# Properties

 Label 390.2.s.a.77.3 Level $390$ Weight $2$ Character 390.77 Analytic conductor $3.114$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$390 = 2 \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 390.s (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.11416567883$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.40960000.1 Defining polynomial: $$x^{8} + 7x^{4} + 1$$ x^8 + 7*x^4 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 77.3 Root $$1.14412 + 1.14412i$$ of defining polynomial Character $$\chi$$ $$=$$ 390.77 Dual form 390.2.s.a.233.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-3.16228 + 3.16228i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +(-0.618034 - 1.61803i) q^{3} +1.00000i q^{4} +(0.707107 + 2.12132i) q^{5} +(0.707107 - 1.58114i) q^{6} +(-3.16228 + 3.16228i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.23607 + 2.00000i) q^{9} +(-1.00000 + 2.00000i) q^{10} -5.65685 q^{11} +(1.61803 - 0.618034i) q^{12} +(3.58114 - 0.418861i) q^{13} -4.47214 q^{14} +(2.99535 - 2.45517i) q^{15} -1.00000 q^{16} +(-2.23607 + 2.23607i) q^{17} +(-2.99535 - 0.166925i) q^{18} +6.32456 q^{19} +(-2.12132 + 0.707107i) q^{20} +(7.07107 + 3.16228i) q^{21} +(-4.00000 - 4.00000i) q^{22} +(1.58114 + 0.707107i) q^{24} +(-4.00000 + 3.00000i) q^{25} +(2.82843 + 2.23607i) q^{26} +(4.61803 + 2.38197i) q^{27} +(-3.16228 - 3.16228i) q^{28} +4.47214 q^{29} +(3.85410 + 0.381966i) q^{30} -3.16228i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.49613 + 9.15298i) q^{33} -3.16228 q^{34} +(-8.94427 - 4.47214i) q^{35} +(-2.00000 - 2.23607i) q^{36} +(-3.16228 + 3.16228i) q^{37} +(4.47214 + 4.47214i) q^{38} +(-2.89100 - 5.53553i) q^{39} +(-2.00000 - 1.00000i) q^{40} +5.65685 q^{41} +(2.76393 + 7.23607i) q^{42} +(-5.00000 + 5.00000i) q^{43} -5.65685i q^{44} +(-5.82378 - 3.32920i) q^{45} +(1.41421 + 1.41421i) q^{47} +(0.618034 + 1.61803i) q^{48} -13.0000i q^{49} +(-4.94975 - 0.707107i) q^{50} +(5.00000 + 2.23607i) q^{51} +(0.418861 + 3.58114i) q^{52} +(4.47214 + 4.47214i) q^{53} +(1.58114 + 4.94975i) q^{54} +(-4.00000 - 12.0000i) q^{55} -4.47214i q^{56} +(-3.90879 - 10.2333i) q^{57} +(3.16228 + 3.16228i) q^{58} -2.82843i q^{59} +(2.45517 + 2.99535i) q^{60} +10.0000 q^{61} +(2.23607 - 2.23607i) q^{62} +(0.746512 - 13.3956i) q^{63} -1.00000i q^{64} +(3.42079 + 7.30056i) q^{65} +(-4.00000 + 8.94427i) q^{66} +(-2.23607 - 2.23607i) q^{68} +(-3.16228 - 9.48683i) q^{70} -1.41421 q^{71} +(0.166925 - 2.99535i) q^{72} +(-3.16228 - 3.16228i) q^{73} -4.47214 q^{74} +(7.32624 + 4.61803i) q^{75} +6.32456i q^{76} +(17.8885 - 17.8885i) q^{77} +(1.86997 - 5.95846i) q^{78} +(-0.707107 - 2.12132i) q^{80} +(1.00000 - 8.94427i) q^{81} +(4.00000 + 4.00000i) q^{82} +(-2.82843 + 2.82843i) q^{83} +(-3.16228 + 7.07107i) q^{84} +(-6.32456 - 3.16228i) q^{85} -7.07107 q^{86} +(-2.76393 - 7.23607i) q^{87} +(4.00000 - 4.00000i) q^{88} +2.82843i q^{89} +(-1.76393 - 6.47214i) q^{90} +(-10.0000 + 12.6491i) q^{91} +(-5.11667 + 1.95440i) q^{93} +2.00000i q^{94} +(4.47214 + 13.4164i) q^{95} +(-0.707107 + 1.58114i) q^{96} +(-9.48683 + 9.48683i) q^{97} +(9.19239 - 9.19239i) q^{98} +(12.6491 - 11.3137i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{3}+O(q^{10})$$ 8 * q + 4 * q^3 $$8 q + 4 q^{3} - 8 q^{10} + 4 q^{12} + 16 q^{13} - 8 q^{16} - 32 q^{22} - 32 q^{25} + 28 q^{27} + 4 q^{30} - 16 q^{36} - 16 q^{40} + 40 q^{42} - 40 q^{43} - 4 q^{48} + 40 q^{51} + 16 q^{52} - 32 q^{55} + 80 q^{61} - 32 q^{66} - 4 q^{75} + 20 q^{78} + 8 q^{81} + 32 q^{82} - 40 q^{87} + 32 q^{88} - 32 q^{90} - 80 q^{91}+O(q^{100})$$ 8 * q + 4 * q^3 - 8 * q^10 + 4 * q^12 + 16 * q^13 - 8 * q^16 - 32 * q^22 - 32 * q^25 + 28 * q^27 + 4 * q^30 - 16 * q^36 - 16 * q^40 + 40 * q^42 - 40 * q^43 - 4 * q^48 + 40 * q^51 + 16 * q^52 - 32 * q^55 + 80 * q^61 - 32 * q^66 - 4 * q^75 + 20 * q^78 + 8 * q^81 + 32 * q^82 - 40 * q^87 + 32 * q^88 - 32 * q^90 - 80 * q^91

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$$.

 $$n$$ $$131$$ $$157$$ $$301$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.500000 + 0.500000i
$$3$$ −0.618034 1.61803i −0.356822 0.934172i
$$4$$ 1.00000i 0.500000i
$$5$$ 0.707107 + 2.12132i 0.316228 + 0.948683i
$$6$$ 0.707107 1.58114i 0.288675 0.645497i
$$7$$ −3.16228 + 3.16228i −1.19523 + 1.19523i −0.219650 + 0.975579i $$0.570491\pi$$
−0.975579 + 0.219650i $$0.929509\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ −2.23607 + 2.00000i −0.745356 + 0.666667i
$$10$$ −1.00000 + 2.00000i −0.316228 + 0.632456i
$$11$$ −5.65685 −1.70561 −0.852803 0.522233i $$-0.825099\pi$$
−0.852803 + 0.522233i $$0.825099\pi$$
$$12$$ 1.61803 0.618034i 0.467086 0.178411i
$$13$$ 3.58114 0.418861i 0.993229 0.116171i
$$14$$ −4.47214 −1.19523
$$15$$ 2.99535 2.45517i 0.773397 0.633922i
$$16$$ −1.00000 −0.250000
$$17$$ −2.23607 + 2.23607i −0.542326 + 0.542326i −0.924210 0.381884i $$-0.875275\pi$$
0.381884 + 0.924210i $$0.375275\pi$$
$$18$$ −2.99535 0.166925i −0.706011 0.0393447i
$$19$$ 6.32456 1.45095 0.725476 0.688247i $$-0.241620\pi$$
0.725476 + 0.688247i $$0.241620\pi$$
$$20$$ −2.12132 + 0.707107i −0.474342 + 0.158114i
$$21$$ 7.07107 + 3.16228i 1.54303 + 0.690066i
$$22$$ −4.00000 4.00000i −0.852803 0.852803i
$$23$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$24$$ 1.58114 + 0.707107i 0.322749 + 0.144338i
$$25$$ −4.00000 + 3.00000i −0.800000 + 0.600000i
$$26$$ 2.82843 + 2.23607i 0.554700 + 0.438529i
$$27$$ 4.61803 + 2.38197i 0.888741 + 0.458410i
$$28$$ −3.16228 3.16228i −0.597614 0.597614i
$$29$$ 4.47214 0.830455 0.415227 0.909718i $$-0.363702\pi$$
0.415227 + 0.909718i $$0.363702\pi$$
$$30$$ 3.85410 + 0.381966i 0.703660 + 0.0697371i
$$31$$ 3.16228i 0.567962i −0.958830 0.283981i $$-0.908345\pi$$
0.958830 0.283981i $$-0.0916552\pi$$
$$32$$ −0.707107 0.707107i −0.125000 0.125000i
$$33$$ 3.49613 + 9.15298i 0.608598 + 1.59333i
$$34$$ −3.16228 −0.542326
$$35$$ −8.94427 4.47214i −1.51186 0.755929i
$$36$$ −2.00000 2.23607i −0.333333 0.372678i
$$37$$ −3.16228 + 3.16228i −0.519875 + 0.519875i −0.917534 0.397658i $$-0.869823\pi$$
0.397658 + 0.917534i $$0.369823\pi$$
$$38$$ 4.47214 + 4.47214i 0.725476 + 0.725476i
$$39$$ −2.89100 5.53553i −0.462930 0.886395i
$$40$$ −2.00000 1.00000i −0.316228 0.158114i
$$41$$ 5.65685 0.883452 0.441726 0.897150i $$-0.354366\pi$$
0.441726 + 0.897150i $$0.354366\pi$$
$$42$$ 2.76393 + 7.23607i 0.426484 + 1.11655i
$$43$$ −5.00000 + 5.00000i −0.762493 + 0.762493i −0.976772 0.214280i $$-0.931260\pi$$
0.214280 + 0.976772i $$0.431260\pi$$
$$44$$ 5.65685i 0.852803i
$$45$$ −5.82378 3.32920i −0.868158 0.496288i
$$46$$ 0 0
$$47$$ 1.41421 + 1.41421i 0.206284 + 0.206284i 0.802686 0.596402i $$-0.203403\pi$$
−0.596402 + 0.802686i $$0.703403\pi$$
$$48$$ 0.618034 + 1.61803i 0.0892055 + 0.233543i
$$49$$ 13.0000i 1.85714i
$$50$$ −4.94975 0.707107i −0.700000 0.100000i
$$51$$ 5.00000 + 2.23607i 0.700140 + 0.313112i
$$52$$ 0.418861 + 3.58114i 0.0580856 + 0.496615i
$$53$$ 4.47214 + 4.47214i 0.614295 + 0.614295i 0.944062 0.329767i $$-0.106970\pi$$
−0.329767 + 0.944062i $$0.606970\pi$$
$$54$$ 1.58114 + 4.94975i 0.215166 + 0.673575i
$$55$$ −4.00000 12.0000i −0.539360 1.61808i
$$56$$ 4.47214i 0.597614i
$$57$$ −3.90879 10.2333i −0.517732 1.35544i
$$58$$ 3.16228 + 3.16228i 0.415227 + 0.415227i
$$59$$ 2.82843i 0.368230i −0.982905 0.184115i $$-0.941058\pi$$
0.982905 0.184115i $$-0.0589419\pi$$
$$60$$ 2.45517 + 2.99535i 0.316961 + 0.386698i
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 2.23607 2.23607i 0.283981 0.283981i
$$63$$ 0.746512 13.3956i 0.0940517 1.68769i
$$64$$ 1.00000i 0.125000i
$$65$$ 3.42079 + 7.30056i 0.424296 + 0.905523i
$$66$$ −4.00000 + 8.94427i −0.492366 + 1.10096i
$$67$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$68$$ −2.23607 2.23607i −0.271163 0.271163i
$$69$$ 0 0
$$70$$ −3.16228 9.48683i −0.377964 1.13389i
$$71$$ −1.41421 −0.167836 −0.0839181 0.996473i $$-0.526743\pi$$
−0.0839181 + 0.996473i $$0.526743\pi$$
$$72$$ 0.166925 2.99535i 0.0196723 0.353006i
$$73$$ −3.16228 3.16228i −0.370117 0.370117i 0.497403 0.867520i $$-0.334287\pi$$
−0.867520 + 0.497403i $$0.834287\pi$$
$$74$$ −4.47214 −0.519875
$$75$$ 7.32624 + 4.61803i 0.845961 + 0.533245i
$$76$$ 6.32456i 0.725476i
$$77$$ 17.8885 17.8885i 2.03859 2.03859i
$$78$$ 1.86997 5.95846i 0.211732 0.674662i
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ −0.707107 2.12132i −0.0790569 0.237171i
$$81$$ 1.00000 8.94427i 0.111111 0.993808i
$$82$$ 4.00000 + 4.00000i 0.441726 + 0.441726i
$$83$$ −2.82843 + 2.82843i −0.310460 + 0.310460i −0.845088 0.534628i $$-0.820452\pi$$
0.534628 + 0.845088i $$0.320452\pi$$
$$84$$ −3.16228 + 7.07107i −0.345033 + 0.771517i
$$85$$ −6.32456 3.16228i −0.685994 0.342997i
$$86$$ −7.07107 −0.762493
$$87$$ −2.76393 7.23607i −0.296325 0.775788i
$$88$$ 4.00000 4.00000i 0.426401 0.426401i
$$89$$ 2.82843i 0.299813i 0.988700 + 0.149906i $$0.0478972\pi$$
−0.988700 + 0.149906i $$0.952103\pi$$
$$90$$ −1.76393 6.47214i −0.185935 0.682223i
$$91$$ −10.0000 + 12.6491i −1.04828 + 1.32599i
$$92$$ 0 0
$$93$$ −5.11667 + 1.95440i −0.530574 + 0.202661i
$$94$$ 2.00000i 0.206284i
$$95$$ 4.47214 + 13.4164i 0.458831 + 1.37649i
$$96$$ −0.707107 + 1.58114i −0.0721688 + 0.161374i
$$97$$ −9.48683 + 9.48683i −0.963242 + 0.963242i −0.999348 0.0361060i $$-0.988505\pi$$
0.0361060 + 0.999348i $$0.488505\pi$$
$$98$$ 9.19239 9.19239i 0.928571 0.928571i
$$99$$ 12.6491 11.3137i 1.27128 1.13707i
$$100$$ −3.00000 4.00000i −0.300000 0.400000i
$$101$$ 4.47214i 0.444994i −0.974933 0.222497i $$-0.928579\pi$$
0.974933 0.222497i $$-0.0714208\pi$$
$$102$$ 1.95440 + 5.11667i 0.193514 + 0.506626i
$$103$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$104$$ −2.23607 + 2.82843i −0.219265 + 0.277350i
$$105$$ −1.70820 + 17.2361i −0.166704 + 1.68207i
$$106$$ 6.32456i 0.614295i
$$107$$ 2.23607 2.23607i 0.216169 0.216169i −0.590713 0.806882i $$-0.701153\pi$$
0.806882 + 0.590713i $$0.201153\pi$$
$$108$$ −2.38197 + 4.61803i −0.229205 + 0.444371i
$$109$$ −3.16228 −0.302891 −0.151446 0.988466i $$-0.548393\pi$$
−0.151446 + 0.988466i $$0.548393\pi$$
$$110$$ 5.65685 11.3137i 0.539360 1.07872i
$$111$$ 7.07107 + 3.16228i 0.671156 + 0.300150i
$$112$$ 3.16228 3.16228i 0.298807 0.298807i
$$113$$ 6.70820 + 6.70820i 0.631055 + 0.631055i 0.948333 0.317278i $$-0.102769\pi$$
−0.317278 + 0.948333i $$0.602769\pi$$
$$114$$ 4.47214 10.0000i 0.418854 0.936586i
$$115$$ 0 0
$$116$$ 4.47214i 0.415227i
$$117$$ −7.16995 + 8.09888i −0.662862 + 0.748742i
$$118$$ 2.00000 2.00000i 0.184115 0.184115i
$$119$$ 14.1421i 1.29641i
$$120$$ −0.381966 + 3.85410i −0.0348686 + 0.351830i
$$121$$ 21.0000 1.90909
$$122$$ 7.07107 + 7.07107i 0.640184 + 0.640184i
$$123$$ −3.49613 9.15298i −0.315235 0.825297i
$$124$$ 3.16228 0.283981
$$125$$ −9.19239 6.36396i −0.822192 0.569210i
$$126$$ 10.0000 8.94427i 0.890871 0.796819i
$$127$$ −2.00000 2.00000i −0.177471 0.177471i 0.612781 0.790253i $$-0.290051\pi$$
−0.790253 + 0.612781i $$0.790051\pi$$
$$128$$ 0.707107 0.707107i 0.0625000 0.0625000i
$$129$$ 11.1803 + 5.00000i 0.984374 + 0.440225i
$$130$$ −2.74342 + 7.58114i −0.240614 + 0.664910i
$$131$$ 17.8885i 1.56293i 0.623949 + 0.781465i $$0.285527\pi$$
−0.623949 + 0.781465i $$0.714473\pi$$
$$132$$ −9.15298 + 3.49613i −0.796665 + 0.304299i
$$133$$ −20.0000 + 20.0000i −1.73422 + 1.73422i
$$134$$ 0 0
$$135$$ −1.78747 + 11.4806i −0.153841 + 0.988096i
$$136$$ 3.16228i 0.271163i
$$137$$ 12.7279 + 12.7279i 1.08742 + 1.08742i 0.995793 + 0.0916263i $$0.0292065\pi$$
0.0916263 + 0.995793i $$0.470793\pi$$
$$138$$ 0 0
$$139$$ 4.00000i 0.339276i −0.985506 0.169638i $$-0.945740\pi$$
0.985506 0.169638i $$-0.0542598\pi$$
$$140$$ 4.47214 8.94427i 0.377964 0.755929i
$$141$$ 1.41421 3.16228i 0.119098 0.266312i
$$142$$ −1.00000 1.00000i −0.0839181 0.0839181i
$$143$$ −20.2580 + 2.36944i −1.69406 + 0.198142i
$$144$$ 2.23607 2.00000i 0.186339 0.166667i
$$145$$ 3.16228 + 9.48683i 0.262613 + 0.787839i
$$146$$ 4.47214i 0.370117i
$$147$$ −21.0344 + 8.03444i −1.73489 + 0.662670i
$$148$$ −3.16228 3.16228i −0.259938 0.259938i
$$149$$ 4.24264i 0.347571i 0.984784 + 0.173785i $$0.0555999\pi$$
−0.984784 + 0.173785i $$0.944400\pi$$
$$150$$ 1.91499 + 8.44588i 0.156358 + 0.689603i
$$151$$ 22.1359i 1.80140i −0.434444 0.900699i $$-0.643055\pi$$
0.434444 0.900699i $$-0.356945\pi$$
$$152$$ −4.47214 + 4.47214i −0.362738 + 0.362738i
$$153$$ 0.527864 9.47214i 0.0426753 0.765777i
$$154$$ 25.2982 2.03859
$$155$$ 6.70820 2.23607i 0.538816 0.179605i
$$156$$ 5.53553 2.89100i 0.443197 0.231465i
$$157$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$158$$ 0 0
$$159$$ 4.47214 10.0000i 0.354663 0.793052i
$$160$$ 1.00000 2.00000i 0.0790569 0.158114i
$$161$$ 0 0
$$162$$ 7.03166 5.61745i 0.552460 0.441348i
$$163$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$164$$ 5.65685i 0.441726i
$$165$$ −16.9443 + 13.8885i −1.31911 + 1.08122i
$$166$$ −4.00000 −0.310460
$$167$$ 12.7279 + 12.7279i 0.984916 + 0.984916i 0.999888 0.0149717i $$-0.00476583\pi$$
−0.0149717 + 0.999888i $$0.504766\pi$$
$$168$$ −7.23607 + 2.76393i −0.558275 + 0.213242i
$$169$$ 12.6491 3.00000i 0.973009 0.230769i
$$170$$ −2.23607 6.70820i −0.171499 0.514496i
$$171$$ −14.1421 + 12.6491i −1.08148 + 0.967302i
$$172$$ −5.00000 5.00000i −0.381246 0.381246i
$$173$$ −13.4164 13.4164i −1.02003 1.02003i −0.999795 0.0202354i $$-0.993558\pi$$
−0.0202354 0.999795i $$-0.506442\pi$$
$$174$$ 3.16228 7.07107i 0.239732 0.536056i
$$175$$ 3.16228 22.1359i 0.239046 1.67332i
$$176$$ 5.65685 0.426401
$$177$$ −4.57649 + 1.74806i −0.343990 + 0.131393i
$$178$$ −2.00000 + 2.00000i −0.149906 + 0.149906i
$$179$$ 17.8885 1.33705 0.668526 0.743689i $$-0.266925\pi$$
0.668526 + 0.743689i $$0.266925\pi$$
$$180$$ 3.32920 5.82378i 0.248144 0.434079i
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ −16.0153 + 1.87320i −1.18714 + 0.138851i
$$183$$ −6.18034 16.1803i −0.456864 1.19609i
$$184$$ 0 0
$$185$$ −8.94427 4.47214i −0.657596 0.328798i
$$186$$ −5.00000 2.23607i −0.366618 0.163956i
$$187$$ 12.6491 12.6491i 0.924995 0.924995i
$$188$$ −1.41421 + 1.41421i −0.103142 + 0.103142i
$$189$$ −22.1359 + 7.07107i −1.61015 + 0.514344i
$$190$$ −6.32456 + 12.6491i −0.458831 + 0.917663i
$$191$$ 8.94427i 0.647185i −0.946197 0.323592i $$-0.895109\pi$$
0.946197 0.323592i $$-0.104891\pi$$
$$192$$ −1.61803 + 0.618034i −0.116772 + 0.0446028i
$$193$$ −9.48683 9.48683i −0.682877 0.682877i 0.277770 0.960648i $$-0.410405\pi$$
−0.960648 + 0.277770i $$0.910405\pi$$
$$194$$ −13.4164 −0.963242
$$195$$ 9.69840 10.0469i 0.694517 0.719477i
$$196$$ 13.0000 0.928571
$$197$$ 1.41421 + 1.41421i 0.100759 + 0.100759i 0.755689 0.654931i $$-0.227302\pi$$
−0.654931 + 0.755689i $$0.727302\pi$$
$$198$$ 16.9443 + 0.944272i 1.20418 + 0.0671065i
$$199$$ 20.0000i 1.41776i 0.705328 + 0.708881i $$0.250800\pi$$
−0.705328 + 0.708881i $$0.749200\pi$$
$$200$$ 0.707107 4.94975i 0.0500000 0.350000i
$$201$$ 0 0
$$202$$ 3.16228 3.16228i 0.222497 0.222497i
$$203$$ −14.1421 + 14.1421i −0.992583 + 0.992583i
$$204$$ −2.23607 + 5.00000i −0.156556 + 0.350070i
$$205$$ 4.00000 + 12.0000i 0.279372 + 0.838116i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −3.58114 + 0.418861i −0.248307 + 0.0290428i
$$209$$ −35.7771 −2.47475
$$210$$ −13.3956 + 10.9799i −0.924386 + 0.757682i
$$211$$ 20.0000 1.37686 0.688428 0.725304i $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ −4.47214 + 4.47214i −0.307148 + 0.307148i
$$213$$ 0.874032 + 2.28825i 0.0598877 + 0.156788i
$$214$$ 3.16228 0.216169
$$215$$ −14.1421 7.07107i −0.964486 0.482243i
$$216$$ −4.94975 + 1.58114i −0.336788 + 0.107583i
$$217$$ 10.0000 + 10.0000i 0.678844 + 0.678844i
$$218$$ −2.23607 2.23607i −0.151446 0.151446i
$$219$$ −3.16228 + 7.07107i −0.213687 + 0.477818i
$$220$$ 12.0000 4.00000i 0.809040 0.269680i
$$221$$ −7.07107 + 8.94427i −0.475651 + 0.601657i
$$222$$ 2.76393 + 7.23607i 0.185503 + 0.485653i
$$223$$ 18.9737 + 18.9737i 1.27057 + 1.27057i 0.945789 + 0.324782i $$0.105291\pi$$
0.324782 + 0.945789i $$0.394709\pi$$
$$224$$ 4.47214 0.298807
$$225$$ 2.94427 14.7082i 0.196285 0.980547i
$$226$$ 9.48683i 0.631055i
$$227$$ −8.48528 8.48528i −0.563188 0.563188i 0.367024 0.930212i $$-0.380377\pi$$
−0.930212 + 0.367024i $$0.880377\pi$$
$$228$$ 10.2333 3.90879i 0.677720 0.258866i
$$229$$ −9.48683 −0.626908 −0.313454 0.949603i $$-0.601486\pi$$
−0.313454 + 0.949603i $$0.601486\pi$$
$$230$$ 0 0
$$231$$ −40.0000 17.8885i −2.63181 1.17698i
$$232$$ −3.16228 + 3.16228i −0.207614 + 0.207614i
$$233$$ −2.23607 2.23607i −0.146490 0.146490i 0.630058 0.776548i $$-0.283031\pi$$
−0.776548 + 0.630058i $$0.783031\pi$$
$$234$$ −10.7967 + 0.656854i −0.705802 + 0.0429399i
$$235$$ −2.00000 + 4.00000i −0.130466 + 0.260931i
$$236$$ 2.82843 0.184115
$$237$$ 0 0
$$238$$ 10.0000 10.0000i 0.648204 0.648204i
$$239$$ 4.24264i 0.274434i 0.990541 + 0.137217i $$0.0438157\pi$$
−0.990541 + 0.137217i $$0.956184\pi$$
$$240$$ −2.99535 + 2.45517i −0.193349 + 0.158481i
$$241$$ 12.6491i 0.814801i 0.913250 + 0.407400i $$0.133565\pi$$
−0.913250 + 0.407400i $$0.866435\pi$$
$$242$$ 14.8492 + 14.8492i 0.954545 + 0.954545i
$$243$$ −15.0902 + 3.90983i −0.968035 + 0.250816i
$$244$$ 10.0000i 0.640184i
$$245$$ 27.5772 9.19239i 1.76184 0.587280i
$$246$$ 4.00000 8.94427i 0.255031 0.570266i
$$247$$ 22.6491 2.64911i 1.44113 0.168559i
$$248$$ 2.23607 + 2.23607i 0.141990 + 0.141990i
$$249$$ 6.32456 + 2.82843i 0.400802 + 0.179244i
$$250$$ −2.00000 11.0000i −0.126491 0.695701i
$$251$$ 17.8885i 1.12911i 0.825394 + 0.564557i $$0.190953\pi$$
−0.825394 + 0.564557i $$0.809047\pi$$
$$252$$ 13.3956 + 0.746512i 0.843845 + 0.0470259i
$$253$$ 0 0
$$254$$ 2.82843i 0.177471i
$$255$$ −1.20788 + 12.1877i −0.0756405 + 0.763226i
$$256$$ 1.00000 0.0625000
$$257$$ 20.1246 20.1246i 1.25534 1.25534i 0.302045 0.953294i $$-0.402331\pi$$
0.953294 0.302045i $$-0.0976694\pi$$
$$258$$ 4.37016 + 11.4412i 0.272074 + 0.712300i
$$259$$ 20.0000i 1.24274i
$$260$$ −7.30056 + 3.42079i −0.452762 + 0.212148i
$$261$$ −10.0000 + 8.94427i −0.618984 + 0.553637i
$$262$$ −12.6491 + 12.6491i −0.781465 + 0.781465i
$$263$$ 8.94427 + 8.94427i 0.551527 + 0.551527i 0.926882 0.375354i $$-0.122479\pi$$
−0.375354 + 0.926882i $$0.622479\pi$$
$$264$$ −8.94427 4.00000i −0.550482 0.246183i
$$265$$ −6.32456 + 12.6491i −0.388514 + 0.777029i
$$266$$ −28.2843 −1.73422
$$267$$ 4.57649 1.74806i 0.280077 0.106980i
$$268$$ 0 0
$$269$$ 22.3607 1.36335 0.681677 0.731653i $$-0.261251\pi$$
0.681677 + 0.731653i $$0.261251\pi$$
$$270$$ −9.38197 + 6.85410i −0.570968 + 0.417127i
$$271$$ 9.48683i 0.576284i −0.957588 0.288142i $$-0.906962\pi$$
0.957588 0.288142i $$-0.0930375\pi$$
$$272$$ 2.23607 2.23607i 0.135582 0.135582i
$$273$$ 26.6470 + 8.36276i 1.61275 + 0.506137i
$$274$$ 18.0000i 1.08742i
$$275$$ 22.6274 16.9706i 1.36448 1.02336i
$$276$$ 0 0
$$277$$ 10.0000 + 10.0000i 0.600842 + 0.600842i 0.940536 0.339694i $$-0.110324\pi$$
−0.339694 + 0.940536i $$0.610324\pi$$
$$278$$ 2.82843 2.82843i 0.169638 0.169638i
$$279$$ 6.32456 + 7.07107i 0.378641 + 0.423334i
$$280$$ 9.48683 3.16228i 0.566947 0.188982i
$$281$$ 8.48528 0.506189 0.253095 0.967442i $$-0.418552\pi$$
0.253095 + 0.967442i $$0.418552\pi$$
$$282$$ 3.23607 1.23607i 0.192705 0.0736068i
$$283$$ 9.00000 9.00000i 0.534994 0.534994i −0.387060 0.922055i $$-0.626509\pi$$
0.922055 + 0.387060i $$0.126509\pi$$
$$284$$ 1.41421i 0.0839181i
$$285$$ 18.9443 15.5279i 1.12216 0.919791i
$$286$$ −16.0000 12.6491i −0.946100 0.747958i
$$287$$ −17.8885 + 17.8885i −1.05593 + 1.05593i
$$288$$ 2.99535 + 0.166925i 0.176503 + 0.00983617i
$$289$$ 7.00000i 0.411765i
$$290$$ −4.47214 + 8.94427i −0.262613 + 0.525226i
$$291$$ 21.2132 + 9.48683i 1.24354 + 0.556128i
$$292$$ 3.16228 3.16228i 0.185058 0.185058i
$$293$$ −11.3137 + 11.3137i −0.660954 + 0.660954i −0.955605 0.294651i $$-0.904797\pi$$
0.294651 + 0.955605i $$0.404797\pi$$
$$294$$ −20.5548 9.19239i −1.19878 0.536111i
$$295$$ 6.00000 2.00000i 0.349334 0.116445i
$$296$$ 4.47214i 0.259938i
$$297$$ −26.1235 13.4744i −1.51584 0.781866i
$$298$$ −3.00000 + 3.00000i −0.173785 + 0.173785i
$$299$$ 0 0
$$300$$ −4.61803 + 7.32624i −0.266622 + 0.422981i
$$301$$ 31.6228i 1.82271i
$$302$$ 15.6525 15.6525i 0.900699 0.900699i
$$303$$ −7.23607 + 2.76393i −0.415701 + 0.158784i
$$304$$ −6.32456 −0.362738
$$305$$ 7.07107 + 21.2132i 0.404888 + 1.21466i
$$306$$ 7.07107 6.32456i 0.404226 0.361551i
$$307$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$308$$ 17.8885 + 17.8885i 1.01929 + 1.01929i
$$309$$ 0 0
$$310$$ 6.32456 + 3.16228i 0.359211 + 0.179605i
$$311$$ 8.94427i 0.507183i −0.967311 0.253592i $$-0.918388\pi$$
0.967311 0.253592i $$-0.0816119\pi$$
$$312$$ 5.95846 + 1.86997i 0.337331 + 0.105866i
$$313$$ −1.00000 + 1.00000i −0.0565233 + 0.0565233i −0.734803 0.678280i $$-0.762726\pi$$
0.678280 + 0.734803i $$0.262726\pi$$
$$314$$ 0 0
$$315$$ 28.9443 7.88854i 1.63082 0.444469i
$$316$$ 0 0
$$317$$ −19.7990 19.7990i −1.11202 1.11202i −0.992877 0.119145i $$-0.961985\pi$$
−0.119145 0.992877i $$-0.538015\pi$$
$$318$$ 10.2333 3.90879i 0.573858 0.219194i
$$319$$ −25.2982 −1.41643
$$320$$ 2.12132 0.707107i 0.118585 0.0395285i
$$321$$ −5.00000 2.23607i −0.279073 0.124805i
$$322$$ 0 0
$$323$$ −14.1421 + 14.1421i −0.786889 + 0.786889i
$$324$$ 8.94427 + 1.00000i 0.496904 + 0.0555556i
$$325$$ −13.0680 + 12.4189i −0.724881 + 0.688874i
$$326$$ 0 0
$$327$$ 1.95440 + 5.11667i 0.108078 + 0.282953i
$$328$$ −4.00000 + 4.00000i −0.220863 + 0.220863i
$$329$$ −8.94427 −0.493114
$$330$$ −21.8021 2.16073i −1.20017 0.118944i
$$331$$ 12.6491i 0.695258i 0.937632 + 0.347629i $$0.113013\pi$$
−0.937632 + 0.347629i $$0.886987\pi$$
$$332$$ −2.82843 2.82843i −0.155230 0.155230i
$$333$$ 0.746512 13.3956i 0.0409086 0.734076i
$$334$$ 18.0000i 0.984916i
$$335$$ 0 0
$$336$$ −7.07107 3.16228i −0.385758 0.172516i
$$337$$ −13.0000 13.0000i −0.708155 0.708155i 0.257992 0.966147i $$-0.416939\pi$$
−0.966147 + 0.257992i $$0.916939\pi$$
$$338$$ 11.0656 + 6.82295i 0.601889 + 0.371120i
$$339$$ 6.70820 15.0000i 0.364340 0.814688i
$$340$$ 3.16228 6.32456i 0.171499 0.342997i
$$341$$ 17.8885i 0.968719i
$$342$$ −18.9443 1.05573i −1.02439 0.0570872i
$$343$$ 18.9737 + 18.9737i 1.02448 + 1.02448i
$$344$$ 7.07107i 0.381246i
$$345$$ 0 0
$$346$$ 18.9737i 1.02003i
$$347$$ −20.1246 + 20.1246i −1.08035 + 1.08035i −0.0838690 + 0.996477i $$0.526728\pi$$
−0.996477 + 0.0838690i $$0.973272\pi$$
$$348$$ 7.23607 2.76393i 0.387894 0.148162i
$$349$$ −3.16228 −0.169273 −0.0846364 0.996412i $$-0.526973\pi$$
−0.0846364 + 0.996412i $$0.526973\pi$$
$$350$$ 17.8885 13.4164i 0.956183 0.717137i
$$351$$ 17.5355 + 6.59584i 0.935978 + 0.352060i
$$352$$ 4.00000 + 4.00000i 0.213201 + 0.213201i
$$353$$ 9.89949 9.89949i 0.526897 0.526897i −0.392749 0.919646i $$-0.628476\pi$$
0.919646 + 0.392749i $$0.128476\pi$$
$$354$$ −4.47214 2.00000i −0.237691 0.106299i
$$355$$ −1.00000 3.00000i −0.0530745 0.159223i
$$356$$ −2.82843 −0.149906
$$357$$ −22.8825 + 8.74032i −1.21107 + 0.462587i
$$358$$ 12.6491 + 12.6491i 0.668526 + 0.668526i
$$359$$ 32.5269i 1.71670i −0.513061 0.858352i $$-0.671488\pi$$
0.513061 0.858352i $$-0.328512\pi$$
$$360$$ 6.47214 1.76393i 0.341112 0.0929674i
$$361$$ 21.0000 1.10526
$$362$$ −15.5563 15.5563i −0.817624 0.817624i
$$363$$ −12.9787 33.9787i −0.681206 1.78342i
$$364$$ −12.6491 10.0000i −0.662994 0.524142i
$$365$$ 4.47214 8.94427i 0.234082 0.468165i
$$366$$ 7.07107 15.8114i 0.369611 0.826475i
$$367$$ −20.0000 20.0000i −1.04399 1.04399i −0.998987 0.0450047i $$-0.985670\pi$$
−0.0450047 0.998987i $$-0.514330\pi$$
$$368$$ 0 0
$$369$$ −12.6491 + 11.3137i −0.658486 + 0.588968i
$$370$$ −3.16228 9.48683i −0.164399 0.493197i
$$371$$ −28.2843 −1.46845
$$372$$ −1.95440 5.11667i −0.101331 0.265287i
$$373$$ 16.0000 16.0000i 0.828449 0.828449i −0.158854 0.987302i $$-0.550780\pi$$
0.987302 + 0.158854i $$0.0507798\pi$$
$$374$$ 17.8885 0.924995
$$375$$ −4.61590 + 18.8067i −0.238364 + 0.971176i
$$376$$ −2.00000 −0.103142
$$377$$ 16.0153 1.87320i 0.824832 0.0964749i
$$378$$ −20.6525 10.6525i −1.06225 0.547904i
$$379$$ −6.32456 −0.324871 −0.162435 0.986719i $$-0.551935\pi$$
−0.162435 + 0.986719i $$0.551935\pi$$
$$380$$ −13.4164 + 4.47214i −0.688247 + 0.229416i
$$381$$ −2.00000 + 4.47214i −0.102463 + 0.229114i
$$382$$ 6.32456 6.32456i 0.323592 0.323592i
$$383$$ 11.3137 11.3137i 0.578103 0.578103i −0.356277 0.934380i $$-0.615954\pi$$
0.934380 + 0.356277i $$0.115954\pi$$
$$384$$ −1.58114 0.707107i −0.0806872 0.0360844i
$$385$$ 50.5964 + 25.2982i 2.57863 + 1.28932i
$$386$$ 13.4164i 0.682877i
$$387$$ 1.18034 21.1803i 0.0600000 1.07666i
$$388$$ −9.48683 9.48683i −0.481621 0.481621i
$$389$$ −13.4164 −0.680239 −0.340119 0.940382i $$-0.610468\pi$$
−0.340119 + 0.940382i $$0.610468\pi$$
$$390$$ 13.9621 0.246460i 0.706997 0.0124800i
$$391$$ 0 0
$$392$$ 9.19239 + 9.19239i 0.464286 + 0.464286i
$$393$$ 28.9443 11.0557i 1.46005 0.557688i
$$394$$ 2.00000i 0.100759i
$$395$$ 0 0
$$396$$ 11.3137 + 12.6491i 0.568535 + 0.635642i
$$397$$ 25.2982 25.2982i 1.26968 1.26968i 0.323429 0.946252i $$-0.395164\pi$$
0.946252 0.323429i $$-0.104836\pi$$
$$398$$ −14.1421 + 14.1421i −0.708881 + 0.708881i
$$399$$ 44.7214 + 20.0000i 2.23887 + 1.00125i
$$400$$ 4.00000 3.00000i 0.200000 0.150000i
$$401$$ −8.48528 −0.423735 −0.211867 0.977298i $$-0.567954\pi$$
−0.211867 + 0.977298i $$0.567954\pi$$
$$402$$ 0 0
$$403$$ −1.32456 11.3246i −0.0659808 0.564116i
$$404$$ 4.47214 0.222497
$$405$$ 19.6808 4.20323i 0.977945 0.208860i
$$406$$ −20.0000 −0.992583
$$407$$ 17.8885 17.8885i 0.886702 0.886702i
$$408$$ −5.11667 + 1.95440i −0.253313 + 0.0967570i
$$409$$ −18.9737 −0.938187 −0.469094 0.883148i $$-0.655419\pi$$
−0.469094 + 0.883148i $$0.655419\pi$$
$$410$$ −5.65685 + 11.3137i −0.279372 + 0.558744i
$$411$$ 12.7279 28.4605i 0.627822 1.40385i
$$412$$ 0 0
$$413$$ 8.94427 + 8.94427i 0.440119 + 0.440119i
$$414$$ 0 0
$$415$$ −8.00000 4.00000i −0.392705 0.196352i
$$416$$ −2.82843 2.23607i −0.138675 0.109632i
$$417$$ −6.47214 + 2.47214i −0.316942 + 0.121061i
$$418$$ −25.2982 25.2982i −1.23738 1.23738i
$$419$$ 13.4164 0.655434 0.327717 0.944776i $$-0.393721\pi$$
0.327717 + 0.944776i $$0.393721\pi$$
$$420$$ −17.2361 1.70820i −0.841034 0.0833518i
$$421$$ 3.16228i 0.154120i −0.997026 0.0770600i $$-0.975447\pi$$
0.997026 0.0770600i $$-0.0245533\pi$$
$$422$$ 14.1421 + 14.1421i 0.688428 + 0.688428i
$$423$$ −5.99070 0.333851i −0.291278 0.0162324i
$$424$$ −6.32456 −0.307148
$$425$$ 2.23607 15.6525i 0.108465 0.759257i
$$426$$ −1.00000 + 2.23607i −0.0484502 + 0.108338i
$$427$$ −31.6228 + 31.6228i −1.53033 + 1.53033i
$$428$$ 2.23607 + 2.23607i 0.108084 + 0.108084i
$$429$$ 16.3539 + 31.3137i 0.789576 + 1.51184i
$$430$$ −5.00000 15.0000i −0.241121 0.723364i
$$431$$ 1.41421 0.0681203 0.0340601 0.999420i $$-0.489156\pi$$
0.0340601 + 0.999420i $$0.489156\pi$$
$$432$$ −4.61803 2.38197i −0.222185 0.114602i
$$433$$ 21.0000 21.0000i 1.00920 1.00920i 0.00923827 0.999957i $$-0.497059\pi$$
0.999957 0.00923827i $$-0.00294067\pi$$
$$434$$ 14.1421i 0.678844i
$$435$$ 13.3956 10.9799i 0.642271 0.526444i
$$436$$ 3.16228i 0.151446i
$$437$$ 0 0
$$438$$ −7.23607 + 2.76393i −0.345753 + 0.132066i
$$439$$ 16.0000i 0.763638i 0.924237 + 0.381819i $$0.124702\pi$$
−0.924237 + 0.381819i $$0.875298\pi$$
$$440$$ 11.3137 + 5.65685i 0.539360 + 0.269680i
$$441$$ 26.0000 + 29.0689i 1.23810 + 1.38423i
$$442$$ −11.3246 + 1.32456i −0.538654 + 0.0630027i
$$443$$ 11.1803 + 11.1803i 0.531194 + 0.531194i 0.920928 0.389734i $$-0.127433\pi$$
−0.389734 + 0.920928i $$0.627433\pi$$
$$444$$ −3.16228 + 7.07107i −0.150075 + 0.335578i
$$445$$ −6.00000 + 2.00000i −0.284427 + 0.0948091i
$$446$$ 26.8328i 1.27057i
$$447$$ 6.86474 2.62210i 0.324691 0.124021i
$$448$$ 3.16228 + 3.16228i 0.149404 + 0.149404i
$$449$$ 31.1127i 1.46830i −0.678988 0.734150i $$-0.737581\pi$$
0.678988 0.734150i $$-0.262419\pi$$
$$450$$ 12.4822 8.31836i 0.588416 0.392131i
$$451$$ −32.0000 −1.50682
$$452$$ −6.70820 + 6.70820i −0.315527 + 0.315527i
$$453$$ −35.8167 + 13.6808i −1.68282 + 0.642778i
$$454$$ 12.0000i 0.563188i
$$455$$ −33.9039 12.2689i −1.58944 0.575176i
$$456$$ 10.0000 + 4.47214i 0.468293 + 0.209427i
$$457$$ 22.1359 22.1359i 1.03548 1.03548i 0.0361286 0.999347i $$-0.488497\pi$$
0.999347 0.0361286i $$-0.0115026\pi$$
$$458$$ −6.70820 6.70820i −0.313454 0.313454i
$$459$$ −15.6525 + 5.00000i −0.730595 + 0.233380i
$$460$$ 0 0
$$461$$ 1.41421 0.0658665 0.0329332 0.999458i $$-0.489515\pi$$
0.0329332 + 0.999458i $$0.489515\pi$$
$$462$$ −15.6352 40.9334i −0.727414 1.90439i
$$463$$ 18.9737 + 18.9737i 0.881781 + 0.881781i 0.993716 0.111935i $$-0.0357047\pi$$
−0.111935 + 0.993716i $$0.535705\pi$$
$$464$$ −4.47214 −0.207614
$$465$$ −7.76393 9.47214i −0.360044 0.439260i
$$466$$ 3.16228i 0.146490i
$$467$$ −6.70820 + 6.70820i −0.310419 + 0.310419i −0.845072 0.534653i $$-0.820442\pi$$
0.534653 + 0.845072i $$0.320442\pi$$
$$468$$ −8.09888 7.16995i −0.374371 0.331431i
$$469$$ 0 0
$$470$$ −4.24264 + 1.41421i −0.195698 + 0.0652328i
$$471$$ 0 0
$$472$$ 2.00000 + 2.00000i 0.0920575 + 0.0920575i
$$473$$ 28.2843 28.2843i 1.30051 1.30051i
$$474$$ 0 0
$$475$$ −25.2982 + 18.9737i −1.16076 + 0.870572i
$$476$$ 14.1421 0.648204
$$477$$ −18.9443 1.05573i −0.867399 0.0483385i
$$478$$ −3.00000 + 3.00000i −0.137217 + 0.137217i
$$479$$ 18.3848i 0.840022i −0.907519 0.420011i $$-0.862026\pi$$
0.907519 0.420011i $$-0.137974\pi$$
$$480$$ −3.85410 0.381966i −0.175915 0.0174343i
$$481$$ −10.0000 + 12.6491i −0.455961 + 0.576750i
$$482$$ −8.94427 + 8.94427i −0.407400 + 0.407400i
$$483$$ 0 0
$$484$$ 21.0000i 0.954545i
$$485$$ −26.8328 13.4164i −1.21842 0.609208i
$$486$$ −13.4350 7.90569i −0.609425 0.358610i
$$487$$ 3.16228 3.16228i 0.143296 0.143296i −0.631819 0.775116i $$-0.717692\pi$$
0.775116 + 0.631819i $$0.217692\pi$$
$$488$$ −7.07107 + 7.07107i −0.320092 + 0.320092i
$$489$$ 0 0
$$490$$ 26.0000 + 13.0000i 1.17456 + 0.587280i
$$491$$ 22.3607i 1.00912i −0.863376 0.504562i $$-0.831654\pi$$
0.863376 0.504562i $$-0.168346\pi$$
$$492$$ 9.15298 3.49613i 0.412648 0.157618i
$$493$$ −10.0000 + 10.0000i −0.450377 + 0.450377i
$$494$$ 17.8885 + 14.1421i 0.804844 + 0.636285i
$$495$$ 32.9443 + 18.8328i 1.48073 + 0.846472i
$$496$$ 3.16228i 0.141990i
$$497$$ 4.47214 4.47214i 0.200603 0.200603i
$$498$$ 2.47214 + 6.47214i 0.110779 + 0.290023i
$$499$$ −12.6491 −0.566252 −0.283126 0.959083i $$-0.591371\pi$$
−0.283126 + 0.959083i $$0.591371\pi$$
$$500$$ 6.36396 9.19239i 0.284605 0.411096i
$$501$$ 12.7279 28.4605i 0.568642 1.27152i
$$502$$ −12.6491 + 12.6491i −0.564557 + 0.564557i
$$503$$ 4.47214 + 4.47214i 0.199403 + 0.199403i 0.799744 0.600341i $$-0.204969\pi$$
−0.600341 + 0.799744i $$0.704969\pi$$
$$504$$ 8.94427 + 10.0000i 0.398410 + 0.445435i
$$505$$ 9.48683 3.16228i 0.422159 0.140720i
$$506$$ 0 0
$$507$$ −12.6717 18.6126i −0.562769 0.826614i
$$508$$ 2.00000 2.00000i 0.0887357 0.0887357i
$$509$$ 24.0416i 1.06563i 0.846233 + 0.532813i $$0.178865\pi$$
−0.846233 + 0.532813i $$0.821135\pi$$
$$510$$ −9.47214 + 7.76393i −0.419433 + 0.343793i
$$511$$ 20.0000 0.884748
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ 29.2070 + 15.0649i 1.28952 + 0.665131i
$$514$$ 28.4605 1.25534
$$515$$ 0 0
$$516$$ −5.00000 + 11.1803i −0.220113 + 0.492187i
$$517$$ −8.00000 8.00000i −0.351840 0.351840i
$$518$$ 14.1421 14.1421i 0.621370 0.621370i
$$519$$ −13.4164 + 30.0000i −0.588915 + 1.31685i
$$520$$ −7.58114 2.74342i −0.332455 0.120307i
$$521$$ 26.8328i 1.17557i −0.809018 0.587784i $$-0.800001\pi$$
0.809018 0.587784i $$-0.199999\pi$$
$$522$$ −13.3956 0.746512i −0.586310 0.0326740i
$$523$$ −15.0000 + 15.0000i −0.655904 + 0.655904i −0.954408 0.298504i $$-0.903512\pi$$
0.298504 + 0.954408i $$0.403512\pi$$
$$524$$ −17.8885 −0.781465
$$525$$ −37.7711 + 8.56409i −1.64847 + 0.373768i
$$526$$ 12.6491i 0.551527i
$$527$$ 7.07107 + 7.07107i 0.308021 + 0.308021i
$$528$$ −3.49613 9.15298i −0.152149 0.398332i
$$529$$ 23.0000i 1.00000i
$$530$$ −13.4164 + 4.47214i −0.582772 + 0.194257i
$$531$$ 5.65685 + 6.32456i 0.245487 + 0.274462i
$$532$$ −20.0000 20.0000i −0.867110 0.867110i
$$533$$ 20.2580 2.36944i 0.877471 0.102632i
$$534$$ 4.47214 + 2.00000i 0.193528 + 0.0865485i
$$535$$ 6.32456 + 3.16228i 0.273434 + 0.136717i
$$536$$ 0 0
$$537$$ −11.0557 28.9443i −0.477090 1.24904i
$$538$$ 15.8114 + 15.8114i 0.681677 + 0.681677i
$$539$$ 73.5391i 3.16755i
$$540$$ −11.4806 1.78747i −0.494048 0.0769205i
$$541$$ 41.1096i 1.76744i 0.468016 + 0.883720i $$0.344969\pi$$
−0.468016 + 0.883720i $$0.655031\pi$$
$$542$$ 6.70820 6.70820i 0.288142 0.288142i
$$543$$ 13.5967 + 35.5967i 0.583492 + 1.52760i
$$544$$ 3.16228 0.135582
$$545$$ −2.23607 6.70820i −0.0957826 0.287348i
$$546$$ 12.9289 + 24.7557i 0.553307 + 1.05944i
$$547$$ 5.00000 + 5.00000i 0.213785 + 0.213785i 0.805873 0.592088i $$-0.201696\pi$$
−0.592088 + 0.805873i $$0.701696\pi$$
$$548$$ −12.7279 + 12.7279i −0.543710 + 0.543710i
$$549$$ −22.3607 + 20.0000i −0.954331 + 0.853579i
$$550$$ 28.0000 + 4.00000i 1.19392 + 0.170561i
$$551$$ 28.2843 1.20495
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 14.1421i 0.600842i
$$555$$ −1.70820 + 17.2361i −0.0725092 + 0.731630i
$$556$$ 4.00000 0.169638
$$557$$ 12.7279 + 12.7279i 0.539299 + 0.539299i 0.923323 0.384024i $$-0.125462\pi$$
−0.384024 + 0.923323i $$0.625462\pi$$
$$558$$ −0.527864 + 9.47214i −0.0223463 + 0.400987i
$$559$$ −15.8114 + 20.0000i −0.668750 + 0.845910i
$$560$$ 8.94427 + 4.47214i 0.377964 + 0.188982i
$$561$$ −28.2843 12.6491i −1.19416 0.534046i
$$562$$ 6.00000 + 6.00000i 0.253095 + 0.253095i
$$563$$ −20.1246 20.1246i −0.848151 0.848151i 0.141751 0.989902i $$-0.454727\pi$$
−0.989902 + 0.141751i $$0.954727\pi$$
$$564$$ 3.16228 + 1.41421i 0.133156 + 0.0595491i
$$565$$ −9.48683 + 18.9737i −0.399114 + 0.798228i
$$566$$ 12.7279 0.534994
$$567$$ 25.1220 + 31.4465i 1.05502 + 1.32063i
$$568$$ 1.00000 1.00000i 0.0419591 0.0419591i
$$569$$ −8.94427 −0.374963 −0.187482 0.982268i $$-0.560033\pi$$
−0.187482 + 0.982268i $$0.560033\pi$$
$$570$$ 24.3755 + 2.41577i 1.02098 + 0.101185i
$$571$$ −10.0000 −0.418487 −0.209243 0.977864i $$-0.567100\pi$$
−0.209243 + 0.977864i $$0.567100\pi$$
$$572$$ −2.36944 20.2580i −0.0990711 0.847029i
$$573$$ −14.4721 + 5.52786i −0.604582 + 0.230930i
$$574$$ −25.2982 −1.05593
$$575$$ 0 0
$$576$$ 2.00000 + 2.23607i 0.0833333 + 0.0931695i
$$577$$ 9.48683 9.48683i 0.394942 0.394942i −0.481503 0.876445i $$-0.659909\pi$$
0.876445 + 0.481503i $$0.159909\pi$$
$$578$$ −4.94975 + 4.94975i −0.205882 + 0.205882i
$$579$$ −9.48683 + 21.2132i −0.394259 + 0.881591i
$$580$$ −9.48683 + 3.16228i −0.393919 + 0.131306i
$$581$$ 17.8885i 0.742142i
$$582$$ 8.29180 + 21.7082i 0.343706 + 0.899834i
$$583$$ −25.2982 25.2982i −1.04775 1.04775i
$$584$$ 4.47214 0.185058
$$585$$ −22.2502 9.48298i −0.919934 0.392073i
$$586$$ −16.0000 −0.660954
$$587$$ −8.48528 8.48528i −0.350225 0.350225i 0.509968 0.860193i $$-0.329657\pi$$
−0.860193 + 0.509968i $$0.829657\pi$$
$$588$$ −8.03444 21.0344i −0.331335 0.867446i
$$589$$ 20.0000i 0.824086i
$$590$$ 5.65685 + 2.82843i 0.232889 + 0.116445i
$$591$$ 1.41421 3.16228i 0.0581730 0.130079i
$$592$$ 3.16228 3.16228i 0.129969 0.129969i
$$593$$ 4.24264 4.24264i 0.174224 0.174224i −0.614608 0.788833i $$-0.710686\pi$$
0.788833 + 0.614608i $$0.210686\pi$$
$$594$$ −8.94427 28.0000i −0.366988 1.14885i
$$595$$ 30.0000 10.0000i 1.22988 0.409960i
$$596$$ −4.24264 −0.173785
$$597$$ 32.3607 12.3607i 1.32443 0.505889i
$$598$$ 0 0
$$599$$ −8.94427 −0.365453 −0.182727 0.983164i $$-0.558492\pi$$
−0.182727 + 0.983164i $$0.558492\pi$$
$$600$$ −8.44588 + 1.91499i −0.344801 + 0.0781791i
$$601$$ −40.0000 −1.63163 −0.815817 0.578310i $$-0.803712\pi$$
−0.815817 + 0.578310i $$0.803712\pi$$
$$602$$ 22.3607 22.3607i 0.911353 0.911353i
$$603$$ 0 0
$$604$$ 22.1359 0.900699
$$605$$ 14.8492 + 44.5477i 0.603708 + 1.81112i
$$606$$ −7.07107 3.16228i −0.287242 0.128459i
$$607$$ 30.0000 + 30.0000i 1.21766 + 1.21766i 0.968448 + 0.249214i $$0.0801723\pi$$
0.249214 + 0.968448i $$0.419828\pi$$
$$608$$ −4.47214 4.47214i −0.181369 0.181369i
$$609$$ 31.6228 + 14.1421i 1.28142 + 0.573068i
$$610$$ −10.0000 + 20.0000i −0.404888 + 0.809776i
$$611$$ 5.65685 + 4.47214i 0.228852 + 0.180923i
$$612$$ 9.47214 + 0.527864i 0.382888 + 0.0213376i
$$613$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$614$$ 0 0
$$615$$ 16.9443 13.8885i 0.683259 0.560040i
$$616$$ 25.2982i 1.01929i
$$617$$ −12.7279 12.7279i −0.512407 0.512407i 0.402856 0.915263i $$-0.368017\pi$$
−0.915263 + 0.402856i $$0.868017\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 2.23607 + 6.70820i 0.0898027 + 0.269408i
$$621$$ 0 0
$$622$$ 6.32456 6.32456i 0.253592 0.253592i
$$623$$ −8.94427 8.94427i −0.358345 0.358345i
$$624$$ 2.89100 + 5.53553i 0.115733 + 0.221599i
$$625$$ 7.00000 24.0000i 0.280000 0.960000i
$$626$$ −1.41421 −0.0565233
$$627$$ 22.1115 + 57.8885i 0.883047 + 2.31185i
$$628$$ 0 0
$$629$$ 14.1421i 0.563884i
$$630$$ 26.0447 + 14.8886i 1.03765 + 0.593178i
$$631$$ 15.8114i 0.629441i −0.949184 0.314721i $$-0.898089\pi$$
0.949184 0.314721i $$-0.101911\pi$$
$$632$$ 0 0
$$633$$ −12.3607 32.3607i −0.491293 1.28622i
$$634$$ 28.0000i 1.11202i
$$635$$ 2.82843 5.65685i 0.112243 0.224485i
$$636$$ 10.0000 + 4.47214i 0.396526 + 0.177332i
$$637$$ −5.44520 46.5548i −0.215746 1.84457i
$$638$$ −17.8885 17.8885i −0.708214 0.708214i
$$639$$ 3.16228 2.82843i 0.125098 0.111891i
$$640$$ 2.00000 + 1.00000i 0.0790569 + 0.0395285i
$$641$$ 49.1935i 1.94303i 0.236986 + 0.971513i $$0.423841\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ −1.95440 5.11667i −0.0771338 0.201939i
$$643$$ −18.9737 18.9737i −0.748248 0.748248i 0.225902 0.974150i $$-0.427467\pi$$
−0.974150 + 0.225902i $$0.927467\pi$$
$$644$$ 0 0
$$645$$ −2.70091 + 27.2526i −0.106348 + 1.07307i
$$646$$ −20.0000 −0.786889
$$647$$ −22.3607 + 22.3607i −0.879089 + 0.879089i −0.993440 0.114351i $$-0.963521\pi$$
0.114351 + 0.993440i $$0.463521\pi$$
$$648$$ 5.61745 + 7.03166i 0.220674 + 0.276230i
$$649$$ 16.0000i 0.628055i
$$650$$ −18.0219 0.458991i −0.706878 0.0180031i
$$651$$ 10.0000 22.3607i 0.391931 0.876384i
$$652$$ 0 0
$$653$$ −17.8885 17.8885i −0.700033 0.700033i 0.264385 0.964417i $$-0.414831\pi$$
−0.964417 + 0.264385i $$0.914831\pi$$
$$654$$ −2.23607 + 5.00000i −0.0874372 + 0.195515i
$$655$$ −37.9473 + 12.6491i −1.48272 + 0.494242i
$$656$$ −5.65685 −0.220863
$$657$$ 13.3956 + 0.746512i 0.522613 + 0.0291242i
$$658$$ −6.32456 6.32456i −0.246557 0.246557i
$$659$$ −31.3050 −1.21947 −0.609734 0.792606i $$-0.708724\pi$$
−0.609734 + 0.792606i $$0.708724\pi$$
$$660$$ −13.8885 16.9443i −0.540611 0.659555i
$$661$$ 41.1096i 1.59898i −0.600680 0.799489i $$-0.705104\pi$$
0.600680 0.799489i $$-0.294896\pi$$
$$662$$ −8.94427 + 8.94427i −0.347629 + 0.347629i
$$663$$ 18.8423 + 5.91336i 0.731774 + 0.229656i
$$664$$ 4.00000i 0.155230i
$$665$$ −56.5685 28.2843i −2.19363 1.09682i
$$666$$ 10.0000 8.94427i 0.387492 0.346583i
$$667$$ 0 0
$$668$$ −12.7279 + 12.7279i −0.492458 + 0.492458i
$$669$$ 18.9737 42.4264i 0.733564 1.64030i
$$670$$ 0 0
$$671$$ −56.5685 −2.18380
$$672$$ −2.76393 7.23607i −0.106621 0.279137i
$$673$$ −15.0000 + 15.0000i −0.578208 + 0.578208i −0.934409 0.356202i $$-0.884072\pi$$
0.356202 + 0.934409i $$0.384072\pi$$
$$674$$ 18.3848i 0.708155i
$$675$$ −25.6180 + 4.32624i −0.986039 + 0.166517i
$$676$$ 3.00000 + 12.6491i 0.115385 + 0.486504i
$$677$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$678$$ 15.3500 5.86319i 0.589514 0.225174i
$$679$$ 60.0000i 2.30259i
$$680$$ 6.70820 2.23607i 0.257248 0.0857493i
$$681$$ −8.48528 + 18.9737i −0.325157 + 0.727072i
$$682$$ −12.6491 + 12.6491i −0.484359 + 0.484359i
$$683$$ 16.9706 16.9706i 0.649361 0.649361i −0.303478 0.952838i $$-0.598148\pi$$
0.952838 + 0.303478i $$0.0981479\pi$$
$$684$$ −12.6491 14.1421i −0.483651 0.540738i
$$685$$ −18.0000 + 36.0000i −0.687745 + 1.37549i
$$686$$ 26.8328i 1.02448i
$$687$$ 5.86319 + 15.3500i 0.223694 + 0.585640i
$$688$$ 5.00000 5.00000i 0.190623 0.190623i
$$689$$ 17.8885 + 14.1421i 0.681499 + 0.538772i
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 13.4164 13.4164i 0.510015 0.510015i
$$693$$ −4.22291 + 75.7771i −0.160415 + 2.87853i
$$694$$ −28.4605 −1.08035
$$695$$ 8.48528 2.82843i 0.321865 0.107288i
$$696$$ 7.07107 + 3.16228i 0.268028 + 0.119866i
$$697$$ −12.6491 + 12.6491i −0.479119 + 0.479119i
$$698$$ −2.23607 2.23607i −0.0846364 0.0846364i
$$699$$ −2.23607 + 5.00000i −0.0845759 + 0.189117i
$$700$$ 22.1359 + 3.16228i 0.836660 + 0.119523i
$$701$$ 49.1935i 1.85801i 0.370064 + 0.929006i $$0.379336\pi$$
−0.370064 + 0.929006i $$0.620664\pi$$
$$702$$ 7.73553 + 17.0635i 0.291959 + 0.644019i
$$703$$ −20.0000 + 20.0000i −0.754314 + 0.754314i
$$704$$ 5.65685i 0.213201i
$$705$$ 7.70820 + 0.763932i 0.290308 + 0.0287713i
$$706$$ 14.0000 0.526897
$$707$$ 14.1421 + 14.1421i 0.531870 + 0.531870i
$$708$$ −1.74806 4.57649i −0.0656963 0.171995i
$$709$$ −47.4342 −1.78143 −0.890714 0.454565i $$-0.849795\pi$$
−0.890714 + 0.454565i $$0.849795\pi$$
$$710$$ 1.41421 2.82843i 0.0530745 0.106149i
$$711$$ 0 0
$$712$$ −2.00000 2.00000i −0.0749532 0.0749532i
$$713$$ 0 0
$$714$$ −22.3607 10.0000i −0.836827 0.374241i
$$715$$ −19.3509 41.2982i −0.723682 1.54447i
$$716$$ 17.8885i 0.668526i
$$717$$ 6.86474 2.62210i 0.256368 0.0979240i
$$718$$ 23.0000 23.0000i 0.858352 0.858352i
$$719$$ 17.8885 0.667130 0.333565 0.942727i $$-0.391748\pi$$
0.333565 + 0.942727i $$0.391748\pi$$
$$720$$ 5.82378 + 3.32920i 0.217039 + 0.124072i
$$721$$ 0 0
$$722$$ 14.8492 + 14.8492i 0.552632 + 0.552632i
$$723$$ 20.4667 7.81758i 0.761164 0.290739i
$$724$$ 22.0000i 0.817624i
$$725$$ −17.8885 + 13.4164i −0.664364 + 0.498273i
$$726$$ 14.8492 33.2039i 0.551107 1.23231i
$$727$$ 18.0000 + 18.0000i 0.667583 + 0.667583i 0.957156 0.289573i $$-0.0935133\pi$$
−0.289573 + 0.957156i $$0.593513\pi$$
$$728$$ −1.87320 16.0153i −0.0694256 0.593568i
$$729$$ 15.6525 + 22.0000i 0.579721 + 0.814815i
$$730$$ 9.48683 3.16228i 0.351123 0.117041i
$$731$$ 22.3607i 0.827040i
$$732$$ 16.1803 6.18034i 0.598043 0.228432i
$$733$$ −9.48683 9.48683i −0.350404 0.350404i 0.509856 0.860260i $$-0.329699\pi$$
−0.860260 + 0.509856i $$0.829699\pi$$
$$734$$ 28.2843i 1.04399i
$$735$$ −31.9172 38.9396i −1.17728 1.43631i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −16.9443 0.944272i −0.623727 0.0347591i
$$739$$ 44.2719 1.62857 0.814284 0.580467i $$-0.197130\pi$$
0.814284 + 0.580467i $$0.197130\pi$$
$$740$$ 4.47214 8.94427i 0.164399 0.328798i
$$741$$ −18.2843 35.0098i −0.671689 1.28612i
$$742$$ −20.0000 20.0000i −0.734223 0.734223i
$$743$$ −16.9706 + 16.9706i −0.622590 + 0.622590i −0.946193 0.323603i $$-0.895106\pi$$
0.323603 + 0.946193i $$0.395106\pi$$
$$744$$ 2.23607 5.00000i 0.0819782 0.183309i
$$745$$ −9.00000 + 3.00000i −0.329734 + 0.109911i
$$746$$ 22.6274 0.828449
$$747$$ 0.667701 11.9814i 0.0244299 0.438377i
$$748$$ 12.6491 + 12.6491i 0.462497 + 0.462497i
$$749$$ 14.1421i 0.516742i
$$750$$ −16.5623 + 10.0344i −0.604770 + 0.366406i
$$751$$ 48.0000 1.75154 0.875772 0.482724i $$-0.160353\pi$$
0.875772 + 0.482724i $$0.160353\pi$$
$$752$$ −1.41421 1.41421i −0.0515711 0.0515711i
$$753$$ 28.9443 11.0557i 1.05479 0.402893i
$$754$$ 12.6491 + 10.0000i 0.460653 + 0.364179i
$$755$$ 46.9574 15.6525i 1.70896 0.569652i
$$756$$ −7.07107 22.1359i −0.257172 0.805076i
$$757$$ −18.0000 18.0000i −0.654221 0.654221i 0.299786 0.954007i $$-0.403085\pi$$
−0.954007 + 0.299786i $$0.903085\pi$$
$$758$$ −4.47214 4.47214i −0.162435 0.162435i
$$759$$ 0 0
$$760$$ −12.6491 6.32456i −0.458831 0.229416i
$$761$$ 36.7696 1.33290 0.666448 0.745552i $$-0.267814\pi$$
0.666448 + 0.745552i $$0.267814\pi$$
$$762$$ −4.57649 + 1.74806i −0.165789 + 0.0633257i
$$763$$ 10.0000 10.0000i 0.362024 0.362024i
$$764$$ 8.94427 0.323592
$$765$$ 20.4667 5.57804i 0.739975 0.201675i
$$766$$ 16.0000 0.578103
$$767$$ −1.18472 10.1290i −0.0427777 0.365737i
$$768$$ −0.618034 1.61803i −0.0223014 0.0583858i
$$769$$ 50.5964 1.82455 0.912277 0.409573i $$-0.134322\pi$$
0.912277 + 0.409573i $$0.134322\pi$$
$$770$$ 17.8885 + 53.6656i 0.644658 + 1.93398i
$$771$$ −45.0000 20.1246i −1.62064 0.724770i
$$772$$ 9.48683 9.48683i 0.341439 0.341439i
$$773$$ 4.24264 4.24264i 0.152597 0.152597i −0.626680 0.779277i $$-0.715587\pi$$
0.779277 + 0.626680i $$0.215587\pi$$
$$774$$ 15.8114 14.1421i 0.568329 0.508329i
$$775$$ 9.48683 + 12.6491i 0.340777 + 0.454369i
$$776$$ 13.4164i 0.481621i
$$777$$ −32.3607 + 12.3607i −1.16093 + 0.443437i
$$778$$ −9.48683 9.48683i