180 3.79423i −0.262243 0.151406i
$$629$$ 20.2679i 0.808136i
$$630$$ 0 0
$$631$$ 6.67949 + 3.85641i 0.265906 + 0.153521i 0.627026 0.778998i $$-0.284272\pi$$
−0.361119 + 0.932520i $$0.617605\pi$$
$$632$$ 2.53590 0.100873
$$633$$ 14.1962 + 8.19615i 0.564246 + 0.325768i
$$634$$ −10.3301 17.8923i −0.410262 0.710594i
$$635$$ 0 0
$$636$$ 6.46410 0.256318
$$637$$ 1.62436 + 0.401924i 0.0643593 + 0.0159248i
$$638$$ 5.66025i 0.224092i
$$639$$ 4.09808 2.36603i 0.162117 0.0935985i
$$640$$ 0 0
$$641$$ −12.9904 + 22.5000i −0.513089 + 0.888697i 0.486796 + 0.873516i $$0.338166\pi$$
−0.999885 + 0.0151806i $$0.995168\pi$$
$$642$$ 10.1962 0.402410
$$643$$ −6.92820 + 12.0000i −0.273222 + 0.473234i −0.969685 0.244359i $$-0.921423\pi$$
0.696463 + 0.717592i $$0.254756\pi$$
$$644$$ −9.92820 5.73205i −0.391226 0.225874i
$$645$$ 0 0
$$646$$ 13.5622 23.4904i 0.533597 0.924217i
$$647$$ 19.2679 11.1244i 0.757501 0.437344i −0.0708966 0.997484i $$-0.522586\pi$$
0.828398 + 0.560140i $$0.189253\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 10.1436 0.398171
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ 6.73205 + 11.6603i 0.263647 + 0.456651i
$$653$$ 15.1244 8.73205i 0.591862 0.341712i −0.173972 0.984751i $$-0.555660\pi$$
0.765833 + 0.643039i $$0.222327\pi$$
$$654$$ −0.732051 + 1.26795i −0.0286255 + 0.0495807i
$$655$$ 0 0
$$656$$ −8.13397 4.69615i −0.317578 0.183354i
$$657$$ −3.13397 + 5.42820i −0.122268 + 0.211774i
$$658$$ −6.00000 −0.233904
$$659$$ −5.12436 + 8.87564i −0.199617 + 0.345746i −0.948404 0.317064i $$-0.897303\pi$$
0.748788 + 0.662810i $$0.230636\pi$$
$$660$$ 0 0
$$661$$ 9.86603 5.69615i 0.383744 0.221555i −0.295702 0.955280i $$-0.595554\pi$$
0.679446 + 0.733726i $$0.262220\pi$$
$$662$$ 20.0000i 0.777322i
$$663$$ −14.3301 + 14.8923i −0.556536 + 0.578369i
$$664$$ 0.196152 0.00761219
$$665$$ 0 0
$$666$$ −1.76795 3.06218i −0.0685066 0.118657i
$$667$$ −16.2224 9.36603i −0.628135 0.362654i
$$668$$ 9.46410 0.366177
$$669$$ 23.3205 + 13.4641i 0.901623 + 0.520552i
$$670$$ 0 0
$$671$$ 11.6603i 0.450139i
$$672$$ 2.36603 + 1.36603i 0.0912714 + 0.0526956i
$$673$$ 24.1865 13.9641i 0.932322 0.538277i 0.0447770 0.998997i $$-0.485742\pi$$
0.887545 + 0.460720i $$0.152409\pi$$
$$674$$ 18.0622 10.4282i 0.695729 0.401679i
$$675$$ 0 0
$$676$$ 11.5000 + 6.06218i 0.442308 + 0.233161i
$$677$$ 45.4641i 1.74733i −0.486530 0.873664i $$-0.661738\pi$$
0.486530 0.873664i $$-0.338262\pi$$
$$678$$ −0.669873 1.16025i −0.0257263 0.0445593i
$$679$$ 8.19615 + 14.1962i 0.314539 + 0.544798i
$$680$$ 0 0
$$681$$ 12.1962i 0.467358i
$$682$$ −0.928203 + 1.60770i −0.0355427 + 0.0615618i
$$683$$ 5.07180 8.78461i 0.194067 0.336134i −0.752527 0.658561i $$-0.771165\pi$$
0.946594 + 0.322427i $$0.104499\pi$$
$$684$$ 4.73205i 0.180934i
$$685$$ 0 0
$$686$$ 8.92820 + 15.4641i 0.340880 + 0.590422i
$$687$$ −5.92820 10.2679i −0.226175 0.391747i
$$688$$ 9.66025i 0.368294i
$$689$$ −16.7942 16.1603i −0.639809 0.615657i
$$690$$ 0 0
$$691$$ −37.8109 + 21.8301i −1.43839 + 0.830457i −0.997738 0.0672190i $$-0.978587\pi$$
−0.440656 + 0.897676i $$0.645254\pi$$
$$692$$ 3.80385 2.19615i 0.144601 0.0834852i
$$693$$ 3.00000 + 1.73205i 0.113961 + 0.0657952i
$$694$$ 33.1244i 1.25738i
$$695$$ 0 0
$$696$$ 3.86603 + 2.23205i 0.146541 + 0.0846057i
$$697$$ −53.8372 −2.03923
$$698$$ 13.2679 + 7.66025i 0.502199 + 0.289945i
$$699$$ 3.92820 + 6.80385i 0.148578 + 0.257345i
$$700$$ 0 0
$$701$$ 3.32051 0.125414 0.0627069 0.998032i $$-0.480027\pi$$
0.0627069 + 0.998032i $$0.480027\pi$$
$$702$$ −0.866025 + 3.50000i −0.0326860 + 0.132099i
$$703$$ 16.7321i 0.631061i
$$704$$ 1.09808 0.633975i 0.0413853 0.0238938i
$$705$$ 0 0
$$706$$ −10.8923 + 18.8660i −0.409937 + 0.710032i
$$707$$ −5.26795 −0.198122
$$708$$ 4.00000 6.92820i 0.150329 0.260378i
$$709$$ 11.3827 + 6.57180i 0.427486 + 0.246809i 0.698275 0.715830i $$-0.253951\pi$$
−0.270789 + 0.962639i $$0.587285\pi$$
$$710$$ 0 0
$$711$$ 1.26795 2.19615i 0.0475518 0.0823622i
$$712$$ 8.19615 4.73205i 0.307164 0.177341i
$$713$$ −3.07180 5.32051i −0.115040 0.199255i
$$714$$ 15.6603 0.586070
$$715$$ 0 0
$$716$$ −16.0526 −0.599912
$$717$$ −3.83013 6.63397i −0.143039 0.247750i
$$718$$ 0.973721 0.562178i 0.0363389 0.0209803i
$$719$$ 14.7321 25.5167i 0.549413 0.951611i −0.448902 0.893581i $$-0.648185\pi$$
0.998315 0.0580299i $$-0.0184819\pi$$
$$720$$ 0 0
$$721$$ 36.1244 + 20.8564i 1.34534 + 0.776733i
$$722$$ 1.69615 2.93782i 0.0631243 0.109334i
$$723$$ 13.5885 0.505360
$$724$$ 9.59808 16.6244i 0.356710 0.617839i
$$725$$ 0 0
$$726$$ −8.13397 + 4.69615i −0.301880 + 0.174291i
$$727$$ 30.9808i 1.14901i 0.818500 + 0.574506i $$0.194806\pi$$
−0.818500 + 0.574506i $$0.805194\pi$$
$$728$$ −2.73205 9.46410i −0.101257 0.350763i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −27.6865 47.9545i −1.02402 1.77366i
$$732$$ −7.96410 4.59808i −0.294362 0.169950i
$$733$$ −19.0000 −0.701781 −0.350891 0.936416i $$-0.614121\pi$$
−0.350891 + 0.936416i $$0.614121\pi$$
$$734$$ 9.75833 + 5.63397i 0.360187 + 0.207954i
$$735$$ 0 0
$$736$$ 4.19615i 0.154672i
$$737$$ −14.4115 8.32051i −0.530856 0.306490i
$$738$$ −8.13397 + 4.69615i −0.299416 + 0.172868i
$$739$$ −2.53590 + 1.46410i −0.0932845 + 0.0538578i −0.545917 0.837840i $$-0.683818\pi$$
0.452632 + 0.891697i $$0.350485\pi$$
$$740$$ 0 0
$$741$$ −11.8301 + 12.2942i −0.434591 + 0.451640i
$$742$$ 17.6603i 0.648328i
$$743$$ −24.1962 41.9090i −0.887671 1.53749i −0.842622 0.538506i $$-0.818989\pi$$
−0.0450491 0.998985i $$-0.514344\pi$$
$$744$$ 0.732051 + 1.26795i 0.0268383 + 0.0464853i
$$745$$ 0 0
$$746$$ 13.7321i 0.502766i
$$747$$ 0.0980762 0.169873i 0.00358842 0.00621533i
$$748$$ 3.63397 6.29423i 0.132871 0.230140i
$$749$$ 27.8564i 1.01785i
$$750$$ 0 0
$$751$$ −24.9545 43.2224i −0.910602 1.57721i −0.813216 0.581962i $$-0.802285\pi$$
−0.0973862 0.995247i $$-0.531048\pi$$
$$752$$ 1.09808 + 1.90192i 0.0400427 + 0.0693560i
$$753$$ 13.4641i 0.490659i
$$754$$ −4.46410 15.4641i −0.162573 0.563169i
$$755$$ 0 0
$$756$$ 2.36603 1.36603i 0.0860515 0.0496819i
$$757$$ 18.1244 10.4641i 0.658741 0.380324i −0.133056 0.991109i $$-0.542479\pi$$
0.791797 + 0.610784i $$0.209146\pi$$
$$758$$ 4.73205 + 2.73205i 0.171876 + 0.0992326i
$$759$$ 5.32051i 0.193122i
$$760$$ 0 0
$$761$$ −9.80385 5.66025i −0.355389 0.205184i 0.311667 0.950191i $$-0.399113\pi$$
−0.667056 + 0.745007i $$0.732446\pi$$
$$762$$ 9.85641 0.357060
$$763$$ −3.46410 2.00000i −0.125409 0.0724049i
$$764$$ 3.46410 + 6.00000i 0.125327 + 0.217072i
$$765$$ 0 0
$$766$$ 1.46410 0.0529001
$$767$$ −27.7128 + 8.00000i −1.00065 + 0.288863i
$$768$$ 1.00000i 0.0360844i
$$769$$ −37.9808 + 21.9282i −1.36962 + 0.790751i −0.990879 0.134751i $$-0.956977\pi$$
−0.378742 + 0.925502i $$0.623643\pi$$
$$770$$ 0 0
$$771$$ 4.66987 8.08846i 0.168181 0.291299i
$$772$$ −11.7321 −0.422246
$$773$$ −24.4641 + 42.3731i −0.879913 + 1.52405i −0.0284768 + 0.999594i $$0.509066\pi$$
−0.851436 + 0.524459i $$0.824268\pi$$
$$774$$ −8.36603 4.83013i −0.300711 0.173615i
$$775$$ 0 0
$$776$$ 3.00000 5.19615i 0.107694 0.186531i
$$777$$ 8.36603 4.83013i 0.300129 0.173280i
$$778$$ −5.89230 10.2058i −0.211249 0.365895i
$$779$$ −44.4449 −1.59240
$$780$$ 0 0
$$781$$ 6.00000 0.214697
$$782$$ 12.0263 + 20.8301i 0.430059 + 0.744884i
$$783$$ 3.86603 2.23205i 0.138160