Properties

 Label 120.2.w.b.53.1 Level $120$ Weight $2$ Character 120.53 Analytic conductor $0.958$ Analytic rank $0$ Dimension $4$ CM discriminant -24 Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$120 = 2^{3} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 120.w (of order $$4$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$0.958204824255$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ x^4 + 9 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

 Embedding label 53.1 Root $$-1.22474 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 120.53 Dual form 120.2.w.b.77.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$$ $$q+(1.00000 - 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-2.22474 + 0.224745i) q^{5} -2.44949 q^{6} +(1.44949 - 1.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-2.00000 + 2.44949i) q^{10} +6.44949 q^{11} +(-2.44949 + 2.44949i) q^{12} -2.89898i q^{14} +(3.00000 + 2.44949i) q^{15} -4.00000 q^{16} +(3.00000 + 3.00000i) q^{18} +(0.449490 + 4.44949i) q^{20} -3.55051 q^{21} +(6.44949 - 6.44949i) q^{22} +4.89898i q^{24} +(4.89898 - 1.00000i) q^{25} +(3.67423 - 3.67423i) q^{27} +(-2.89898 - 2.89898i) q^{28} +9.34847i q^{29} +(5.44949 - 0.550510i) q^{30} -4.89898 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-7.89898 - 7.89898i) q^{33} +(-2.89898 + 3.55051i) q^{35} +6.00000 q^{36} +(4.89898 + 4.00000i) q^{40} +(-3.55051 + 3.55051i) q^{42} -12.8990i q^{44} +(-0.674235 - 6.67423i) q^{45} +(4.89898 + 4.89898i) q^{48} +2.79796i q^{49} +(3.89898 - 5.89898i) q^{50} +(-2.44949 - 2.44949i) q^{53} -7.34847i q^{54} +(-14.3485 + 1.44949i) q^{55} -5.79796 q^{56} +(9.34847 + 9.34847i) q^{58} -0.651531i q^{59} +(4.89898 - 6.00000i) q^{60} +(-4.89898 + 4.89898i) q^{62} +(4.34847 + 4.34847i) q^{63} +8.00000i q^{64} -15.7980 q^{66} +(0.651531 + 6.44949i) q^{70} +(6.00000 - 6.00000i) q^{72} +(2.10102 + 2.10102i) q^{73} +(-7.22474 - 4.77526i) q^{75} +(9.34847 - 9.34847i) q^{77} -14.6969i q^{79} +(8.89898 - 0.898979i) q^{80} -9.00000 q^{81} +(-4.00000 - 4.00000i) q^{83} +7.10102i q^{84} +(11.4495 - 11.4495i) q^{87} +(-12.8990 - 12.8990i) q^{88} +(-7.34847 - 6.00000i) q^{90} +(6.00000 + 6.00000i) q^{93} +9.79796 q^{96} +(-10.7980 + 10.7980i) q^{97} +(2.79796 + 2.79796i) q^{98} +19.3485i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{2} - 4 q^{5} - 4 q^{7} - 8 q^{8}+O(q^{10})$$ 4 * q + 4 * q^2 - 4 * q^5 - 4 * q^7 - 8 * q^8 $$4 q + 4 q^{2} - 4 q^{5} - 4 q^{7} - 8 q^{8} - 8 q^{10} + 16 q^{11} + 12 q^{15} - 16 q^{16} + 12 q^{18} - 8 q^{20} - 24 q^{21} + 16 q^{22} + 8 q^{28} + 12 q^{30} - 16 q^{32} - 12 q^{33} + 8 q^{35} + 24 q^{36} - 24 q^{42} + 12 q^{45} - 4 q^{50} - 28 q^{55} + 16 q^{56} + 8 q^{58} - 12 q^{63} - 24 q^{66} + 32 q^{70} + 24 q^{72} + 28 q^{73} - 24 q^{75} + 8 q^{77} + 16 q^{80} - 36 q^{81} - 16 q^{83} + 36 q^{87} - 32 q^{88} + 24 q^{93} - 4 q^{97} - 28 q^{98}+O(q^{100})$$ 4 * q + 4 * q^2 - 4 * q^5 - 4 * q^7 - 8 * q^8 - 8 * q^10 + 16 * q^11 + 12 * q^15 - 16 * q^16 + 12 * q^18 - 8 * q^20 - 24 * q^21 + 16 * q^22 + 8 * q^28 + 12 * q^30 - 16 * q^32 - 12 * q^33 + 8 * q^35 + 24 * q^36 - 24 * q^42 + 12 * q^45 - 4 * q^50 - 28 * q^55 + 16 * q^56 + 8 * q^58 - 12 * q^63 - 24 * q^66 + 32 * q^70 + 24 * q^72 + 28 * q^73 - 24 * q^75 + 8 * q^77 + 16 * q^80 - 36 * q^81 - 16 * q^83 + 36 * q^87 - 32 * q^88 + 24 * q^93 - 4 * q^97 - 28 * q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$41$$ $$61$$ $$97$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000i 0.707107 0.707107i
$$3$$ −1.22474 1.22474i −0.707107 0.707107i
$$4$$ 2.00000i 1.00000i
$$5$$ −2.22474 + 0.224745i −0.994936 + 0.100509i
$$6$$ −2.44949 −1.00000
$$7$$ 1.44949 1.44949i 0.547856 0.547856i −0.377964 0.925820i $$-0.623376\pi$$
0.925820 + 0.377964i $$0.123376\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ 3.00000i 1.00000i
$$10$$ −2.00000 + 2.44949i −0.632456 + 0.774597i
$$11$$ 6.44949 1.94459 0.972297 0.233748i $$-0.0750991\pi$$
0.972297 + 0.233748i $$0.0750991\pi$$
$$12$$ −2.44949 + 2.44949i −0.707107 + 0.707107i
$$13$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$14$$ 2.89898i 0.774785i
$$15$$ 3.00000 + 2.44949i 0.774597 + 0.632456i
$$16$$ −4.00000 −1.00000
$$17$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$18$$ 3.00000 + 3.00000i 0.707107 + 0.707107i
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0.449490 + 4.44949i 0.100509 + 0.994936i
$$21$$ −3.55051 −0.774785
$$22$$ 6.44949 6.44949i 1.37504 1.37504i
$$23$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$24$$ 4.89898i 1.00000i
$$25$$ 4.89898 1.00000i 0.979796 0.200000i
$$26$$ 0 0
$$27$$ 3.67423 3.67423i 0.707107 0.707107i
$$28$$ −2.89898 2.89898i −0.547856 0.547856i
$$29$$ 9.34847i 1.73597i 0.496593 + 0.867984i $$0.334584\pi$$
−0.496593 + 0.867984i $$0.665416\pi$$
$$30$$ 5.44949 0.550510i 0.994936 0.100509i
$$31$$ −4.89898 −0.879883 −0.439941 0.898027i $$-0.645001\pi$$
−0.439941 + 0.898027i $$0.645001\pi$$
$$32$$ −4.00000 + 4.00000i −0.707107 + 0.707107i
$$33$$ −7.89898 7.89898i −1.37504 1.37504i
$$34$$ 0 0
$$35$$ −2.89898 + 3.55051i −0.490017 + 0.600146i
$$36$$ 6.00000 1.00000
$$37$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 4.89898 + 4.00000i 0.774597 + 0.632456i
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ −3.55051 + 3.55051i −0.547856 + 0.547856i
$$43$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$44$$ 12.8990i 1.94459i
$$45$$ −0.674235 6.67423i −0.100509 0.994936i
$$46$$ 0 0
$$47$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$48$$ 4.89898 + 4.89898i 0.707107 + 0.707107i
$$49$$ 2.79796i 0.399708i
$$50$$ 3.89898 5.89898i 0.551399 0.834242i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.44949 2.44949i −0.336463 0.336463i 0.518571 0.855034i $$-0.326464\pi$$
−0.855034 + 0.518571i $$0.826464\pi$$
$$54$$ 7.34847i 1.00000i
$$55$$ −14.3485 + 1.44949i −1.93475 + 0.195449i
$$56$$ −5.79796 −0.774785
$$57$$ 0 0
$$58$$ 9.34847 + 9.34847i 1.22751 + 1.22751i
$$59$$ 0.651531i 0.0848221i −0.999100 0.0424110i $$-0.986496\pi$$
0.999100 0.0424110i $$-0.0135039\pi$$
$$60$$ 4.89898 6.00000i 0.632456 0.774597i
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ −4.89898 + 4.89898i −0.622171 + 0.622171i
$$63$$ 4.34847 + 4.34847i 0.547856 + 0.547856i
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ −15.7980 −1.94459
$$67$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0.651531 + 6.44949i 0.0778728 + 0.770861i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 6.00000 6.00000i 0.707107 0.707107i
$$73$$ 2.10102 + 2.10102i 0.245906 + 0.245906i 0.819288 0.573382i $$-0.194369\pi$$
−0.573382 + 0.819288i $$0.694369\pi$$
$$74$$ 0 0
$$75$$ −7.22474 4.77526i −0.834242 0.551399i
$$76$$ 0 0
$$77$$ 9.34847 9.34847i 1.06536 1.06536i
$$78$$ 0 0
$$79$$ 14.6969i 1.65353i −0.562544 0.826767i $$-0.690177\pi$$
0.562544 0.826767i $$-0.309823\pi$$
$$80$$ 8.89898 0.898979i 0.994936 0.100509i
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ −4.00000 4.00000i −0.439057 0.439057i 0.452638 0.891695i $$-0.350483\pi$$
−0.891695 + 0.452638i $$0.850483\pi$$
$$84$$ 7.10102i 0.774785i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 11.4495 11.4495i 1.22751 1.22751i
$$88$$ −12.8990 12.8990i −1.37504 1.37504i
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ −7.34847 6.00000i −0.774597 0.632456i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 6.00000 + 6.00000i 0.622171 + 0.622171i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 9.79796 1.00000
$$97$$ −10.7980 + 10.7980i −1.09637 + 1.09637i −0.101535 + 0.994832i $$0.532375\pi$$
−0.994832 + 0.101535i $$0.967625\pi$$
$$98$$ 2.79796 + 2.79796i 0.282637 + 0.282637i
$$99$$ 19.3485i 1.94459i
$$100$$ −2.00000 9.79796i −0.200000 0.979796i
$$101$$ 16.4495 1.63679 0.818393 0.574659i $$-0.194865\pi$$
0.818393 + 0.574659i $$0.194865\pi$$
$$102$$ 0 0
$$103$$ 14.3485 + 14.3485i 1.41380 + 1.41380i 0.724066 + 0.689730i $$0.242271\pi$$
0.689730 + 0.724066i $$0.257729\pi$$
$$104$$ 0 0
$$105$$ 7.89898 0.797959i 0.770861 0.0778728i
$$106$$ −4.89898 −0.475831
$$107$$ −8.00000 + 8.00000i −0.773389 + 0.773389i −0.978697 0.205308i $$-0.934180\pi$$
0.205308 + 0.978697i $$0.434180\pi$$
$$108$$ −7.34847 7.34847i −0.707107 0.707107i
$$109$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$110$$ −12.8990 + 15.7980i −1.22987 + 1.50628i
$$111$$ 0 0
$$112$$ −5.79796 + 5.79796i −0.547856 + 0.547856i
$$113$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 18.6969 1.73597
$$117$$ 0 0
$$118$$ −0.651531 0.651531i −0.0599783 0.0599783i
$$119$$ 0 0
$$120$$ −1.10102 10.8990i −0.100509 0.994936i
$$121$$ 30.5959 2.78145
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 9.79796i 0.879883i
$$125$$ −10.6742 + 3.32577i −0.954733 + 0.297465i
$$126$$ 8.69694 0.774785
$$127$$ −8.55051 + 8.55051i −0.758735 + 0.758735i −0.976092 0.217357i $$-0.930256\pi$$
0.217357 + 0.976092i $$0.430256\pi$$
$$128$$ 8.00000 + 8.00000i 0.707107 + 0.707107i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −13.5505 −1.18391 −0.591957 0.805970i $$-0.701644\pi$$
−0.591957 + 0.805970i $$0.701644\pi$$
$$132$$ −15.7980 + 15.7980i −1.37504 + 1.37504i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −7.34847 + 9.00000i −0.632456 + 0.774597i
$$136$$ 0 0
$$137$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 7.10102 + 5.79796i 0.600146 + 0.490017i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 12.0000i 1.00000i
$$145$$ −2.10102 20.7980i −0.174480 1.72718i
$$146$$ 4.20204 0.347763
$$147$$ 3.42679 3.42679i 0.282637 0.282637i
$$148$$ 0 0
$$149$$ 15.1464i 1.24084i −0.784268 0.620422i $$-0.786961\pi$$
0.784268 0.620422i $$-0.213039\pi$$
$$150$$ −12.0000 + 2.44949i −0.979796 + 0.200000i
$$151$$ 2.00000 0.162758 0.0813788 0.996683i $$-0.474068\pi$$
0.0813788 + 0.996683i $$0.474068\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 18.6969i 1.50664i
$$155$$ 10.8990 1.10102i 0.875427 0.0884361i
$$156$$ 0 0
$$157$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$158$$ −14.6969 14.6969i −1.16923 1.16923i
$$159$$ 6.00000i 0.475831i
$$160$$ 8.00000 9.79796i 0.632456 0.774597i
$$161$$ 0 0
$$162$$ −9.00000 + 9.00000i −0.707107 + 0.707107i
$$163$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$164$$ 0 0
$$165$$ 19.3485 + 15.7980i 1.50628 + 1.22987i
$$166$$ −8.00000 −0.620920
$$167$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$168$$ 7.10102 + 7.10102i 0.547856 + 0.547856i
$$169$$ 13.0000i 1.00000i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −14.0000 14.0000i −1.06440 1.06440i −0.997778 0.0666220i $$-0.978778\pi$$
−0.0666220 0.997778i $$-0.521222\pi$$
$$174$$ 22.8990i 1.73597i
$$175$$ 5.65153 8.55051i 0.427216 0.646358i
$$176$$ −25.7980 −1.94459
$$177$$ −0.797959 + 0.797959i −0.0599783 + 0.0599783i
$$178$$ 0 0
$$179$$ 25.1464i 1.87953i −0.341818 0.939766i $$-0.611043\pi$$
0.341818 0.939766i $$-0.388957\pi$$
$$180$$ −13.3485 + 1.34847i −0.994936 + 0.100509i
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 12.0000 0.879883
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 10.6515i 0.774785i
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 9.79796 9.79796i 0.707107 0.707107i
$$193$$ −17.8990 17.8990i −1.28840 1.28840i −0.935760 0.352636i $$-0.885285\pi$$
−0.352636 0.935760i $$-0.614715\pi$$
$$194$$ 21.5959i 1.55050i
$$195$$ 0 0
$$196$$ 5.59592 0.399708
$$197$$ −17.1464 + 17.1464i −1.22163 + 1.22163i −0.254581 + 0.967051i $$0.581938\pi$$
−0.967051 + 0.254581i $$0.918062\pi$$
$$198$$ 19.3485 + 19.3485i 1.37504 + 1.37504i
$$199$$ 14.0000i 0.992434i −0.868199 0.496217i $$-0.834722\pi$$
0.868199 0.496217i $$-0.165278\pi$$
$$200$$ −11.7980 7.79796i −0.834242 0.551399i
$$201$$ 0 0
$$202$$ 16.4495 16.4495i 1.15738 1.15738i
$$203$$ 13.5505 + 13.5505i 0.951059 + 0.951059i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 28.6969 1.99941
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 7.10102 8.69694i 0.490017 0.600146i
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ −4.89898 + 4.89898i −0.336463 + 0.336463i
$$213$$ 0 0
$$214$$ 16.0000i 1.09374i
$$215$$ 0 0
$$216$$ −14.6969 −1.00000
$$217$$ −7.10102 + 7.10102i −0.482049 + 0.482049i
$$218$$ 0 0
$$219$$ 5.14643i 0.347763i
$$220$$ 2.89898 + 28.6969i 0.195449 + 1.93475i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −5.65153 5.65153i −0.378454 0.378454i 0.492090 0.870544i $$-0.336233\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ 11.5959i 0.774785i
$$225$$ 3.00000 + 14.6969i 0.200000 + 0.979796i
$$226$$ 0 0
$$227$$ 7.34847 7.34847i 0.487735 0.487735i −0.419856 0.907591i $$-0.637919\pi$$
0.907591 + 0.419856i $$0.137919\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ −22.8990 −1.50664
$$232$$ 18.6969 18.6969i 1.22751 1.22751i
$$233$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.30306 −0.0848221
$$237$$ −18.0000 + 18.0000i −1.16923 + 1.16923i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ −12.0000 9.79796i −0.774597 0.632456i
$$241$$ −29.3939 −1.89343 −0.946713 0.322078i $$-0.895619\pi$$
−0.946713 + 0.322078i $$0.895619\pi$$
$$242$$ 30.5959 30.5959i 1.96678 1.96678i
$$243$$ 11.0227 + 11.0227i 0.707107 + 0.707107i
$$244$$ 0 0
$$245$$ −0.628827 6.22474i −0.0401743 0.397684i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 9.79796 + 9.79796i 0.622171 + 0.622171i
$$249$$ 9.79796i 0.620920i
$$250$$ −7.34847 + 14.0000i −0.464758 + 0.885438i
$$251$$ −18.0454 −1.13902 −0.569508 0.821986i $$-0.692866\pi$$
−0.569508 + 0.821986i $$0.692866\pi$$
$$252$$ 8.69694 8.69694i 0.547856 0.547856i
$$253$$ 0 0
$$254$$ 17.1010i 1.07301i
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −28.0454 −1.73597
$$262$$ −13.5505 + 13.5505i −0.837153 + 0.837153i
$$263$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$264$$ 31.5959i 1.94459i
$$265$$ 6.00000 + 4.89898i 0.368577 + 0.300942i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 29.3485i 1.78941i 0.446660 + 0.894704i $$0.352613\pi$$
−0.446660 + 0.894704i $$0.647387\pi$$
$$270$$ 1.65153 + 16.3485i 0.100509 + 0.994936i
$$271$$ 22.0000 1.33640 0.668202 0.743980i $$-0.267064\pi$$
0.668202 + 0.743980i $$0.267064\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 31.5959 6.44949i 1.90531 0.388919i
$$276$$ 0 0
$$277$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$278$$ 0 0
$$279$$ 14.6969i 0.879883i
$$280$$ 12.8990 1.30306i 0.770861 0.0778728i
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −12.0000 12.0000i −0.707107 0.707107i
$$289$$ 17.0000i 1.00000i
$$290$$ −22.8990 18.6969i −1.34467 1.09792i
$$291$$ 26.4495 1.55050
$$292$$ 4.20204 4.20204i 0.245906 0.245906i
$$293$$ 22.0454 + 22.0454i 1.28791 + 1.28791i 0.936056 + 0.351850i $$0.114447\pi$$
0.351850 + 0.936056i $$0.385553\pi$$
$$294$$ 6.85357i 0.399708i
$$295$$ 0.146428 + 1.44949i 0.00852538 + 0.0843926i
$$296$$ 0 0
$$297$$ 23.6969 23.6969i 1.37504 1.37504i
$$298$$ −15.1464 15.1464i −0.877409 0.877409i
$$299$$ 0 0
$$300$$ −9.55051 + 14.4495i −0.551399 + 0.834242i
$$301$$ 0 0
$$302$$ 2.00000 2.00000i 0.115087 0.115087i
$$303$$ −20.1464 20.1464i −1.15738 1.15738i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ −18.6969 18.6969i −1.06536 1.06536i
$$309$$ 35.1464i 1.99941i
$$310$$ 9.79796 12.0000i 0.556487 0.681554i
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 12.1010 + 12.1010i 0.683990 + 0.683990i 0.960897 0.276907i $$-0.0893093\pi$$
−0.276907 + 0.960897i $$0.589309\pi$$
$$314$$ 0 0
$$315$$ −10.6515 8.69694i −0.600146 0.490017i
$$316$$ −29.3939 −1.65353
$$317$$ 22.0000 22.0000i 1.23564 1.23564i 0.273879 0.961764i $$-0.411693\pi$$
0.961764 0.273879i $$-0.0883068\pi$$
$$318$$ 6.00000 + 6.00000i 0.336463 + 0.336463i
$$319$$ 60.2929i 3.37575i
$$320$$ −1.79796 17.7980i −0.100509 0.994936i
$$321$$ 19.5959 1.09374
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 18.0000i 1.00000i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 35.1464 3.55051i 1.93475 0.195449i
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ −8.00000 + 8.00000i −0.439057 + 0.439057i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 14.2020 0.774785
$$337$$ 3.69694 3.69694i 0.201385 0.201385i −0.599208 0.800593i $$-0.704518\pi$$
0.800593 + 0.599208i $$0.204518\pi$$
$$338$$ 13.0000 + 13.0000i 0.707107 + 0.707107i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −31.5959 −1.71101
$$342$$ 0 0
$$343$$ 14.2020 + 14.2020i 0.766838 + 0.766838i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −28.0000 −1.50529
$$347$$ −17.1464 + 17.1464i −0.920468 + 0.920468i −0.997062 0.0765939i $$-0.975596\pi$$
0.0765939 + 0.997062i $$0.475596\pi$$
$$348$$ −22.8990 22.8990i −1.22751 1.22751i
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ −2.89898 14.2020i −0.154957 0.759131i
$$351$$ 0 0
$$352$$ −25.7980 + 25.7980i −1.37504 + 1.37504i
$$353$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$354$$ 1.59592i 0.0848221i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −25.1464 25.1464i −1.32903 1.32903i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ −12.0000 + 14.6969i −0.632456 + 0.774597i
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ −37.4722 37.4722i −1.96678 1.96678i
$$364$$ 0 0
$$365$$ −5.14643 4.20204i −0.269376 0.219945i
$$366$$ 0 0
$$367$$ 21.4495 21.4495i 1.11965 1.11965i 0.127862 0.991792i $$-0.459188\pi$$
0.991792 0.127862i $$-0.0408116\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −7.10102 −0.368667
$$372$$ 12.0000 12.0000i 0.622171 0.622171i
$$373$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$374$$ 0 0
$$375$$ 17.1464 + 9.00000i 0.885438 + 0.464758i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ −10.6515 10.6515i −0.547856 0.547856i
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 20.9444 1.07301
$$382$$ 0 0
$$383$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$384$$ 19.5959i 1.00000i
$$385$$ −18.6969 + 22.8990i −0.952884 + 1.16704i
$$386$$ −35.7980 −1.82207
$$387$$ 0 0
$$388$$ 21.5959 + 21.5959i 1.09637 + 1.09637i
$$389$$ 4.85357i 0.246086i 0.992401 + 0.123043i $$0.0392653\pi$$
−0.992401 + 0.123043i $$0.960735\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 5.59592 5.59592i 0.282637 0.282637i
$$393$$ 16.5959 + 16.5959i 0.837153 + 0.837153i
$$394$$ 34.2929i 1.72765i
$$395$$ 3.30306 + 32.6969i 0.166195 + 1.64516i
$$396$$ 38.6969 1.94459
$$397$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$398$$ −14.0000 14.0000i −0.701757 0.701757i
$$399$$ 0 0
$$400$$ −19.5959 + 4.00000i −0.979796 + 0.200000i
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 32.8990i 1.63679i
$$405$$ 20.0227 2.02270i 0.994936 0.100509i
$$406$$ 27.1010 1.34500
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 39.1918i 1.93791i −0.247234 0.968956i $$-0.579522\pi$$
0.247234 0.968956i $$-0.420478\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 28.6969 28.6969i 1.41380 1.41380i
$$413$$ −0.944387 0.944387i −0.0464703 0.0464703i
$$414$$ 0 0
$$415$$ 9.79796 + 8.00000i 0.480963 + 0.392705i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 20.6515i 1.00889i −0.863443 0.504447i $$-0.831697\pi$$
0.863443 0.504447i $$-0.168303\pi$$
$$420$$ −1.59592 15.7980i −0.0778728 0.770861i
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 9.79796i 0.475831i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 16.0000 + 16.0000i 0.773389 + 0.773389i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −14.6969 + 14.6969i −0.707107 + 0.707107i
$$433$$ 26.5959 + 26.5959i 1.27812 + 1.27812i 0.941720 + 0.336399i $$0.109209\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 14.2020i 0.681720i
$$435$$ −22.8990 + 28.0454i −1.09792 + 1.34467i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −5.14643 5.14643i −0.245906 0.245906i
$$439$$ 34.0000i 1.62273i −0.584539 0.811366i $$-0.698725\pi$$
0.584539 0.811366i $$-0.301275\pi$$
$$440$$ 31.5959 + 25.7980i 1.50628 + 1.22987i
$$441$$ −8.39388 −0.399708
$$442$$ 0 0
$$443$$ 22.0454 + 22.0454i 1.04741 + 1.04741i 0.998819 + 0.0485901i $$0.0154728\pi$$
0.0485901 + 0.998819i $$0.484527\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −11.3031 −0.535215
$$447$$ −18.5505 + 18.5505i −0.877409 + 0.877409i
$$448$$ 11.5959 + 11.5959i 0.547856 + 0.547856i
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 17.6969 + 11.6969i 0.834242 + 0.551399i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −2.44949 2.44949i −0.115087 0.115087i
$$454$$ 14.6969i 0.689761i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 9.20204 9.20204i 0.430453 0.430453i −0.458329 0.888783i $$-0.651552\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 40.9444 1.90697 0.953485 0.301440i $$-0.0974673\pi$$
0.953485 + 0.301440i $$0.0974673\pi$$
$$462$$ −22.8990 + 22.8990i −1.06536 + 1.06536i
$$463$$ −30.1464 30.1464i −1.40102 1.40102i −0.796862 0.604161i $$-0.793508\pi$$
−0.604161 0.796862i $$-0.706492\pi$$
$$464$$ 37.3939i 1.73597i
$$465$$ −14.6969 12.0000i −0.681554 0.556487i
$$466$$ 0 0
$$467$$ −28.0000 + 28.0000i −1.29569 + 1.29569i −0.364471 + 0.931215i $$0.618750\pi$$
−0.931215 + 0.364471i $$0.881250\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.30306 + 1.30306i −0.0599783 + 0.0599783i
$$473$$ 0 0
$$474$$ 36.0000i 1.65353i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 7.34847 7.34847i 0.336463 0.336463i
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ −21.7980 + 2.20204i −0.994936 + 0.100509i
$$481$$ 0 0
$$482$$ −29.3939 + 29.3939i −1.33885 + 1.33885i
$$483$$ 0 0
$$484$$ 61.1918i 2.78145i
$$485$$ 21.5959 26.4495i 0.980620 1.20101i
$$486$$ 22.0454 1.00000
$$487$$ −23.0454 + 23.0454i −1.04429 + 1.04429i −0.0453143 + 0.998973i $$0.514429\pi$$
−0.998973 + 0.0453143i $$0.985571\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −6.85357 5.59592i −0.309613 0.252798i
$$491$$ 10.9444 0.493913 0.246957 0.969027i $$-0.420569\pi$$
0.246957 + 0.969027i $$0.420569\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −4.34847 43.0454i −0.195449 1.93475i
$$496$$ 19.5959 0.879883
$$497$$ 0 0
$$498$$ 9.79796 + 9.79796i 0.439057 + 0.439057i
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 6.65153 + 21.3485i 0.297465 + 0.954733i
$$501$$ 0 0
$$502$$ −18.0454 + 18.0454i −0.805406 + 0.805406i
$$503$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$504$$ 17.3939i 0.774785i
$$505$$ −36.5959 + 3.69694i −1.62850 + 0.164512i
$$506$$ 0 0
$$507$$ 15.9217 15.9217i 0.707107 0.707107i
$$508$$ 17.1010 + 17.1010i 0.758735 + 0.758735i
$$509$$ 33.8434i 1.50008i 0.661392 + 0.750040i $$0.269966\pi$$
−0.661392 + 0.750040i $$0.730034\pi$$
$$510$$ 0 0
$$511$$ 6.09082 0.269442
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −35.1464 28.6969i −1.54874 1.26454i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 34.2929i 1.50529i
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ −28.0454 + 28.0454i −1.22751 + 1.22751i
$$523$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$524$$ 27.1010i 1.18391i
$$525$$ −17.3939 + 3.55051i −0.759131 + 0.154957i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 31.5959 + 31.5959i 1.37504 + 1.37504i
$$529$$ 23.0000i 1.00000i
$$530$$ 10.8990 1.10102i 0.473421 0.0478253i
$$531$$ 1.95459 0.0848221
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 16.0000 19.5959i 0.691740 0.847205i
$$536$$ 0 0
$$537$$ −30.7980 + 30.7980i −1.32903 + 1.32903i
$$538$$ 29.3485 + 29.3485i 1.26530 + 1.26530i
$$539$$ 18.0454i 0.777271i
$$540$$ 18.0000 + 14.6969i 0.774597 + 0.632456i
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 22.0000 22.0000i 0.944981 0.944981i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 25.1464 38.0454i 1.07225 1.62226i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −21.3031 21.3031i −0.905898 0.905898i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 31.8434 31.8434i 1.34925 1.34925i 0.462767 0.886480i $$-0.346857\pi$$
0.886480 0.462767i $$-0.153143\pi$$
$$558$$ −14.6969 14.6969i −0.622171 0.622171i
$$559$$ 0 0
$$560$$ 11.5959 14.2020i 0.490017 0.600146i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −26.9444 26.9444i −1.13557 1.13557i −0.989235 0.146336i $$-0.953252\pi$$
−0.146336 0.989235i $$-0.546748\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −13.0454 + 13.0454i −0.547856 + 0.547856i
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −24.0000 −1.00000
$$577$$ 33.6969 33.6969i 1.40282 1.40282i 0.611842 0.790980i $$-0.290429\pi$$
0.790980 0.611842i $$-0.209571\pi$$
$$578$$ −17.0000 17.0000i −0.707107 0.707107i
$$579$$ 43.8434i 1.82207i
$$580$$ −41.5959 + 4.20204i −1.72718 + 0.174480i
$$581$$ −11.5959 −0.481080
$$582$$ 26.4495 26.4495i 1.09637 1.09637i
$$583$$ −15.7980 15.7980i −0.654285 0.654285i
$$584$$ 8.40408i 0.347763i
$$585$$ 0 0
$$586$$ 44.0908 1.82137
$$587$$ 32.0000 32.0000i 1.32078 1.32078i 0.407638 0.913144i $$-0.366353\pi$$
0.913144 0.407638i $$-0.133647\pi$$
$$588$$ −6.85357 6.85357i −0.282637 0.282637i
$$589$$ 0 0
$$590$$ 1.59592 + 1.30306i 0.0657029 + 0.0536462i
$$591$$ 42.0000 1.72765
$$592$$ 0 0
$$593$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$594$$ 47.3939i 1.94459i
$$595$$ 0 0
$$596$$ −30.2929 −1.24084
$$597$$ −17.1464 + 17.1464i −0.701757 + 0.701757i
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 4.89898 + 24.0000i 0.200000 + 0.979796i
$$601$$ 2.00000 0.0815817 0.0407909 0.999168i $$-0.487012\pi$$
0.0407909 + 0.999168i $$0.487012\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 4.00000i 0.162758i
$$605$$ −68.0681 + 6.87628i −2.76736 + 0.279560i
$$606$$ −40.2929 −1.63679
$$607$$ −33.0454 + 33.0454i −1.34127 + 1.34127i −0.446476 + 0.894795i $$0.647321\pi$$
−0.894795 + 0.446476i $$0.852679\pi$$
$$608$$ 0 0
$$609$$ 33.1918i 1.34500i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −37.3939 −1.50664
$$617$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$618$$ −35.1464 35.1464i −1.41380 1.41380i
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ −2.20204 21.7980i −0.0884361 0.875427i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 23.0000 9.79796i 0.920000 0.391918i
$$626$$ 24.2020 0.967308
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ −19.3485 + 1.95459i −0.770861 + 0.0778728i
$$631$$ −4.89898 −0.195025 −0.0975126 0.995234i $$-0.531089\pi$$
−0.0975126 + 0.995234i $$0.531089\pi$$
$$632$$ −29.3939 + 29.3939i −1.16923 + 1.16923i
$$633$$ 0 0
$$634$$ 44.0000i 1.74746i
$$635$$ 17.1010 20.9444i 0.678633 0.831153i
$$636$$ 12.0000 0.475831
$$637$$ 0 0
$$638$$ 60.2929 + 60.2929i 2.38702 + 2.38702i
$$639$$ 0 0
$$640$$ −19.5959 16.0000i −0.774597 0.632456i
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 19.5959 19.5959i 0.773389 0.773389i
$$643$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$648$$ 18.0000 + 18.0000i 0.707107 + 0.707107i
$$649$$ 4.20204i 0.164945i
$$650$$ 0 0
$$651$$ 17.3939 0.681720
$$652$$ 0 0
$$653$$ −34.0000 34.0000i −1.33052 1.33052i −0.904901 0.425622i $$-0.860055\pi$$
−0.425622 0.904901i $$-0.639945\pi$$
$$654$$ 0 0
$$655$$ 30.1464 3.04541i 1.17792 0.118994i
$$656$$ 0 0
$$657$$ −6.30306 + 6.30306i −0.245906 + 0.245906i
$$658$$ 0 0
$$659$$ 14.8536i 0.578613i 0.957237 + 0.289307i $$0.0934247\pi$$
−0.957237 + 0.289307i $$0.906575\pi$$
$$660$$ 31.5959 38.6969i 1.22987 1.50628i
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 16.0000i 0.620920i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 13.8434i 0.535215i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 14.2020 14.2020i 0.547856 0.547856i
$$673$$ 36.5959 + 36.5959i 1.41067 + 1.41067i 0.755367 + 0.655302i $$0.227459\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 7.39388i 0.284801i
$$675$$ 14.3258 21.6742i 0.551399 0.834242i
$$676$$ 26.0000 1.00000
$$677$$ 2.00000 2.00000i 0.0768662 0.0768662i −0.667628 0.744495i $$-0.732690\pi$$
0.744495 + 0.667628i $$0.232690\pi$$
$$678$$ 0 0
$$679$$ 31.3031i 1.20130i
$$680$$ 0 0
$$681$$ −18.0000 −0.689761
$$682$$ −31.5959 + 31.5959i −1.20987 + 1.20987i
$$683$$ −4.00000 4.00000i −0.153056 0.153056i 0.626426 0.779481i $$-0.284517\pi$$
−0.779481 + 0.626426i $$0.784517\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 28.4041 1.08447
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ −28.0000 + 28.0000i −1.06440 + 1.06440i
$$693$$ 28.0454 + 28.0454i 1.06536 + 1.06536i
$$694$$ 34.2929i 1.30174i
$$695$$ 0 0
$$696$$ −45.7980 −1.73597
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −17.1010 11.3031i −0.646358 0.427216i
$$701$$ 0.944387 0.0356690 0.0178345 0.999841i $$-0.494323\pi$$
0.0178345 + 0.999841i $$0.494323\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 51.5959i 1.94459i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 23.8434 23.8434i 0.896722 0.896722i
$$708$$ 1.59592 + 1.59592i 0.0599783 + 0.0599783i
$$709$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$710$$ 0 0
$$711$$ 44.0908 1.65353
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −50.2929 −1.87953
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 2.69694 + 26.6969i 0.100509 + 0.994936i
$$721$$ 41.5959 1.54911
$$722$$ −19.0000 + 19.0000i −0.707107 + 0.707107i
$$723$$ 36.0000 + 36.0000i 1.33885 + 1.33885i
$$724$$ 0 0
$$725$$ 9.34847 + 45.7980i 0.347193 + 1.70089i
$$726$$ −74.9444 −2.78145
$$727$$ 25.9444 25.9444i 0.962224 0.962224i −0.0370879 0.999312i $$-0.511808\pi$$
0.999312 + 0.0370879i $$0.0118082\pi$$
$$728$$ 0 0
$$729$$ 27.0000i 1.00000i
$$730$$ −9.34847 + 0.944387i −0.346002 + 0.0349533i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ 42.8990i 1.58343i
$$735$$ −6.85357 + 8.39388i −0.252798 + 0.309613i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −7.10102 + 7.10102i −0.260687 + 0.260687i
$$743$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$744$$ 24.0000i 0.879883i
$$745$$ 3.40408 + 33.6969i 0.124716 + 1.23456i
$$746$$ 0 0
$$747$$ 12.0000 12.0000i 0.439057 0.439057i
$$748$$ 0 0
$$749$$ 23.1918i 0.847411i
$$750$$ 26.1464 8.14643i 0.954733 0.297465i
$$751$$ −53.8888 −1.96643 −0.983215 0.182453i $$-0.941596\pi$$
−0.983215 + 0.182453i $$0.941596\pi$$
$$752$$ 0 0
$$753$$ 22.1010 + 22.1010i 0.805406 + 0.805406i
$$754$$ 0 0
$$755$$ −4.44949 + 0.449490i −0.161934 + 0.0163586i
$$756$$ −21.3031 −0.774785
$$757$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 20.9444 20.9444i 0.758735 0.758735i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −19.5959 19.5959i −0.707107 0.707107i
$$769$$ 26.0000i 0.937584i 0.883309 + 0.468792i $$0.155311\pi$$
−0.883309 + 0.468792i $$0.844689\pi$$
$$770$$ 4.20204 + 41.5959i 0.151431 + 1.49901i
$$771$$ 0 0
$$772$$ −35.7980 + 35.7980i −1.28840 + 1.28840i
$$773$$ −14.0000 14.0000i −0.503545 0.503545i 0.408993 0.912538i $$-0.365880\pi$$
−0.912538 + 0.408993i $$0.865880\pi$$
$$774$$ 0 0
$$775$$ −24.0000 + 4.89898i −0.862105 + 0.175977i
$$776$$ 43.1918 1.55050
$$777$$ 0 0
$$778$$ 4.85357 + 4.85357i 0.174009 + 0.174009i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 34.3485 + 34.3485i 1.22751 + 1.22751i
$$784$$ 11.1918i 0.399708i
$$785$$ 0 0
$$786$$ 33.1918 1.18391
$$787$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$788$$ 34.2929 + 34.2929i 1.22163 + 1.22163i
$$789$$ 0 0
$$790$$ 36.0000 + 29.3939i 1.28082 + 1.04579i
$$791$$ 0 0
$$792$$ 38.6969 38.6969i 1.37504 1.37504i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ &