# Properties

 Label 1950.2.y.j.199.1 Level $1950$ Weight $2$ Character 1950.199 Analytic conductor $15.571$ Analytic rank $0$ Dimension $8$ 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: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.17284886784.1 Defining polynomial: $$x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 199.1 Root $$-1.80668 + 1.80668i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.199 Dual form 1950.2.y.j.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-0.661290 - 1.14539i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$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} +(-0.661290 - 1.14539i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.99528 - 2.30668i) q^{11} +1.00000i q^{12} +(1.66129 + 3.20002i) q^{13} +1.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} -1.00000 q^{18} +(-1.98387 + 1.14539i) q^{19} +1.32258i q^{21} +(3.99528 - 2.30668i) q^{22} +(7.50670 + 4.33399i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.60194 - 0.161290i) q^{26} -1.00000i q^{27} +(-0.661290 + 1.14539i) q^{28} +(-1.01141 + 1.75182i) q^{29} -10.1321i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.30668 + 3.99528i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(3.40475 - 5.89721i) q^{37} -2.29078i q^{38} +(0.161290 - 3.60194i) q^{39} +(-4.02283 - 2.32258i) q^{41} +(-1.14539 - 0.661290i) q^{42} +(-7.45269 + 4.30281i) q^{43} +4.61335i q^{44} +(-7.50670 + 4.33399i) q^{46} -9.10926 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.62539 - 4.54731i) q^{49} -4.00000 q^{51} +(1.94065 - 3.03873i) q^{52} +0.826674i q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.661290 - 1.14539i) q^{56} +2.29078 q^{57} +(-1.01141 - 1.75182i) q^{58} +(-2.72064 + 1.57076i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(8.77464 + 5.06604i) q^{62} +(0.661290 - 1.14539i) q^{63} +1.00000 q^{64} -4.61335 q^{66} +(-1.59053 + 2.75488i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-4.33399 - 7.50670i) q^{69} +(-9.81724 + 5.66799i) q^{71} +(0.500000 + 0.866025i) q^{72} +6.28304 q^{73} +(3.40475 + 5.89721i) q^{74} +(1.98387 + 1.14539i) q^{76} +6.10153i q^{77} +(3.03873 + 1.94065i) q^{78} -2.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.02283 - 2.32258i) q^{82} -15.8719 q^{83} +(1.14539 - 0.661290i) q^{84} -8.60562i q^{86} +(1.75182 - 1.01141i) q^{87} +(-3.99528 - 2.30668i) q^{88} +(-10.2746 - 5.93207i) q^{89} +(2.56667 - 4.01896i) q^{91} -8.66799i q^{92} +(-5.06604 + 8.77464i) q^{93} +(4.55463 - 7.88885i) q^{94} +1.00000i q^{96} +(4.40947 + 7.63743i) q^{97} +(2.62539 + 4.54731i) q^{98} -4.61335i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + O(q^{10})$$ $$8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + 6q^{11} + 6q^{13} - 4q^{14} - 4q^{16} - 8q^{18} + 6q^{19} - 6q^{22} + 6q^{23} - 12q^{26} + 2q^{28} + 8q^{29} - 4q^{32} + 2q^{33} + 4q^{36} - 10q^{37} - 6q^{39} - 48q^{43} - 6q^{46} - 16q^{47} - 14q^{49} - 32q^{51} + 6q^{52} + 2q^{56} + 8q^{58} - 24q^{59} - 16q^{61} + 30q^{62} - 2q^{63} + 8q^{64} - 4q^{66} - 12q^{67} - 4q^{69} - 12q^{71} + 4q^{72} + 24q^{73} - 10q^{74} - 6q^{76} - 6q^{78} + 20q^{79} - 4q^{81} - 32q^{83} + 6q^{87} + 6q^{88} - 42q^{89} - 10q^{91} + 4q^{93} + 8q^{94} + 36q^{97} - 14q^{98} + O(q^{100})$$

## Character values

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

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

## 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
$$7$$ −0.661290 1.14539i −0.249944 0.432916i 0.713566 0.700588i $$-0.247079\pi$$
−0.963510 + 0.267672i $$0.913746\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −3.99528 2.30668i −1.20462 0.695489i −0.243043 0.970015i $$-0.578146\pi$$
−0.961580 + 0.274526i $$0.911479\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 1.66129 + 3.20002i 0.460759 + 0.887525i
$$14$$ 1.32258 0.353474
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 3.46410 2.00000i 0.840168 0.485071i −0.0171533 0.999853i $$-0.505460\pi$$
0.857321 + 0.514782i $$0.172127\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −1.98387 + 1.14539i −0.455131 + 0.262770i −0.709995 0.704207i $$-0.751303\pi$$
0.254864 + 0.966977i $$0.417969\pi$$
$$20$$ 0 0
$$21$$ 1.32258i 0.288611i
$$22$$ 3.99528 2.30668i 0.851797 0.491785i
$$23$$ 7.50670 + 4.33399i 1.56525 + 0.903700i 0.996710 + 0.0810471i $$0.0258264\pi$$
0.568544 + 0.822653i $$0.307507\pi$$
$$24$$ −0.866025 0.500000i −0.176777 0.102062i
$$25$$ 0 0
$$26$$ −3.60194 0.161290i −0.706399 0.0316315i
$$27$$ 1.00000i 0.192450i
$$28$$ −0.661290 + 1.14539i −0.124972 + 0.216458i
$$29$$ −1.01141 + 1.75182i −0.187815 + 0.325305i −0.944521 0.328450i $$-0.893474\pi$$
0.756707 + 0.653755i $$0.226807\pi$$
$$30$$ 0 0
$$31$$ 10.1321i 1.81978i −0.414853 0.909888i $$-0.636167\pi$$
0.414853 0.909888i $$-0.363833\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 2.30668 + 3.99528i 0.401541 + 0.695489i
$$34$$ 4.00000i 0.685994i
$$35$$ 0 0
$$36$$ 0.500000 0.866025i 0.0833333 0.144338i
$$37$$ 3.40475 5.89721i 0.559738 0.969495i −0.437780 0.899082i $$-0.644235\pi$$
0.997518 0.0704126i $$-0.0224316\pi$$
$$38$$ 2.29078i 0.371613i
$$39$$ 0.161290 3.60194i 0.0258270 0.576772i
$$40$$ 0 0
$$41$$ −4.02283 2.32258i −0.628260 0.362726i 0.151818 0.988408i $$-0.451487\pi$$
−0.780078 + 0.625682i $$0.784821\pi$$
$$42$$ −1.14539 0.661290i −0.176737 0.102039i
$$43$$ −7.45269 + 4.30281i −1.13652 + 0.656173i −0.945568 0.325426i $$-0.894492\pi$$
−0.190957 + 0.981598i $$0.561159\pi$$
$$44$$ 4.61335i 0.695489i
$$45$$ 0 0
$$46$$ −7.50670 + 4.33399i −1.10680 + 0.639012i
$$47$$ −9.10926 −1.32872 −0.664361 0.747412i $$-0.731296\pi$$
−0.664361 + 0.747412i $$0.731296\pi$$
$$48$$ 0.866025 0.500000i 0.125000 0.0721688i
$$49$$ 2.62539 4.54731i 0.375056 0.649616i
$$50$$ 0 0
$$51$$ −4.00000 −0.560112
$$52$$ 1.94065 3.03873i 0.269120 0.421396i
$$53$$ 0.826674i 0.113552i 0.998387 + 0.0567762i $$0.0180821\pi$$
−0.998387 + 0.0567762i $$0.981918\pi$$
$$54$$ 0.866025 + 0.500000i 0.117851 + 0.0680414i
$$55$$ 0 0
$$56$$ −0.661290 1.14539i −0.0883686 0.153059i
$$57$$ 2.29078 0.303421
$$58$$ −1.01141 1.75182i −0.132805 0.230025i
$$59$$ −2.72064 + 1.57076i −0.354197 + 0.204496i −0.666532 0.745476i $$-0.732222\pi$$
0.312335 + 0.949972i $$0.398889\pi$$
$$60$$ 0 0
$$61$$ −0.267949 0.464102i −0.0343074 0.0594221i 0.848362 0.529417i $$-0.177589\pi$$
−0.882669 + 0.469995i $$0.844256\pi$$
$$62$$ 8.77464 + 5.06604i 1.11438 + 0.643388i
$$63$$ 0.661290 1.14539i 0.0833147 0.144305i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.61335 −0.567865
$$67$$ −1.59053 + 2.75488i −0.194314 + 0.336562i −0.946675 0.322189i $$-0.895581\pi$$
0.752361 + 0.658751i $$0.228915\pi$$
$$68$$ −3.46410 2.00000i −0.420084 0.242536i
$$69$$ −4.33399 7.50670i −0.521751 0.903700i
$$70$$ 0 0
$$71$$ −9.81724 + 5.66799i −1.16509 + 0.672666i −0.952519 0.304479i $$-0.901518\pi$$
−0.212573 + 0.977145i $$0.568184\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 6.28304 0.735375 0.367687 0.929949i $$-0.380150\pi$$
0.367687 + 0.929949i $$0.380150\pi$$
$$74$$ 3.40475 + 5.89721i 0.395795 + 0.685536i
$$75$$ 0 0
$$76$$ 1.98387 + 1.14539i 0.227565 + 0.131385i
$$77$$ 6.10153i 0.695334i
$$78$$ 3.03873 + 1.94065i 0.344068 + 0.219736i
$$79$$ −2.96774 −0.333897 −0.166948 0.985966i $$-0.553391\pi$$
−0.166948 + 0.985966i $$0.553391\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 4.02283 2.32258i 0.444247 0.256486i
$$83$$ −15.8719 −1.74216 −0.871082 0.491138i $$-0.836581\pi$$
−0.871082 + 0.491138i $$0.836581\pi$$
$$84$$ 1.14539 0.661290i 0.124972 0.0721526i
$$85$$ 0 0
$$86$$ 8.60562i 0.927968i
$$87$$ 1.75182 1.01141i 0.187815 0.108435i
$$88$$ −3.99528 2.30668i −0.425899 0.245893i
$$89$$ −10.2746 5.93207i −1.08911 0.628798i −0.155771 0.987793i $$-0.549786\pi$$
−0.933339 + 0.358995i $$0.883119\pi$$
$$90$$ 0 0
$$91$$ 2.56667 4.01896i 0.269060 0.421302i
$$92$$ 8.66799i 0.903700i
$$93$$ −5.06604 + 8.77464i −0.525324 + 0.909888i
$$94$$ 4.55463 7.88885i 0.469774 0.813673i
$$95$$ 0 0
$$96$$ 1.00000i 0.102062i
$$97$$ 4.40947 + 7.63743i 0.447714 + 0.775463i 0.998237 0.0593568i $$-0.0189050\pi$$
−0.550523 + 0.834820i $$0.685572\pi$$
$$98$$ 2.62539 + 4.54731i 0.265205 + 0.459348i
$$99$$ 4.61335i 0.463660i
$$100$$ 0 0
$$101$$ −3.61335 + 6.25851i −0.359542 + 0.622745i −0.987884 0.155192i $$-0.950400\pi$$
0.628342 + 0.777937i $$0.283734\pi$$
$$102$$ 2.00000 3.46410i 0.198030 0.342997i
$$103$$ 18.4000i 1.81301i −0.422196 0.906505i $$-0.638740\pi$$
0.422196 0.906505i $$-0.361260\pi$$
$$104$$ 1.66129 + 3.20002i 0.162903 + 0.313788i
$$105$$ 0 0
$$106$$ −0.715920 0.413337i −0.0695363 0.0401468i
$$107$$ 2.66025 + 1.53590i 0.257176 + 0.148481i 0.623046 0.782185i $$-0.285895\pi$$
−0.365869 + 0.930666i $$0.619228\pi$$
$$108$$ −0.866025 + 0.500000i −0.0833333 + 0.0481125i
$$109$$ 13.2267i 1.26689i −0.773788 0.633445i $$-0.781640\pi$$
0.773788 0.633445i $$-0.218360\pi$$
$$110$$ 0 0
$$111$$ −5.89721 + 3.40475i −0.559738 + 0.323165i
$$112$$ 1.32258 0.124972
$$113$$ −7.00306 + 4.04322i −0.658792 + 0.380354i −0.791817 0.610759i $$-0.790864\pi$$
0.133024 + 0.991113i $$0.457531\pi$$
$$114$$ −1.14539 + 1.98387i −0.107275 + 0.185806i
$$115$$ 0 0
$$116$$ 2.02283 0.187815
$$117$$ −1.94065 + 3.03873i −0.179413 + 0.280931i
$$118$$ 3.14152i 0.289201i
$$119$$ −4.58155 2.64516i −0.419990 0.242481i
$$120$$ 0 0
$$121$$ 5.14152 + 8.90538i 0.467411 + 0.809580i
$$122$$ 0.535898 0.0485180
$$123$$ 2.32258 + 4.02283i 0.209420 + 0.362726i
$$124$$ −8.77464 + 5.06604i −0.787986 + 0.454944i
$$125$$ 0 0
$$126$$ 0.661290 + 1.14539i 0.0589124 + 0.102039i
$$127$$ −9.93490 5.73592i −0.881580 0.508980i −0.0104008 0.999946i $$-0.503311\pi$$
−0.871179 + 0.490966i $$0.836644\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 8.60562 0.757683
$$130$$ 0 0
$$131$$ −15.9906 −1.39710 −0.698551 0.715560i $$-0.746172\pi$$
−0.698551 + 0.715560i $$0.746172\pi$$
$$132$$ 2.30668 3.99528i 0.200771 0.347745i
$$133$$ 2.62383 + 1.51487i 0.227515 + 0.131356i
$$134$$ −1.59053 2.75488i −0.137401 0.237985i
$$135$$ 0 0
$$136$$ 3.46410 2.00000i 0.297044 0.171499i
$$137$$ −8.03486 13.9168i −0.686465 1.18899i −0.972974 0.230914i $$-0.925828\pi$$
0.286509 0.958077i $$-0.407505\pi$$
$$138$$ 8.66799 0.737868
$$139$$ 4.66129 + 8.07359i 0.395365 + 0.684793i 0.993148 0.116865i $$-0.0372846\pi$$
−0.597782 + 0.801658i $$0.703951\pi$$
$$140$$ 0 0
$$141$$ 7.88885 + 4.55463i 0.664361 + 0.383569i
$$142$$ 11.3360i 0.951294i
$$143$$ 0.744087 16.6170i 0.0622237 1.38959i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ −3.14152 + 5.44128i −0.259994 + 0.450323i
$$147$$ −4.54731 + 2.62539i −0.375056 + 0.216539i
$$148$$ −6.80951 −0.559738
$$149$$ −3.53788 + 2.04259i −0.289834 + 0.167336i −0.637867 0.770146i $$-0.720183\pi$$
0.348033 + 0.937482i $$0.386850\pi$$
$$150$$ 0 0
$$151$$ 19.9811i 1.62604i −0.582235 0.813021i $$-0.697822\pi$$
0.582235 0.813021i $$-0.302178\pi$$
$$152$$ −1.98387 + 1.14539i −0.160913 + 0.0929032i
$$153$$ 3.46410 + 2.00000i 0.280056 + 0.161690i
$$154$$ −5.28408 3.05076i −0.425803 0.245838i
$$155$$ 0 0
$$156$$ −3.20002 + 1.66129i −0.256206 + 0.133010i
$$157$$ 7.13379i 0.569338i −0.958626 0.284669i $$-0.908116\pi$$
0.958626 0.284669i $$-0.0918838\pi$$
$$158$$ 1.48387 2.57014i 0.118050 0.204469i
$$159$$ 0.413337 0.715920i 0.0327797 0.0567762i
$$160$$ 0 0
$$161$$ 11.4641i 0.903498i
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −4.94735 8.56906i −0.387506 0.671180i 0.604607 0.796524i $$-0.293330\pi$$
−0.992113 + 0.125343i $$0.959997\pi$$
$$164$$ 4.64516i 0.362726i
$$165$$ 0 0
$$166$$ 7.93593 13.7454i 0.615948 1.06685i
$$167$$ 12.0187 20.8171i 0.930037 1.61087i 0.146785 0.989168i $$-0.453108\pi$$
0.783253 0.621704i $$-0.213559\pi$$
$$168$$ 1.32258i 0.102039i
$$169$$ −7.48023 + 10.6323i −0.575402 + 0.817870i
$$170$$ 0 0
$$171$$ −1.98387 1.14539i −0.151710 0.0875900i
$$172$$ 7.45269 + 4.30281i 0.568262 + 0.328086i
$$173$$ −2.18946 + 1.26408i −0.166461 + 0.0961065i −0.580916 0.813963i $$-0.697306\pi$$
0.414455 + 0.910070i $$0.363972\pi$$
$$174$$ 2.02283i 0.153350i
$$175$$ 0 0
$$176$$ 3.99528 2.30668i 0.301156 0.173872i
$$177$$ 3.14152 0.236131
$$178$$ 10.2746 5.93207i 0.770117 0.444627i
$$179$$ 3.13784 5.43490i 0.234533 0.406223i −0.724604 0.689166i $$-0.757977\pi$$
0.959137 + 0.282942i $$0.0913105\pi$$
$$180$$ 0 0
$$181$$ −12.2830 −0.912991 −0.456496 0.889726i $$-0.650896\pi$$
−0.456496 + 0.889726i $$0.650896\pi$$
$$182$$ 2.19719 + 4.23228i 0.162866 + 0.313717i
$$183$$ 0.535898i 0.0396147i
$$184$$ 7.50670 + 4.33399i 0.553401 + 0.319506i
$$185$$ 0 0
$$186$$ −5.06604 8.77464i −0.371460 0.643388i
$$187$$ −18.4534 −1.34945
$$188$$ 4.55463 + 7.88885i 0.332181 + 0.575354i
$$189$$ −1.14539 + 0.661290i −0.0833147 + 0.0481018i
$$190$$ 0 0
$$191$$ 4.87357 + 8.44128i 0.352639 + 0.610789i 0.986711 0.162485i $$-0.0519509\pi$$
−0.634072 + 0.773274i $$0.718618\pi$$
$$192$$ −0.866025 0.500000i −0.0625000 0.0360844i
$$193$$ 6.88130 11.9188i 0.495327 0.857932i −0.504658 0.863319i $$-0.668382\pi$$
0.999985 + 0.00538741i $$0.00171487\pi$$
$$194$$ −8.81894 −0.633163
$$195$$ 0 0
$$196$$ −5.25078 −0.375056
$$197$$ −5.07076 + 8.78282i −0.361277 + 0.625750i −0.988171 0.153354i $$-0.950992\pi$$
0.626894 + 0.779104i $$0.284326\pi$$
$$198$$ 3.99528 + 2.30668i 0.283932 + 0.163928i
$$199$$ −4.78668 8.29078i −0.339319 0.587717i 0.644986 0.764194i $$-0.276863\pi$$
−0.984305 + 0.176477i $$0.943530\pi$$
$$200$$ 0 0
$$201$$ 2.75488 1.59053i 0.194314 0.112187i
$$202$$ −3.61335 6.25851i −0.254235 0.440348i
$$203$$ 2.67535 0.187773
$$204$$ 2.00000 + 3.46410i 0.140028 + 0.242536i
$$205$$ 0 0
$$206$$ 15.9349 + 9.20002i 1.11024 + 0.640996i
$$207$$ 8.66799i 0.602467i
$$208$$ −3.60194 0.161290i −0.249750 0.0111834i
$$209$$ 10.5682 0.731015
$$210$$ 0 0
$$211$$ 0.542594 0.939800i 0.0373537 0.0646985i −0.846744 0.532000i $$-0.821441\pi$$
0.884098 + 0.467302i $$0.154774\pi$$
$$212$$ 0.715920 0.413337i 0.0491696 0.0283881i
$$213$$ 11.3360 0.776728
$$214$$ −2.66025 + 1.53590i −0.181851 + 0.104992i
$$215$$ 0 0
$$216$$ 1.00000i 0.0680414i
$$217$$ −11.6052 + 6.70025i −0.787810 + 0.454842i
$$218$$ 11.4547 + 6.61335i 0.775808 + 0.447913i
$$219$$ −5.44128 3.14152i −0.367687 0.212284i
$$220$$ 0 0
$$221$$ 12.1549 + 7.76261i 0.817628 + 0.522170i
$$222$$ 6.80951i 0.457024i
$$223$$ −12.4708 + 21.6001i −0.835106 + 1.44645i 0.0588375 + 0.998268i $$0.481261\pi$$
−0.893944 + 0.448179i $$0.852073\pi$$
$$224$$ −0.661290 + 1.14539i −0.0441843 + 0.0765294i
$$225$$ 0 0
$$226$$ 8.08643i 0.537902i
$$227$$ 9.66025 + 16.7321i 0.641174 + 1.11055i 0.985171 + 0.171575i $$0.0548855\pi$$
−0.343998 + 0.938971i $$0.611781\pi$$
$$228$$ −1.14539 1.98387i −0.0758551 0.131385i
$$229$$ 4.15491i 0.274564i −0.990532 0.137282i $$-0.956163\pi$$
0.990532 0.137282i $$-0.0438367\pi$$
$$230$$ 0 0
$$231$$ 3.05076 5.28408i 0.200726 0.347667i
$$232$$ −1.01141 + 1.75182i −0.0664025 + 0.115013i
$$233$$ 16.9665i 1.11151i 0.831346 + 0.555756i $$0.187571\pi$$
−0.831346 + 0.555756i $$0.812429\pi$$
$$234$$ −1.66129 3.20002i −0.108602 0.209192i
$$235$$ 0 0
$$236$$ 2.72064 + 1.57076i 0.177098 + 0.102248i
$$237$$ 2.57014 + 1.48387i 0.166948 + 0.0963877i
$$238$$ 4.58155 2.64516i 0.296978 0.171460i
$$239$$ 6.34416i 0.410370i 0.978723 + 0.205185i $$0.0657795\pi$$
−0.978723 + 0.205185i $$0.934220\pi$$
$$240$$ 0 0
$$241$$ 20.9452 12.0927i 1.34920 0.778962i 0.361065 0.932541i $$-0.382413\pi$$
0.988136 + 0.153579i $$0.0490800\pi$$
$$242$$ −10.2830 −0.661019
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ −0.267949 + 0.464102i −0.0171537 + 0.0297111i
$$245$$ 0 0
$$246$$ −4.64516 −0.296165
$$247$$ −6.96104 4.44560i −0.442921 0.282867i
$$248$$ 10.1321i 0.643388i
$$249$$ 13.7454 + 7.93593i 0.871082 + 0.502919i
$$250$$ 0 0
$$251$$ 4.41249 + 7.64265i 0.278514 + 0.482400i 0.971016 0.239016i $$-0.0768249\pi$$
−0.692502 + 0.721416i $$0.743492\pi$$
$$252$$ −1.32258 −0.0833147
$$253$$ −19.9942 34.6311i −1.25703 2.17724i
$$254$$ 9.93490 5.73592i 0.623371 0.359903i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −7.26157 4.19247i −0.452964 0.261519i 0.256117 0.966646i $$-0.417557\pi$$
−0.709081 + 0.705127i $$0.750890\pi$$
$$258$$ −4.30281 + 7.45269i −0.267881 + 0.463984i
$$259$$ −9.00612 −0.559613
$$260$$ 0 0
$$261$$ −2.02283 −0.125210
$$262$$ 7.99528 13.8482i 0.493950 0.855547i
$$263$$ −1.66389 0.960648i −0.102600 0.0592361i 0.447822 0.894123i $$-0.352200\pi$$
−0.550422 + 0.834887i $$0.685533\pi$$
$$264$$ 2.30668 + 3.99528i 0.141966 + 0.245893i
$$265$$ 0 0
$$266$$ −2.62383 + 1.51487i −0.160877 + 0.0928824i
$$267$$ 5.93207 + 10.2746i 0.363037 + 0.628798i
$$268$$ 3.18106 0.194314
$$269$$ −16.1549 27.9811i −0.984982 1.70604i −0.642014 0.766693i $$-0.721901\pi$$
−0.342968 0.939347i $$-0.611432\pi$$
$$270$$ 0 0
$$271$$ 20.3105 + 11.7263i 1.23378 + 0.712322i 0.967815 0.251662i $$-0.0809770\pi$$
0.265962 + 0.963983i $$0.414310\pi$$
$$272$$ 4.00000i 0.242536i
$$273$$ −4.23228 + 2.19719i −0.256149 + 0.132980i
$$274$$ 16.0697 0.970808
$$275$$ 0 0
$$276$$ −4.33399 + 7.50670i −0.260876 + 0.451850i
$$277$$ −7.79913 + 4.50283i −0.468604 + 0.270549i −0.715655 0.698454i $$-0.753872\pi$$
0.247051 + 0.969002i $$0.420538\pi$$
$$278$$ −9.32258 −0.559131
$$279$$ 8.77464 5.06604i 0.525324 0.303296i
$$280$$ 0 0
$$281$$ 1.71696i 0.102425i 0.998688 + 0.0512125i $$0.0163086\pi$$
−0.998688 + 0.0512125i $$0.983691\pi$$
$$282$$ −7.88885 + 4.55463i −0.469774 + 0.271224i
$$283$$ −1.34172 0.774645i −0.0797572 0.0460479i 0.459591 0.888131i $$-0.347996\pi$$
−0.539348 + 0.842083i $$0.681329\pi$$
$$284$$ 9.81724 + 5.66799i 0.582546 + 0.336333i
$$285$$ 0 0
$$286$$ 14.0187 + 8.95292i 0.828945 + 0.529397i
$$287$$ 6.14359i 0.362645i
$$288$$ 0.500000 0.866025i 0.0294628 0.0510310i
$$289$$ −0.500000 + 0.866025i −0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ 8.81894i 0.516976i
$$292$$ −3.14152 5.44128i −0.183844 0.318427i
$$293$$ 15.2028 + 26.3321i 0.888160 + 1.53834i 0.842049 + 0.539402i $$0.181350\pi$$
0.0461113 + 0.998936i $$0.485317\pi$$
$$294$$ 5.25078i 0.306232i
$$295$$ 0 0
$$296$$ 3.40475 5.89721i 0.197897 0.342768i
$$297$$ −2.30668 + 3.99528i −0.133847 + 0.231830i
$$298$$ 4.08519i 0.236649i
$$299$$ −1.39806 + 31.2216i −0.0808518 + 1.80559i
$$300$$ 0 0
$$301$$ 9.85677 + 5.69081i 0.568135 + 0.328013i
$$302$$ 17.3042 + 9.99057i 0.995743 + 0.574892i
$$303$$ 6.25851 3.61335i 0.359542 0.207582i
$$304$$ 2.29078i 0.131385i
$$305$$ 0 0
$$306$$ −3.46410 + 2.00000i −0.198030 + 0.114332i
$$307$$ 9.82622 0.560812 0.280406 0.959882i $$-0.409531\pi$$
0.280406 + 0.959882i $$0.409531\pi$$
$$308$$ 5.28408 3.05076i 0.301088 0.173833i
$$309$$ −9.20002 + 15.9349i −0.523371 + 0.906505i
$$310$$ 0 0
$$311$$ −3.40049 −0.192824 −0.0964121 0.995342i $$-0.530737\pi$$
−0.0964121 + 0.995342i $$0.530737\pi$$
$$312$$ 0.161290 3.60194i 0.00913124 0.203920i
$$313$$ 16.2340i 0.917599i −0.888540 0.458800i $$-0.848280\pi$$
0.888540 0.458800i $$-0.151720\pi$$
$$314$$ 6.17804 + 3.56690i 0.348647 + 0.201292i
$$315$$ 0 0
$$316$$ 1.48387 + 2.57014i 0.0834742 + 0.144582i
$$317$$ 23.5231 1.32119 0.660596 0.750742i $$-0.270304\pi$$
0.660596 + 0.750742i $$0.270304\pi$$
$$318$$ 0.413337 + 0.715920i 0.0231788 + 0.0401468i
$$319$$ 8.08176 4.66601i 0.452492 0.261246i
$$320$$ 0 0
$$321$$ −1.53590 2.66025i −0.0857255 0.148481i
$$322$$ 9.92820 + 5.73205i 0.553277 + 0.319435i
$$323$$ −4.58155 + 7.93548i −0.254924 + 0.441542i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 9.89470 0.548016
$$327$$ −6.61335 + 11.4547i −0.365719 + 0.633445i
$$328$$ −4.02283 2.32258i −0.222123 0.128243i
$$329$$ 6.02386 + 10.4336i 0.332106 + 0.575225i
$$330$$ 0 0
$$331$$ 15.6667 9.04520i 0.861122 0.497169i −0.00326597 0.999995i $$-0.501040\pi$$
0.864388 + 0.502826i $$0.167706\pi$$
$$332$$ 7.93593 + 13.7454i 0.435541 + 0.754379i
$$333$$ 6.80951 0.373159
$$334$$ 12.0187 + 20.8171i 0.657636 + 1.13906i
$$335$$ 0 0
$$336$$ −1.14539 0.661290i −0.0624860 0.0360763i
$$337$$ 5.69900i 0.310444i 0.987880 + 0.155222i $$0.0496093\pi$$
−0.987880 + 0.155222i $$0.950391\pi$$
$$338$$ −5.46774 11.7942i −0.297406 0.641521i
$$339$$ 8.08643 0.439195
$$340$$ 0 0
$$341$$ −23.3715 + 40.4806i −1.26564 + 2.19214i
$$342$$ 1.98387 1.14539i 0.107275 0.0619355i
$$343$$ −16.2026 −0.874860
$$344$$ −7.45269 + 4.30281i −0.401822 + 0.231992i
$$345$$ 0 0
$$346$$ 2.52817i 0.135915i
$$347$$ 13.6374 7.87357i 0.732095 0.422676i −0.0870928 0.996200i $$-0.527758\pi$$
0.819188 + 0.573525i $$0.194424\pi$$
$$348$$ −1.75182 1.01141i −0.0939073 0.0542174i
$$349$$ −13.2679 7.66025i −0.710217 0.410044i 0.100924 0.994894i $$-0.467820\pi$$
−0.811141 + 0.584850i $$0.801153\pi$$
$$350$$ 0 0
$$351$$ 3.20002 1.66129i 0.170804 0.0886731i
$$352$$ 4.61335i 0.245893i
$$353$$ −0.599964 + 1.03917i −0.0319328 + 0.0553093i −0.881550 0.472090i $$-0.843500\pi$$
0.849617 + 0.527400i $$0.176833\pi$$
$$354$$ −1.57076 + 2.72064i −0.0834850 + 0.144600i
$$355$$ 0 0
$$356$$ 11.8641i 0.628798i
$$357$$ 2.64516 + 4.58155i 0.139997 + 0.242481i
$$358$$ 3.13784 + 5.43490i 0.165840 + 0.287243i
$$359$$ 16.2830i 0.859386i −0.902975 0.429693i $$-0.858622\pi$$
0.902975 0.429693i $$-0.141378\pi$$
$$360$$ 0 0
$$361$$ −6.87617 + 11.9099i −0.361904 + 0.626836i
$$362$$ 6.14152 10.6374i 0.322791 0.559091i
$$363$$ 10.2830i 0.539720i
$$364$$ −4.76386 0.213319i −0.249694 0.0111809i
$$365$$ 0 0
$$366$$ −0.464102 0.267949i −0.0242590 0.0140059i
$$367$$ −17.0040 9.81724i −0.887599 0.512456i −0.0144428 0.999896i $$-0.504597\pi$$
−0.873156 + 0.487440i $$0.837931\pi$$
$$368$$ −7.50670 + 4.33399i −0.391314 + 0.225925i
$$369$$ 4.64516i 0.241817i
$$370$$ 0 0
$$371$$ 0.946862 0.546671i 0.0491586 0.0283817i
$$372$$ 10.1321 0.525324
$$373$$ −2.21484 + 1.27874i −0.114680 + 0.0662106i −0.556243 0.831020i $$-0.687758\pi$$
0.441563 + 0.897230i $$0.354424\pi$$
$$374$$ 9.22671 15.9811i 0.477102 0.826365i
$$375$$ 0 0
$$376$$ −9.10926 −0.469774
$$377$$ −7.28610 0.326261i −0.375253 0.0168033i
$$378$$ 1.32258i 0.0680262i
$$379$$ 13.0846 + 7.55440i 0.672111 + 0.388044i 0.796876 0.604143i $$-0.206484\pi$$
−0.124765 + 0.992186i $$0.539818\pi$$
$$380$$ 0 0
$$381$$ 5.73592 + 9.93490i 0.293860 + 0.508980i
$$382$$ −9.74715 −0.498707
$$383$$ −9.36517 16.2210i −0.478538 0.828852i 0.521159 0.853459i $$-0.325500\pi$$
−0.999697 + 0.0246073i $$0.992166\pi$$
$$384$$ 0.866025 0.500000i 0.0441942 0.0255155i
$$385$$ 0 0
$$386$$ 6.88130 + 11.9188i 0.350249 + 0.606649i
$$387$$ −7.45269 4.30281i −0.378841 0.218724i
$$388$$ 4.40947 7.63743i 0.223857 0.387732i
$$389$$ −6.96899 −0.353342 −0.176671 0.984270i $$-0.556533\pi$$
−0.176671 + 0.984270i $$0.556533\pi$$
$$390$$ 0 0
$$391$$ 34.6719 1.75344
$$392$$ 2.62539 4.54731i 0.132602 0.229674i
$$393$$ 13.8482 + 7.99528i 0.698551 + 0.403309i
$$394$$ −5.07076 8.78282i −0.255461 0.442472i
$$395$$ 0 0
$$396$$ −3.99528 + 2.30668i −0.200771 + 0.115915i
$$397$$ 9.28606 + 16.0839i 0.466054 + 0.807229i 0.999248 0.0387637i $$-0.0123420\pi$$
−0.533195 + 0.845993i $$0.679009\pi$$
$$398$$ 9.57336 0.479869
$$399$$ −1.51487 2.62383i −0.0758382 0.131356i
$$400$$ 0 0
$$401$$ −25.7126 14.8452i −1.28403 0.741333i −0.306444 0.951889i $$-0.599139\pi$$
−0.977582 + 0.210556i $$0.932473\pi$$
$$402$$ 3.18106i 0.158657i
$$403$$ 32.4229 16.8323i 1.61510 0.838478i
$$404$$ 7.22671 0.359542
$$405$$ 0 0
$$406$$ −1.33767 + 2.31692i −0.0663877 + 0.114987i
$$407$$ −27.2059 + 15.7073i −1.34855 + 0.778584i
$$408$$ −4.00000 −0.198030
$$409$$ 21.0752 12.1678i 1.04210 0.601657i 0.121673 0.992570i $$-0.461174\pi$$
0.920427 + 0.390913i $$0.127841\pi$$
$$410$$ 0 0
$$411$$ 16.0697i 0.792661i
$$412$$ −15.9349 + 9.20002i −0.785056 + 0.453252i
$$413$$ 3.59826 + 2.07746i 0.177059 + 0.102225i
$$414$$ −7.50670 4.33399i −0.368934 0.213004i
$$415$$ 0 0
$$416$$ 1.94065 3.03873i 0.0951483 0.148986i
$$417$$ 9.32258i 0.456529i
$$418$$ −5.28408 + 9.15229i −0.258453 + 0.447653i
$$419$$ −1.44128 + 2.49636i −0.0704109 + 0.121955i −0.899081 0.437781i $$-0.855764\pi$$
0.828671 + 0.559737i $$0.189098\pi$$
$$420$$ 0 0
$$421$$ 4.94707i 0.241106i −0.992707 0.120553i $$-0.961533\pi$$
0.992707 0.120553i $$-0.0384667\pi$$
$$422$$ 0.542594 + 0.939800i 0.0264131 + 0.0457488i
$$423$$ −4.55463 7.88885i −0.221454 0.383569i
$$424$$ 0.826674i 0.0401468i
$$425$$ 0 0
$$426$$ −5.66799 + 9.81724i −0.274615 + 0.475647i
$$427$$ −0.354384 + 0.613811i −0.0171499 + 0.0297044i
$$428$$ 3.07180i 0.148481i
$$429$$ −8.95292 + 14.0187i −0.432251 + 0.676831i
$$430$$ 0 0
$$431$$ −15.3829 8.88130i −0.740967 0.427797i 0.0814539 0.996677i $$-0.474044\pi$$
−0.822421 + 0.568880i $$0.807377\pi$$
$$432$$ 0.866025 + 0.500000i 0.0416667 + 0.0240563i
$$433$$ −31.0362 + 17.9188i −1.49151 + 0.861121i −0.999953 0.00972676i $$-0.996904\pi$$
−0.491553 + 0.870848i $$0.663570\pi$$
$$434$$ 13.4005i 0.643244i
$$435$$ 0 0
$$436$$ −11.4547 + 6.61335i −0.548579 + 0.316722i
$$437$$ −19.8564 −0.949861
$$438$$ 5.44128 3.14152i 0.259994 0.150108i
$$439$$ −5.04520 + 8.73854i −0.240794 + 0.417068i −0.960941 0.276754i $$-0.910741\pi$$
0.720147 + 0.693822i $$0.244075\pi$$
$$440$$ 0 0
$$441$$ 5.25078 0.250037
$$442$$ −12.8001 + 6.64516i −0.608837 + 0.316078i
$$443$$ 13.6981i 0.650816i 0.945574 + 0.325408i $$0.105502\pi$$
−0.945574 + 0.325408i $$0.894498\pi$$
$$444$$ 5.89721 + 3.40475i 0.279869 + 0.161582i
$$445$$ 0 0
$$446$$ −12.4708 21.6001i −0.590509 1.02279i
$$447$$ 4.08519 0.193223
$$448$$ −0.661290 1.14539i −0.0312430 0.0541145i
$$449$$ −13.2613 + 7.65639i −0.625837 + 0.361327i −0.779138 0.626852i $$-0.784343\pi$$
0.153301 + 0.988180i $$0.451010\pi$$
$$450$$ 0 0
$$451$$ 10.7149 + 18.5587i 0.504544 + 0.873896i
$$452$$ 7.00306 + 4.04322i 0.329396 + 0.190177i
$$453$$ −9.99057 + 17.3042i −0.469398 + 0.813021i
$$454$$ −19.3205 −0.906756
$$455$$ 0 0
$$456$$ 2.29078 0.107275
$$457$$ −7.77770 + 13.4714i −0.363826 + 0.630164i −0.988587 0.150651i $$-0.951863\pi$$
0.624761 + 0.780816i $$0.285196\pi$$
$$458$$ 3.59826 + 2.07746i 0.168136 + 0.0970732i
$$459$$ −2.00000 3.46410i −0.0933520 0.161690i
$$460$$ 0 0
$$461$$ 13.5473 7.82154i 0.630961 0.364286i −0.150163 0.988661i $$-0.547980\pi$$
0.781124 + 0.624376i $$0.214647\pi$$
$$462$$ 3.05076 + 5.28408i 0.141934 + 0.245838i
$$463$$ −13.7170 −0.637481 −0.318741 0.947842i $$-0.603260\pi$$
−0.318741 + 0.947842i $$0.603260\pi$$
$$464$$ −1.01141 1.75182i −0.0469537 0.0813261i
$$465$$ 0 0
$$466$$ −14.6934 8.48325i −0.680659 0.392979i
$$467$$ 0.943666i 0.0436677i 0.999762 + 0.0218338i $$0.00695048\pi$$
−0.999762 + 0.0218338i $$0.993050\pi$$
$$468$$ 3.60194 + 0.161290i 0.166500 + 0.00745563i
$$469$$ 4.20720 0.194271
$$470$$ 0 0
$$471$$ −3.56690 + 6.17804i −0.164354 + 0.284669i
$$472$$ −2.72064 + 1.57076i −0.125228 + 0.0723001i
$$473$$ 39.7008 1.82544
$$474$$ −2.57014 + 1.48387i −0.118050 + 0.0681564i
$$475$$ 0 0
$$476$$ 5.29032i 0.242481i
$$477$$ −0.715920 + 0.413337i −0.0327797 + 0.0189254i
$$478$$ −5.49420 3.17208i −0.251299 0.145088i
$$479$$ 9.61460 + 5.55099i 0.439302 + 0.253631i 0.703302 0.710892i $$-0.251708\pi$$
−0.263999 + 0.964523i $$0.585042\pi$$
$$480$$ 0 0
$$481$$ 24.5275 + 1.09830i 1.11836 + 0.0500784i
$$482$$ 24.1855i 1.10162i
$$483$$ −5.73205 + 9.92820i −0.260817 + 0.451749i
$$484$$ 5.14152 8.90538i 0.233706 0.404790i
$$485$$ 0 0
$$486$$ 1.00000i 0.0453609i
$$487$$ 16.4708 + 28.5283i 0.746363 + 1.29274i 0.949555 + 0.313600i $$0.101535\pi$$
−0.203192 + 0.979139i $$0.565132\pi$$
$$488$$ −0.267949 0.464102i −0.0121295 0.0210089i
$$489$$ 9.89470i 0.447454i
$$490$$ 0 0
$$491$$ 14.2257 24.6396i 0.641996 1.11197i −0.342991 0.939339i $$-0.611440\pi$$
0.984987 0.172630i $$-0.0552266\pi$$
$$492$$ 2.32258 4.02283i 0.104710 0.181363i
$$493$$ 8.09130i 0.364414i
$$494$$ 7.33052 3.80564i 0.329816 0.171224i
$$495$$ 0 0
$$496$$ 8.77464 + 5.06604i 0.393993 + 0.227472i
$$497$$ 12.9841 + 7.49636i 0.582416 + 0.336258i
$$498$$ −13.7454 + 7.93593i −0.615948 + 0.355618i
$$499$$ 4.10926i 0.183956i 0.995761 + 0.0919779i $$0.0293189\pi$$
−0.995761 + 0.0919779i $$0.970681\pi$$
$$500$$ 0 0
$$501$$ −20.8171 + 12.0187i −0.930037 + 0.536957i
$$502$$ −8.82497 −0.393878
$$503$$ 4.96753 2.86800i 0.221491 0.127878i −0.385149 0.922854i $$-0.625850\pi$$
0.606641 + 0.794976i $$0.292517\pi$$
$$504$$ 0.661290 1.14539i 0.0294562 0.0510196i
$$505$$ 0 0
$$506$$ 39.9885 1.77771
$$507$$ 11.7942 5.46774i 0.523800 0.242831i
$$508$$ 11.4718i 0.508980i
$$509$$ 13.1129 + 7.57076i 0.581221 + 0.335568i 0.761618 0.648026i $$-0.224405\pi$$
−0.180397 + 0.983594i $$0.557738\pi$$
$$510$$ 0 0
$$511$$ −4.15491 7.19652i −0.183803 0.318355i
$$512$$ 1.00000 0.0441942
$$513$$ 1.14539 + 1.98387i 0.0505701 + 0.0875900i
$$514$$ 7.26157 4.19247i 0.320294 0.184922i
$$515$$ 0 0
$$516$$ −4.30281 7.45269i −0.189421 0.328086i
$$517$$ 36.3941 + 21.0121i 1.60061 + 0.924112i
$$518$$ 4.50306 7.79953i 0.197853 0.342691i
$$519$$ 2.52817 0.110974
$$520$$ 0 0
$$521$$ 8.93027 0.391242 0.195621 0.980680i $$-0.437328\pi$$
0.195621 + 0.980680i $$0.437328\pi$$
$$522$$ 1.01141 1.75182i 0.0442683 0.0766750i
$$523$$ 8.50166 + 4.90844i 0.371752 + 0.214631i 0.674223 0.738527i $$-0.264478\pi$$
−0.302472 + 0.953158i $$0.597812\pi$$
$$524$$ 7.99528 + 13.8482i 0.349276 + 0.604963i
$$525$$ 0 0
$$526$$ 1.66389 0.960648i 0.0725491 0.0418863i
$$527$$ −20.2642 35.0986i −0.882721 1.52892i
$$528$$ −4.61335 −0.200771
$$529$$ 26.0670 + 45.1493i 1.13335 + 1.96301i
$$530$$ 0 0
$$531$$ −2.72064 1.57076i −0.118066 0.0681652i
$$532$$ 3.02973i 0.131356i
$$533$$ 0.749217 16.7316i 0.0324522 0.724726i
$$534$$ −11.8641 −0.513411
$$535$$ 0 0
$$536$$ −1.59053 + 2.75488i −0.0687004 + 0.118993i
$$537$$ −5.43490 + 3.13784i −0.234533 + 0.135408i
$$538$$ 32.3098 1.39298
$$539$$ −20.9784 + 12.1119i −0.903602 + 0.521695i
$$540$$ 0 0
$$541$$ 3.80826i 0.163730i 0.996643 + 0.0818650i $$0.0260876\pi$$
−0.996643 + 0.0818650i $$0.973912\pi$$
$$542$$ −20.3105 + 11.7263i −0.872413 + 0.503688i
$$543$$ 10.6374 + 6.14152i 0.456496 + 0.263558i
$$544$$ −3.46410 2.00000i −0.148522 0.0857493i
$$545$$ 0 0
$$546$$ 0.213319 4.76386i 0.00912920 0.203874i
$$547$$ 45.5847i 1.94906i −0.224257 0.974530i $$-0.571995\pi$$
0.224257 0.974530i $$-0.428005\pi$$
$$548$$ −8.03486 + 13.9168i −0.343232 + 0.594496i
$$549$$ 0.267949 0.464102i 0.0114358 0.0198074i
$$550$$ 0 0
$$551$$ 4.63384i 0.197408i
$$552$$ −4.33399 7.50670i −0.184467 0.319506i
$$553$$ 1.96254 + 3.39921i 0.0834555 + 0.144549i
$$554$$ 9.00566i 0.382614i
$$555$$ 0 0
$$556$$ 4.66129 8.07359i 0.197683 0.342397i
$$557$$ −18.4296 + 31.9209i −0.780885 + 1.35253i 0.150541 + 0.988604i $$0.451898\pi$$
−0.931427 + 0.363929i $$0.881435\pi$$
$$558$$ 10.1321i 0.428925i
$$559$$ −26.1502 16.7005i −1.10603 0.706357i
$$560$$ 0 0
$$561$$ 15.9811 + 9.22671i 0.674724 + 0.389552i
$$562$$ −1.48693 0.858478i −0.0627223 0.0362127i
$$563$$ −29.2491 + 16.8870i −1.23270 + 0.711701i −0.967592 0.252518i $$-0.918741\pi$$
−0.265109 + 0.964218i $$0.585408\pi$$
$$564$$ 9.10926i 0.383569i
$$565$$ 0 0
$$566$$ 1.34172 0.774645i 0.0563969 0.0325607i
$$567$$ 1.32258 0.0555431
$$568$$ −9.81724 + 5.66799i −0.411922 + 0.237823i
$$569$$ 12.7159 22.0246i 0.533079 0.923320i −0.466175 0.884693i $$-0.654368\pi$$
0.999254 0.0386274i $$-0.0122985\pi$$
$$570$$ 0 0
$$571$$ 13.3682 0.559443 0.279722 0.960081i $$-0.409758\pi$$
0.279722 + 0.960081i $$0.409758\pi$$
$$572$$ −14.7628 + 7.66412i −0.617264 + 0.320453i
$$573$$ 9.74715i 0.407193i
$$574$$ −5.32051 3.07180i −0.222074 0.128214i
$$575$$ 0 0
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ −9.57428 −0.398582 −0.199291 0.979940i $$-0.563864\pi$$
−0.199291 + 0.979940i $$0.563864\pi$$
$$578$$ −0.500000 0.866025i −0.0207973 0.0360219i
$$579$$ −11.9188 + 6.88130i −0.495327 + 0.285977i
$$580$$ 0 0
$$581$$ 10.4959 + 18.1794i 0.435444 + 0.754210i
$$582$$ 7.63743 + 4.40947i 0.316582 + 0.182778i
$$583$$ 1.90687 3.30279i 0.0789745 0.136788i
$$584$$ 6.28304 0.259994
$$585$$ 0 0
$$586$$ −30.4057 −1.25605
$$587$$ 0.700246 1.21286i 0.0289023 0.0500602i −0.851212 0.524821i $$-0.824132\pi$$
0.880115 + 0.474761i $$0.157466\pi$$
$$588$$ 4.54731 + 2.62539i 0.187528 + 0.108269i
$$589$$ 11.6052 + 20.1007i 0.478183 + 0.828237i
$$590$$ 0 0
$$591$$ 8.78282 5.07076i 0.361277 0.208583i
$$592$$ 3.40475 + 5.89721i 0.139935 + 0.242374i
$$593$$ 10.7303 0.440643 0.220321 0.975427i $$-0.429289\pi$$
0.220321 + 0.975427i $$0.429289\pi$$
$$594$$ −2.30668 3.99528i −0.0946441 0.163928i
$$595$$ 0 0
$$596$$ 3.53788 + 2.04259i 0.144917 + 0.0836679i
$$597$$ 9.57336i 0.391812i
$$598$$ −26.3397 16.8215i −1.07711 0.687884i
$$599$$ 40.7967 1.66691 0.833453 0.552590i $$-0.186360\pi$$
0.833453 + 0.552590i $$0.186360\pi$$
$$600$$ 0 0
$$601$$ −21.4416 + 37.1379i −0.874621 + 1.51489i −0.0174548 + 0.999848i $$0.505556\pi$$
−0.857166 + 0.515040i $$0.827777\pi$$
$$602$$ −9.85677 + 5.69081i −0.401732 + 0.231940i
$$603$$ −3.18106 −0.129543
$$604$$ −17.3042 + 9.99057i −0.704097 + 0.406510i
$$605$$ 0 0
$$606$$ 7.22671i 0.293565i
$$607$$ 5.95161 3.43616i 0.241568 0.139470i −0.374329 0.927296i $$-0.622127\pi$$
0.615897 + 0.787826i $$0.288794\pi$$
$$608$$ 1.98387 + 1.14539i 0.0804565 + 0.0464516i
$$609$$ −2.31692 1.33767i −0.0938863 0.0542053i
$$610$$ 0 0
$$611$$ −15.1331 29.1498i −0.612221 1.17927i
$$612$$ 4.00000i 0.161690i
$$613$$ 0.380681 0.659358i 0.0153755 0.0266312i −0.858235 0.513257i $$-0.828439\pi$$
0.873611 + 0.486625i $$0.161772\pi$$
$$614$$ −4.91311 + 8.50975i −0.198277 + 0.343426i
$$615$$ 0 0
$$616$$ 6.10153i 0.245838i
$$617$$ −12.3011 21.3061i −0.495224 0.857753i 0.504761 0.863259i $$-0.331581\pi$$
−0.999985 + 0.00550613i $$0.998247\pi$$
$$618$$ −9.20002 15.9349i −0.370079 0.640996i
$$619$$ 17.2035i 0.691468i −0.938333 0.345734i $$-0.887630\pi$$
0.938333 0.345734i $$-0.112370\pi$$
$$620$$ 0 0
$$621$$ 4.33399 7.50670i 0.173917 0.301233i
$$622$$ 1.70025 2.94491i 0.0681737 0.118080i
$$623$$ 15.6913i 0.628657i
$$624$$ 3.03873 + 1.94065i 0.121646 + 0.0776883i
$$625$$ 0 0
$$626$$ 14.0590 + 8.11699i 0.561912 + 0.324420i
$$627$$ −9.15229 5.28408i −0.365507 0.211026i
$$628$$ −6.17804 + 3.56690i −0.246531 + 0.142335i
$$629$$ 27.2380i 1.08605i
$$630$$ 0 0
$$631$$ 2.08519 1.20388i 0.0830100 0.0479259i −0.457920 0.888993i $$-0.651406\pi$$
0.540930 + 0.841067i $$0.318072\pi$$
$$632$$ −2.96774 −0.118050
$$633$$ −0.939800 + 0.542594i −0.0373537 + 0.0215662i
$$634$$ −11.7616 + 20.3716i −0.467112 + 0.809061i
$$635$$ 0 0
$$636$$ −0.826674 −0.0327797
$$637$$ 18.9130 + 0.846898i 0.749361 + 0.0335553i
$$638$$ 9.33201i 0.369458i
$$639$$ −9.81724 5.66799i −0.388364 0.224222i
$$640$$ 0 0
$$641$$ −9.73875 16.8680i −0.384657 0.666246i 0.607064 0.794653i $$-0.292347\pi$$
−0.991722 + 0.128407i $$0.959014\pi$$
$$642$$ 3.07180 0.121234
$$643$$ −11.9772 20.7451i −0.472334 0.818106i 0.527165 0.849763i $$-0.323255\pi$$
−0.999499 + 0.0316570i $$0.989922\pi$$
$$644$$ −9.92820 + 5.73205i −0.391226 + 0.225874i
$$645$$ 0 0
$$646$$ −4.58155 7.93548i −0.180259 0.312217i
$$647$$ −15.7710 9.10540i −0.620022 0.357970i 0.156855 0.987622i $$-0.449864\pi$$
−0.776878 + 0.629652i $$0.783198\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ 14.4930 0.568898
$$650$$ 0 0
$$651$$ 13.4005 0.525207
$$652$$ −4.94735 + 8.56906i −0.193753 + 0.335590i
$$653$$ 41.7065 + 24.0793i 1.63210 + 0.942294i 0.983444 + 0.181213i $$0.0580024\pi$$
0.648657 + 0.761081i $$0.275331\pi$$
$$654$$ −6.61335 11.4547i −0.258603 0.447913i
$$655$$ 0 0
$$656$$ 4.02283 2.32258i 0.157065 0.0906815i
$$657$$ 3.14152 + 5.44128i 0.122562 + 0.212284i
$$658$$ −12.0477 −0.469669
$$659$$ −18.4127 31.8917i −0.717257 1.24233i −0.962083 0.272758i $$-0.912064\pi$$
0.244826 0.969567i $$-0.421269\pi$$
$$660$$ 0 0
$$661$$ −19.5131 11.2659i −0.758971 0.438192i 0.0699555 0.997550i $$-0.477714\pi$$
−0.828926 + 0.559358i $$0.811048\pi$$
$$662$$ 18.0904i 0.703103i
$$663$$ −6.64516 12.8001i −0.258077 0.497114i
$$664$$ −15.8719 −0.615948
$$665$$ 0 0
$$666$$ −3.40475 + 5.89721i −0.131932 + 0.228512i
$$667$$ −15.1847 + 8.76691i −0.587955 + 0.339456i
$$668$$ −24.0375 −0.930037
$$669$$ 21.6001 12.4708i 0.835106 0.482149i
$$670$$ 0 0
$$671$$ 2.47229i 0.0954417i
$$672$$ 1.14539 0.661290i 0.0441843 0.0255098i
$$673$$ 20.5627 + 11.8719i 0.792633 + 0.457627i 0.840889 0.541208i $$-0.182033\pi$$
−0.0482556 + 0.998835i $$0.515366\pi$$
$$674$$ −4.93548 2.84950i −0.190108 0.109759i
$$675$$ 0 0
$$676$$ 12.9480 + 1.16191i 0.497999 + 0.0446890i
$$677$$ 1.16559i 0.0447975i −0.999749 0.0223987i $$-0.992870\pi$$
0.999749 0.0223987i $$-0.00713033\pi$$
$$678$$ −4.04322 + 7.00306i −0.155279 + 0.268951i
$$679$$ 5.83188 10.1011i 0.223807 0.387645i
$$680$$ 0 0
$$681$$ 19.3205i 0.740363i
$$682$$ −23.3715 40.4806i −0.894939 1.55008i
$$683$$ 6.93593 + 12.0134i 0.265396 + 0.459680i 0.967667 0.252230i $$-0.0811639\pi$$
−0.702271 + 0.711910i $$0.747831\pi$$
$$684$$ 2.29078i 0.0875900i
$$685$$ 0 0
$$686$$ 8.10132 14.0319i 0.309310 0.535740i
$$687$$ −2.07746 + 3.59826i −0.0792599 + 0.137282i
$$688$$ 8.60562i 0.328086i
$$689$$ −2.64537 + 1.37334i −0.100781 + 0.0523203i
$$690$$ 0 0
$$691$$ −35.6967 20.6095i −1.35797 0.784022i −0.368616 0.929582i $$-0.620168\pi$$
−0.989349 + 0.145560i $$0.953502\pi$$
$$692$$ 2.18946 + 1.26408i 0.0832307 + 0.0480532i
$$693$$ −5.28408 + 3.05076i −0.200726 + 0.115889i
$$694$$ 15.7471i 0.597753i
$$695$$ 0 0
$$696$$ 1.75182 1.01141i 0.0664025 0.0383375i
$$697$$ −18.5806 −0.703792
$$698$$ 13.2679 7.66025i 0.502199 0.289945i
$$699$$ 8.48325 14.6934i 0.320866 0.555756i
$$700$$ 0 0
$$701$$ −23.0112 −0.869122 −0.434561 0.900642i $$-0.643096\pi$$
−0.434561 + 0.900642i $$0.643096\pi$$
$$702$$ −0.161290 + 3.60194i −0.00608749 + 0.135947i
$$703$$ 15.5991i 0.588329i
$$704$$ −3.99528 2.30668i −0.150578 0.0869362i
$$705$$ 0 0
$$706$$ −0.599964 1.03917i −0.0225799 0.0391096i
$$707$$ 9.55790 0.359462
$$708$$ −1.57076 2.72064i −0.0590328 0.102248i
$$709$$ 14.7944 8.54156i 0.555616 0.320785i −0.195768 0.980650i $$-0.562720\pi$$
0.751384 + 0.659865i $$0.229387\pi$$
$$710$$ 0 0
$$711$$ −1.48387 2.57014i −0.0556495 0.0963877i
$$712$$ −10.2746 5.93207i −0.385059 0.222314i
$$713$$ 43.9124 76.0585i 1.64453 2.84841i
$$714$$ −5.29032 −0.197985
$$715$$ 0 0
$$716$$ −6.27568 −0.234533
$$717$$ 3.17208 5.49420i 0.118463 0.205185i
$$718$$ 14.1015 + 8.14152i 0.526264 + 0.303839i
$$719$$ 21.8564 + 37.8564i 0.815106 + 1.41181i 0.909251 + 0.416247i $$0.136655\pi$$
−0.0941451 + 0.995558i $$0.530012\pi$$
$$720$$ 0 0
$$721$$ −21.0752 + 12.1678i −0.784880 + 0.453151i
$$722$$ −6.87617 11.9099i −0.255905 0.443240i
$$723$$ −24.1855 −0.899467
$$724$$ 6.14152 + 10.6374i 0.228248 + 0.395337i
$$725$$ 0 0
$$726$$ 8.90538 + 5.14152i 0.330510 + 0.190820i
$$727$$ 31.8453i 1.18108i −0.807010 0.590538i $$-0.798916\pi$$
0.807010 0.590538i $$-0.201084\pi$$
$$728$$ 2.56667 4.01896i 0.0951270 0.148953i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −17.2112 + 29.8108i −0.636581 + 1.10259i
$$732$$ 0.464102 0.267949i 0.0171537 0.00990369i
$$733$$ 5.96774 0.220423 0.110212 0.993908i $$-0.464847\pi$$
0.110212 + 0.993908i $$0.464847\pi$$
$$734$$ 17.0040 9.81724i 0.627627 0.362361i
$$735$$ 0 0
$$736$$ 8.66799i 0.319506i
$$737$$ 12.7092 7.33767i 0.468150 0.270287i
$$738$$ 4.02283 + 2.32258i 0.148082 + 0.0854953i
$$739$$ −9.37833 5.41458i −0.344988 0.199179i 0.317488 0.948262i $$-0.397161\pi$$
−0.662475 + 0.749084i $$0.730494\pi$$
$$740$$ 0 0
$$741$$ 3.80564 + 7.33052i 0.139804 + 0.269293i
$$742$$ 1.09334i 0.0401378i
$$743$$ −9.92515 + 17.1909i −0.364118 + 0.630671i −0.988634 0.150341i $$-0.951963\pi$$
0.624516 + 0.781012i $$0.285296\pi$$
$$744$$ −5.06604 + 8.77464i −0.185730 + 0.321694i
$$745$$ 0 0
$$746$$ 2.55748i 0.0936359i
$$747$$ −7.93593 13.7454i −0.290361 0.502919i
$$748$$ 9.22671 + 15.9811i 0.337362 + 0.584328i
$$749$$ 4.06270i 0.148448i
$$750$$ 0 0
$$751$$ −7.66538 + 13.2768i −0.279714 + 0.484479i −0.971314 0.237802i $$-0.923573\pi$$
0.691600 + 0.722281i $$0.256906\pi$$
$$752$$ 4.55463 7.88885i 0.166090 0.287677i
$$753$$ 8.82497i 0.321600i
$$754$$ 3.92560 6.14682i 0.142962 0.223854i
$$755$$ 0 0
$$756$$ 1.14539 + 0.661290i 0.0416573 + 0.0240509i
$$757$$ 39.1125 + 22.5816i 1.42157 + 0.820744i 0.996433 0.0843855i $$-0.0268927\pi$$
0.425137 + 0.905129i $$0.360226\pi$$
$$758$$ −13.0846 + 7.55440i −0.475254 + 0.274388i
$$759$$ 39.9885i 1.45149i
$$760$$ 0 0
$$761$$ −18.7978 + 10.8529i −0.681419 + 0.393418i −0.800390 0.599480i $$-0.795374\pi$$
0.118970 + 0.992898i $$0.462041\pi$$
$$762$$ −11.4718 −0.415581
$$763$$ −15.1497 + 8.74669i −0.548456 + 0.316651i
$$764$$ 4.87357 8.44128i 0.176320 0.305395i
$$765$$ 0 0
$$766$$ 18.7303 0.676755
$$767$$ −9.54623 6.09660i −0.344694 0.220136i
$$768$$ 1.00000i 0.0360844i
$$769$$ −36.4711 21.0566i −1.31518 0.759321i −0.332233 0.943197i $$-0.607802\pi$$
−0.982949 + 0.183877i $$0.941135\pi$$
$$770$$ 0 0
$$771$$ 4.19247 + 7.26157i 0.150988 + 0.261519i
$$772$$ −13.7626 −0.495327
$$773$$ 14.8803 + 25.7734i 0.535206 + 0.927004i 0.999153 + 0.0411413i $$0.0130994\pi$$
−0.463947 + 0.885863i $$0.653567\pi$$
$$774$$ 7.45269 4.30281i 0.267881 0.154661i
$$775$$ 0 0
$$776$$ 4.40947 + 7.63743i 0.158291 + 0.274168i
$$777$$ 7.79953 + 4.50306i 0.279806 + 0.161546i
$$778$$ 3.48449 6.03532i 0.124925 0.216377i
$$779$$ 10.6410 0.381254
$$780$$ 0 0
$$781$$ 52.2969 1.87133
$$782$$ −17.3360 + 30.0268i −0.619933 + 1.07376i
$$783$$ 1.75182 + 1.01141i 0.0626049 + 0.0361450i
$$784$$ 2.62539 + 4.54731i 0.0937640 + 0.162404i
$$785$$