# Properties

 Label 950.2.e.o.201.4 Level $950$ Weight $2$ Character 950.201 Analytic conductor $7.586$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$10$$ Relative dimension: $$5$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 10 x^{8} - 12 x^{7} + 85 x^{6} - 70 x^{5} + 186 x^{4} - 110 x^{3} + 285 x^{2} - 150 x + 100$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 201.4 Root $$-0.664633 + 1.15118i$$ of defining polynomial Character $$\chi$$ $$=$$ 950.201 Dual form 950.2.e.o.501.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +6.39380 q^{11} -1.32927 q^{12} +(0.429320 + 0.743604i) q^{13} +(1.16463 - 2.01720i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.34506 + 4.06176i) q^{17} +1.23305 q^{18} +(3.75178 - 2.21903i) q^{19} +(1.54811 - 2.68140i) q^{21} +(3.19690 - 5.53719i) q^{22} +(-1.73531 - 3.00565i) q^{23} +(-0.664633 + 1.15118i) q^{24} +0.858640 q^{26} +5.62685 q^{27} +(-1.16463 - 2.01720i) q^{28} +(2.21048 + 3.82866i) q^{29} -8.25244 q^{31} +(0.500000 + 0.866025i) q^{32} +(4.24953 - 7.36040i) q^{33} +(2.34506 + 4.06176i) q^{34} +(0.616527 - 1.06786i) q^{36} -9.76821 q^{37} +(-0.0458469 - 4.35866i) q^{38} +1.14136 q^{39} +(-1.84506 + 3.19574i) q^{41} +(-1.54811 - 2.68140i) q^{42} +(3.56232 - 6.17012i) q^{43} +(-3.19690 - 5.53719i) q^{44} -3.47063 q^{46} +(-3.59684 - 6.22992i) q^{47} +(0.664633 + 1.15118i) q^{48} -1.57452 q^{49} +(3.11721 + 5.39916i) q^{51} +(0.429320 - 0.743604i) q^{52} +(-3.10295 - 5.37446i) q^{53} +(2.81343 - 4.87300i) q^{54} -2.32927 q^{56} +(-0.0609427 - 5.79381i) q^{57} +4.42096 q^{58} +(3.09395 - 5.35888i) q^{59} +(4.01037 + 6.94616i) q^{61} +(-4.12622 + 7.14682i) q^{62} +(1.43605 + 2.48732i) q^{63} +1.00000 q^{64} +(-4.24953 - 7.36040i) q^{66} +(-2.45257 - 4.24798i) q^{67} +4.69012 q^{68} -4.61338 q^{69} +(-1.10005 + 1.90535i) q^{71} +(-0.616527 - 1.06786i) q^{72} +(-2.32859 + 4.03323i) q^{73} +(-4.88411 + 8.45952i) q^{74} +(-3.79763 - 2.13962i) q^{76} +14.8928 q^{77} +(0.570680 - 0.988447i) q^{78} +(-5.79153 + 10.0312i) q^{79} +(1.89021 - 3.27394i) q^{81} +(1.84506 + 3.19574i) q^{82} -6.07809 q^{83} -3.09621 q^{84} +(-3.56232 - 6.17012i) q^{86} +5.87663 q^{87} -6.39380 q^{88} +(-5.64947 - 9.78517i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.73531 + 3.00565i) q^{92} +(-5.48484 + 9.50002i) q^{93} -7.19369 q^{94} +1.32927 q^{96} +(-5.67500 + 9.82939i) q^{97} +(-0.787262 + 1.36358i) q^{98} +(3.94195 + 6.82766i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q + 5q^{2} - 5q^{4} + 10q^{7} - 10q^{8} - 5q^{9} + O(q^{10})$$ $$10q + 5q^{2} - 5q^{4} + 10q^{7} - 10q^{8} - 5q^{9} - 6q^{11} + 2q^{13} + 5q^{14} - 5q^{16} - 4q^{17} - 10q^{18} + 11q^{19} + 20q^{21} - 3q^{22} - 13q^{23} + 4q^{26} - 36q^{27} - 5q^{28} + 2q^{29} - 8q^{31} + 5q^{32} - 2q^{33} + 4q^{34} - 5q^{36} - 10q^{37} + 13q^{38} + 16q^{39} + q^{41} - 20q^{42} + 3q^{44} - 26q^{46} + 10q^{47} - 20q^{49} + 4q^{51} + 2q^{52} - 5q^{53} - 18q^{54} - 10q^{56} + 10q^{57} + 4q^{58} + 22q^{59} - 2q^{61} - 4q^{62} - 23q^{63} + 10q^{64} + 2q^{66} - 4q^{67} + 8q^{68} - 24q^{69} - 22q^{71} + 5q^{72} - 26q^{73} - 5q^{74} + 2q^{76} - 10q^{77} + 8q^{78} + 2q^{79} - 5q^{81} - q^{82} - 12q^{83} - 40q^{84} + 20q^{87} + 6q^{88} - q^{89} + 10q^{91} - 13q^{92} - 6q^{93} + 20q^{94} - 8q^{97} - 10q^{98} + 13q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$$.

 $$n$$ $$77$$ $$401$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0.664633 1.15118i 0.383726 0.664633i −0.607866 0.794040i $$-0.707974\pi$$
0.991592 + 0.129407i $$0.0413074\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ −0.664633 1.15118i −0.271335 0.469966i
$$7$$ 2.32927 0.880379 0.440190 0.897905i $$-0.354911\pi$$
0.440190 + 0.897905i $$0.354911\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0.616527 + 1.06786i 0.205509 + 0.355952i
$$10$$ 0 0
$$11$$ 6.39380 1.92780 0.963901 0.266260i $$-0.0857880\pi$$
0.963901 + 0.266260i $$0.0857880\pi$$
$$12$$ −1.32927 −0.383726
$$13$$ 0.429320 + 0.743604i 0.119072 + 0.206239i 0.919400 0.393324i $$-0.128675\pi$$
−0.800328 + 0.599562i $$0.795341\pi$$
$$14$$ 1.16463 2.01720i 0.311261 0.539120i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.34506 + 4.06176i −0.568760 + 0.985122i 0.427929 + 0.903813i $$0.359243\pi$$
−0.996689 + 0.0813093i $$0.974090\pi$$
$$18$$ 1.23305 0.290634
$$19$$ 3.75178 2.21903i 0.860718 0.509081i
$$20$$ 0 0
$$21$$ 1.54811 2.68140i 0.337824 0.585129i
$$22$$ 3.19690 5.53719i 0.681581 1.18053i
$$23$$ −1.73531 3.00565i −0.361838 0.626721i 0.626426 0.779481i $$-0.284517\pi$$
−0.988263 + 0.152760i $$0.951184\pi$$
$$24$$ −0.664633 + 1.15118i −0.135668 + 0.234983i
$$25$$ 0 0
$$26$$ 0.858640 0.168393
$$27$$ 5.62685 1.08289
$$28$$ −1.16463 2.01720i −0.220095 0.381216i
$$29$$ 2.21048 + 3.82866i 0.410476 + 0.710965i 0.994942 0.100453i $$-0.0320293\pi$$
−0.584466 + 0.811418i $$0.698696\pi$$
$$30$$ 0 0
$$31$$ −8.25244 −1.48218 −0.741091 0.671405i $$-0.765691\pi$$
−0.741091 + 0.671405i $$0.765691\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 4.24953 7.36040i 0.739748 1.28128i
$$34$$ 2.34506 + 4.06176i 0.402174 + 0.696586i
$$35$$ 0 0
$$36$$ 0.616527 1.06786i 0.102754 0.177976i
$$37$$ −9.76821 −1.60588 −0.802942 0.596057i $$-0.796733\pi$$
−0.802942 + 0.596057i $$0.796733\pi$$
$$38$$ −0.0458469 4.35866i −0.00743735 0.707068i
$$39$$ 1.14136 0.182764
$$40$$ 0 0
$$41$$ −1.84506 + 3.19574i −0.288150 + 0.499090i −0.973368 0.229248i $$-0.926373\pi$$
0.685218 + 0.728338i $$0.259707\pi$$
$$42$$ −1.54811 2.68140i −0.238878 0.413749i
$$43$$ 3.56232 6.17012i 0.543249 0.940934i −0.455466 0.890253i $$-0.650527\pi$$
0.998715 0.0506811i $$-0.0161392\pi$$
$$44$$ −3.19690 5.53719i −0.481951 0.834763i
$$45$$ 0 0
$$46$$ −3.47063 −0.511716
$$47$$ −3.59684 6.22992i −0.524654 0.908727i −0.999588 0.0287055i $$-0.990862\pi$$
0.474934 0.880021i $$-0.342472\pi$$
$$48$$ 0.664633 + 1.15118i 0.0959315 + 0.166158i
$$49$$ −1.57452 −0.224932
$$50$$ 0 0
$$51$$ 3.11721 + 5.39916i 0.436496 + 0.756033i
$$52$$ 0.429320 0.743604i 0.0595360 0.103119i
$$53$$ −3.10295 5.37446i −0.426222 0.738239i 0.570311 0.821429i $$-0.306823\pi$$
−0.996534 + 0.0831897i $$0.973489\pi$$
$$54$$ 2.81343 4.87300i 0.382859 0.663131i
$$55$$ 0 0
$$56$$ −2.32927 −0.311261
$$57$$ −0.0609427 5.79381i −0.00807206 0.767409i
$$58$$ 4.42096 0.580500
$$59$$ 3.09395 5.35888i 0.402798 0.697667i −0.591264 0.806478i $$-0.701371\pi$$
0.994062 + 0.108811i $$0.0347043\pi$$
$$60$$ 0 0
$$61$$ 4.01037 + 6.94616i 0.513475 + 0.889365i 0.999878 + 0.0156304i $$0.00497553\pi$$
−0.486403 + 0.873735i $$0.661691\pi$$
$$62$$ −4.12622 + 7.14682i −0.524030 + 0.907647i
$$63$$ 1.43605 + 2.48732i 0.180926 + 0.313373i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −4.24953 7.36040i −0.523081 0.906002i
$$67$$ −2.45257 4.24798i −0.299629 0.518973i 0.676422 0.736515i $$-0.263530\pi$$
−0.976051 + 0.217541i $$0.930196\pi$$
$$68$$ 4.69012 0.568760
$$69$$ −4.61338 −0.555386
$$70$$ 0 0
$$71$$ −1.10005 + 1.90535i −0.130552 + 0.226124i −0.923890 0.382659i $$-0.875008\pi$$
0.793337 + 0.608782i $$0.208342\pi$$
$$72$$ −0.616527 1.06786i −0.0726584 0.125848i
$$73$$ −2.32859 + 4.03323i −0.272540 + 0.472054i −0.969512 0.245045i $$-0.921197\pi$$
0.696971 + 0.717099i $$0.254531\pi$$
$$74$$ −4.88411 + 8.45952i −0.567766 + 0.983399i
$$75$$ 0 0
$$76$$ −3.79763 2.13962i −0.435618 0.245432i
$$77$$ 14.8928 1.69720
$$78$$ 0.570680 0.988447i 0.0646168 0.111920i
$$79$$ −5.79153 + 10.0312i −0.651598 + 1.12860i 0.331137 + 0.943583i $$0.392568\pi$$
−0.982735 + 0.185018i $$0.940766\pi$$
$$80$$ 0 0
$$81$$ 1.89021 3.27394i 0.210023 0.363771i
$$82$$ 1.84506 + 3.19574i 0.203753 + 0.352910i
$$83$$ −6.07809 −0.667157 −0.333579 0.942722i $$-0.608256\pi$$
−0.333579 + 0.942722i $$0.608256\pi$$
$$84$$ −3.09621 −0.337824
$$85$$ 0 0
$$86$$ −3.56232 6.17012i −0.384135 0.665341i
$$87$$ 5.87663 0.630041
$$88$$ −6.39380 −0.681581
$$89$$ −5.64947 9.78517i −0.598843 1.03723i −0.992992 0.118180i $$-0.962294\pi$$
0.394149 0.919046i $$-0.371039\pi$$
$$90$$ 0 0
$$91$$ 1.00000 + 1.73205i 0.104828 + 0.181568i
$$92$$ −1.73531 + 3.00565i −0.180919 + 0.313361i
$$93$$ −5.48484 + 9.50002i −0.568751 + 0.985106i
$$94$$ −7.19369 −0.741972
$$95$$ 0 0
$$96$$ 1.32927 0.135668
$$97$$ −5.67500 + 9.82939i −0.576209 + 0.998024i 0.419700 + 0.907663i $$0.362135\pi$$
−0.995909 + 0.0903607i $$0.971198\pi$$
$$98$$ −0.787262 + 1.36358i −0.0795254 + 0.137742i
$$99$$ 3.94195 + 6.82766i 0.396181 + 0.686205i
$$100$$ 0 0
$$101$$ −1.11042 1.92331i −0.110491 0.191377i 0.805477 0.592627i $$-0.201909\pi$$
−0.915968 + 0.401250i $$0.868576\pi$$
$$102$$ 6.23441 0.617299
$$103$$ 3.26464 0.321675 0.160837 0.986981i $$-0.448581\pi$$
0.160837 + 0.986981i $$0.448581\pi$$
$$104$$ −0.429320 0.743604i −0.0420983 0.0729164i
$$105$$ 0 0
$$106$$ −6.20589 −0.602770
$$107$$ 10.0000 0.966736 0.483368 0.875417i $$-0.339413\pi$$
0.483368 + 0.875417i $$0.339413\pi$$
$$108$$ −2.81343 4.87300i −0.270722 0.468904i
$$109$$ 1.51717 2.62782i 0.145319 0.251699i −0.784173 0.620542i $$-0.786913\pi$$
0.929492 + 0.368843i $$0.120246\pi$$
$$110$$ 0 0
$$111$$ −6.49227 + 11.2449i −0.616219 + 1.06732i
$$112$$ −1.16463 + 2.01720i −0.110047 + 0.190608i
$$113$$ 4.97420 0.467933 0.233966 0.972245i $$-0.424829\pi$$
0.233966 + 0.972245i $$0.424829\pi$$
$$114$$ −5.04806 2.84413i −0.472794 0.266377i
$$115$$ 0 0
$$116$$ 2.21048 3.82866i 0.205238 0.355482i
$$117$$ −0.529375 + 0.916904i −0.0489407 + 0.0847678i
$$118$$ −3.09395 5.35888i −0.284821 0.493325i
$$119$$ −5.46226 + 9.46092i −0.500725 + 0.867281i
$$120$$ 0 0
$$121$$ 29.8806 2.71642
$$122$$ 8.02074 0.726164
$$123$$ 2.45257 + 4.24798i 0.221141 + 0.383028i
$$124$$ 4.12622 + 7.14682i 0.370545 + 0.641803i
$$125$$ 0 0
$$126$$ 2.87211 0.255868
$$127$$ −7.14949 12.3833i −0.634415 1.09884i −0.986639 0.162923i $$-0.947908\pi$$
0.352224 0.935916i $$-0.385426\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ −4.73527 8.20172i −0.416917 0.722121i
$$130$$ 0 0
$$131$$ −1.18947 + 2.06022i −0.103924 + 0.180002i −0.913298 0.407292i $$-0.866473\pi$$
0.809374 + 0.587294i $$0.199807\pi$$
$$132$$ −8.49905 −0.739748
$$133$$ 8.73890 5.16872i 0.757759 0.448185i
$$134$$ −4.90515 −0.423740
$$135$$ 0 0
$$136$$ 2.34506 4.06176i 0.201087 0.348293i
$$137$$ −4.54585 7.87364i −0.388378 0.672690i 0.603854 0.797095i $$-0.293631\pi$$
−0.992232 + 0.124405i $$0.960298\pi$$
$$138$$ −2.30669 + 3.99531i −0.196359 + 0.340103i
$$139$$ 10.5329 + 18.2435i 0.893389 + 1.54739i 0.835786 + 0.549055i $$0.185012\pi$$
0.0576028 + 0.998340i $$0.481654\pi$$
$$140$$ 0 0
$$141$$ −9.56232 −0.805293
$$142$$ 1.10005 + 1.90535i 0.0923145 + 0.159893i
$$143$$ 2.74498 + 4.75445i 0.229547 + 0.397587i
$$144$$ −1.23305 −0.102754
$$145$$ 0 0
$$146$$ 2.32859 + 4.03323i 0.192715 + 0.333793i
$$147$$ −1.04648 + 1.81256i −0.0863122 + 0.149497i
$$148$$ 4.88411 + 8.45952i 0.401471 + 0.695368i
$$149$$ 3.17889 5.50600i 0.260425 0.451069i −0.705930 0.708282i $$-0.749471\pi$$
0.966355 + 0.257212i $$0.0828040\pi$$
$$150$$ 0 0
$$151$$ −3.05559 −0.248660 −0.124330 0.992241i $$-0.539678\pi$$
−0.124330 + 0.992241i $$0.539678\pi$$
$$152$$ −3.75178 + 2.21903i −0.304310 + 0.179987i
$$153$$ −5.78317 −0.467541
$$154$$ 7.44642 12.8976i 0.600050 1.03932i
$$155$$ 0 0
$$156$$ −0.570680 0.988447i −0.0456910 0.0791391i
$$157$$ −4.07136 + 7.05180i −0.324930 + 0.562795i −0.981498 0.191472i $$-0.938674\pi$$
0.656568 + 0.754267i $$0.272007\pi$$
$$158$$ 5.79153 + 10.0312i 0.460749 + 0.798041i
$$159$$ −8.24928 −0.654210
$$160$$ 0 0
$$161$$ −4.04200 7.00096i −0.318554 0.551753i
$$162$$ −1.89021 3.27394i −0.148509 0.257225i
$$163$$ −13.4100 −1.05035 −0.525177 0.850993i $$-0.676001\pi$$
−0.525177 + 0.850993i $$0.676001\pi$$
$$164$$ 3.69012 0.288150
$$165$$ 0 0
$$166$$ −3.03905 + 5.26378i −0.235876 + 0.408549i
$$167$$ 6.49232 + 11.2450i 0.502391 + 0.870166i 0.999996 + 0.00276265i $$0.000879380\pi$$
−0.497606 + 0.867403i $$0.665787\pi$$
$$168$$ −1.54811 + 2.68140i −0.119439 + 0.206874i
$$169$$ 6.13137 10.6198i 0.471644 0.816911i
$$170$$ 0 0
$$171$$ 4.68269 + 2.63827i 0.358094 + 0.201754i
$$172$$ −7.12464 −0.543249
$$173$$ −1.05780 + 1.83216i −0.0804228 + 0.139296i −0.903432 0.428732i $$-0.858960\pi$$
0.823009 + 0.568029i $$0.192294\pi$$
$$174$$ 2.93831 5.08931i 0.222753 0.385819i
$$175$$ 0 0
$$176$$ −3.19690 + 5.53719i −0.240975 + 0.417381i
$$177$$ −4.11268 7.12338i −0.309128 0.535426i
$$178$$ −11.2989 −0.846892
$$179$$ −9.87938 −0.738420 −0.369210 0.929346i $$-0.620372\pi$$
−0.369210 + 0.929346i $$0.620372\pi$$
$$180$$ 0 0
$$181$$ −7.53974 13.0592i −0.560425 0.970684i −0.997459 0.0712395i $$-0.977305\pi$$
0.437034 0.899445i $$-0.356029\pi$$
$$182$$ 2.00000 0.148250
$$183$$ 10.6617 0.788135
$$184$$ 1.73531 + 3.00565i 0.127929 + 0.221579i
$$185$$ 0 0
$$186$$ 5.48484 + 9.50002i 0.402168 + 0.696575i
$$187$$ −14.9938 + 25.9701i −1.09646 + 1.89912i
$$188$$ −3.59684 + 6.22992i −0.262327 + 0.454363i
$$189$$ 13.1064 0.953352
$$190$$ 0 0
$$191$$ 8.84192 0.639779 0.319889 0.947455i $$-0.396354\pi$$
0.319889 + 0.947455i $$0.396354\pi$$
$$192$$ 0.664633 1.15118i 0.0479657 0.0830791i
$$193$$ −9.34642 + 16.1885i −0.672770 + 1.16527i 0.304346 + 0.952562i $$0.401562\pi$$
−0.977115 + 0.212710i $$0.931771\pi$$
$$194$$ 5.67500 + 9.82939i 0.407441 + 0.705709i
$$195$$ 0 0
$$196$$ 0.787262 + 1.36358i 0.0562330 + 0.0973984i
$$197$$ 16.3169 1.16253 0.581267 0.813713i $$-0.302557\pi$$
0.581267 + 0.813713i $$0.302557\pi$$
$$198$$ 7.88390 0.560284
$$199$$ 1.57452 + 2.72715i 0.111615 + 0.193323i 0.916422 0.400214i $$-0.131064\pi$$
−0.804807 + 0.593537i $$0.797731\pi$$
$$200$$ 0 0
$$201$$ −6.52024 −0.459902
$$202$$ −2.22085 −0.156258
$$203$$ 5.14879 + 8.91797i 0.361374 + 0.625919i
$$204$$ 3.11721 5.39916i 0.218248 0.378017i
$$205$$ 0 0
$$206$$ 1.63232 2.82726i 0.113729 0.196985i
$$207$$ 2.13973 3.70613i 0.148722 0.257594i
$$208$$ −0.858640 −0.0595360
$$209$$ 23.9882 14.1881i 1.65930 0.981408i
$$210$$ 0 0
$$211$$ 3.95415 6.84879i 0.272215 0.471490i −0.697214 0.716863i $$-0.745577\pi$$
0.969429 + 0.245373i $$0.0789104\pi$$
$$212$$ −3.10295 + 5.37446i −0.213111 + 0.369119i
$$213$$ 1.46226 + 2.53272i 0.100193 + 0.173539i
$$214$$ 5.00000 8.66025i 0.341793 0.592003i
$$215$$ 0 0
$$216$$ −5.62685 −0.382859
$$217$$ −19.2221 −1.30488
$$218$$ −1.51717 2.62782i −0.102756 0.177978i
$$219$$ 3.09531 + 5.36123i 0.209162 + 0.362279i
$$220$$ 0 0
$$221$$ −4.02712 −0.270894
$$222$$ 6.49227 + 11.2449i 0.435733 + 0.754711i
$$223$$ 4.16463 7.21336i 0.278884 0.483042i −0.692223 0.721683i $$-0.743369\pi$$
0.971108 + 0.238641i $$0.0767020\pi$$
$$224$$ 1.16463 + 2.01720i 0.0778153 + 0.134780i
$$225$$ 0 0
$$226$$ 2.48710 4.30778i 0.165439 0.286549i
$$227$$ 11.3680 0.754523 0.377261 0.926107i $$-0.376866\pi$$
0.377261 + 0.926107i $$0.376866\pi$$
$$228$$ −4.98712 + 2.94968i −0.330280 + 0.195348i
$$229$$ −2.25560 −0.149054 −0.0745270 0.997219i $$-0.523745\pi$$
−0.0745270 + 0.997219i $$0.523745\pi$$
$$230$$ 0 0
$$231$$ 9.89827 17.1443i 0.651259 1.12801i
$$232$$ −2.21048 3.82866i −0.145125 0.251364i
$$233$$ −7.96900 + 13.8027i −0.522067 + 0.904246i 0.477604 + 0.878575i $$0.341505\pi$$
−0.999670 + 0.0256705i $$0.991828\pi$$
$$234$$ 0.529375 + 0.916904i 0.0346063 + 0.0599399i
$$235$$ 0 0
$$236$$ −6.18791 −0.402798
$$237$$ 7.69848 + 13.3342i 0.500070 + 0.866147i
$$238$$ 5.46226 + 9.46092i 0.354066 + 0.613260i
$$239$$ 6.63412 0.429126 0.214563 0.976710i $$-0.431167\pi$$
0.214563 + 0.976710i $$0.431167\pi$$
$$240$$ 0 0
$$241$$ 11.0397 + 19.1213i 0.711130 + 1.23171i 0.964433 + 0.264326i $$0.0851494\pi$$
−0.253304 + 0.967387i $$0.581517\pi$$
$$242$$ 14.9403 25.8774i 0.960400 1.66346i
$$243$$ 5.92769 + 10.2671i 0.380261 + 0.658632i
$$244$$ 4.01037 6.94616i 0.256738 0.444683i
$$245$$ 0 0
$$246$$ 4.90515 0.312741
$$247$$ 3.26080 + 1.83717i 0.207480 + 0.116896i
$$248$$ 8.25244 0.524030
$$249$$ −4.03970 + 6.99696i −0.256006 + 0.443415i
$$250$$ 0 0
$$251$$ −4.72558 8.18494i −0.298276 0.516629i 0.677466 0.735554i $$-0.263078\pi$$
−0.975742 + 0.218926i $$0.929745\pi$$
$$252$$ 1.43605 2.48732i 0.0904630 0.156686i
$$253$$ −11.0952 19.2175i −0.697552 1.20819i
$$254$$ −14.2990 −0.897198
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −13.3945 23.1999i −0.835524 1.44717i −0.893603 0.448859i $$-0.851831\pi$$
0.0580783 0.998312i $$-0.481503\pi$$
$$258$$ −9.47053 −0.589610
$$259$$ −22.7528 −1.41379
$$260$$ 0 0
$$261$$ −2.72564 + 4.72095i −0.168713 + 0.292219i
$$262$$ 1.18947 + 2.06022i 0.0734854 + 0.127281i
$$263$$ 7.19364 12.4598i 0.443579 0.768301i −0.554373 0.832268i $$-0.687042\pi$$
0.997952 + 0.0639670i $$0.0203752\pi$$
$$264$$ −4.24953 + 7.36040i −0.261540 + 0.453001i
$$265$$ 0 0
$$266$$ −0.106790 10.1525i −0.00654769 0.622488i
$$267$$ −15.0193 −0.919166
$$268$$ −2.45257 + 4.24798i −0.149815 + 0.259487i
$$269$$ −6.44486 + 11.1628i −0.392950 + 0.680609i −0.992837 0.119475i $$-0.961879\pi$$
0.599887 + 0.800085i $$0.295212\pi$$
$$270$$ 0 0
$$271$$ −10.0907 + 17.4776i −0.612966 + 1.06169i 0.377772 + 0.925899i $$0.376690\pi$$
−0.990738 + 0.135790i $$0.956643\pi$$
$$272$$ −2.34506 4.06176i −0.142190 0.246280i
$$273$$ 2.65853 0.160902
$$274$$ −9.09169 −0.549249
$$275$$ 0 0
$$276$$ 2.30669 + 3.99531i 0.138846 + 0.240489i
$$277$$ −7.40098 −0.444682 −0.222341 0.974969i $$-0.571370\pi$$
−0.222341 + 0.974969i $$0.571370\pi$$
$$278$$ 21.0658 1.26344
$$279$$ −5.08785 8.81242i −0.304602 0.527586i
$$280$$ 0 0
$$281$$ −1.36083 2.35703i −0.0811805 0.140609i 0.822577 0.568654i $$-0.192536\pi$$
−0.903757 + 0.428045i $$0.859202\pi$$
$$282$$ −4.78116 + 8.28121i −0.284714 + 0.493139i
$$283$$ −10.2721 + 17.7918i −0.610613 + 1.05761i 0.380524 + 0.924771i $$0.375744\pi$$
−0.991137 + 0.132842i $$0.957590\pi$$
$$284$$ 2.20011 0.130552
$$285$$ 0 0
$$286$$ 5.48997 0.324629
$$287$$ −4.29763 + 7.44372i −0.253681 + 0.439389i
$$288$$ −0.616527 + 1.06786i −0.0363292 + 0.0629240i
$$289$$ −2.49860 4.32771i −0.146977 0.254571i
$$290$$ 0 0
$$291$$ 7.54358 + 13.0659i 0.442213 + 0.765935i
$$292$$ 4.65717 0.272540
$$293$$ −26.7315 −1.56167 −0.780836 0.624736i $$-0.785206\pi$$
−0.780836 + 0.624736i $$0.785206\pi$$
$$294$$ 1.04648 + 1.81256i 0.0610319 + 0.105710i
$$295$$ 0 0
$$296$$ 9.76821 0.567766
$$297$$ 35.9769 2.08759
$$298$$ −3.17889 5.50600i −0.184148 0.318954i
$$299$$ 1.49001 2.58077i 0.0861694 0.149250i
$$300$$ 0 0
$$301$$ 8.29759 14.3718i 0.478265 0.828379i
$$302$$ −1.52779 + 2.64622i −0.0879147 + 0.152273i
$$303$$ −2.95210 −0.169594
$$304$$ 0.0458469 + 4.35866i 0.00262950 + 0.249986i
$$305$$ 0 0
$$306$$ −2.89158 + 5.00837i −0.165301 + 0.286310i
$$307$$ −6.38026 + 11.0509i −0.364141 + 0.630710i −0.988638 0.150317i $$-0.951971\pi$$
0.624497 + 0.781027i $$0.285304\pi$$
$$308$$ −7.44642 12.8976i −0.424299 0.734908i
$$309$$ 2.16979 3.75818i 0.123435 0.213795i
$$310$$ 0 0
$$311$$ −6.96646 −0.395031 −0.197516 0.980300i $$-0.563287\pi$$
−0.197516 + 0.980300i $$0.563287\pi$$
$$312$$ −1.14136 −0.0646168
$$313$$ 13.0846 + 22.6632i 0.739585 + 1.28100i 0.952682 + 0.303968i $$0.0983115\pi$$
−0.213097 + 0.977031i $$0.568355\pi$$
$$314$$ 4.07136 + 7.05180i 0.229760 + 0.397956i
$$315$$ 0 0
$$316$$ 11.5831 0.651598
$$317$$ 4.37870 + 7.58413i 0.245932 + 0.425967i 0.962393 0.271660i $$-0.0875725\pi$$
−0.716461 + 0.697627i $$0.754239\pi$$
$$318$$ −4.12464 + 7.14408i −0.231298 + 0.400620i
$$319$$ 14.1334 + 24.4797i 0.791316 + 1.37060i
$$320$$ 0 0
$$321$$ 6.64633 11.5118i 0.370962 0.642525i
$$322$$ −8.08401 −0.450504
$$323$$ 0.215028 + 20.4426i 0.0119645 + 1.13746i
$$324$$ −3.78042 −0.210023
$$325$$ 0 0
$$326$$ −6.70501 + 11.6134i −0.371356 + 0.643208i
$$327$$ −2.01672 3.49306i −0.111525 0.193167i
$$328$$ 1.84506 3.19574i 0.101876 0.176455i
$$329$$ −8.37800 14.5111i −0.461894 0.800024i
$$330$$ 0 0
$$331$$ −9.34738 −0.513779 −0.256889 0.966441i $$-0.582698\pi$$
−0.256889 + 0.966441i $$0.582698\pi$$
$$332$$ 3.03905 + 5.26378i 0.166789 + 0.288888i
$$333$$ −6.02237 10.4310i −0.330024 0.571618i
$$334$$ 12.9846 0.710488
$$335$$ 0 0
$$336$$ 1.54811 + 2.68140i 0.0844561 + 0.146282i
$$337$$ 4.87376 8.44159i 0.265490 0.459843i −0.702202 0.711978i $$-0.747799\pi$$
0.967692 + 0.252135i $$0.0811328\pi$$
$$338$$ −6.13137 10.6198i −0.333502 0.577643i
$$339$$ 3.30601 5.72618i 0.179558 0.311003i
$$340$$ 0 0
$$341$$ −52.7644 −2.85735
$$342$$ 4.62615 2.73619i 0.250154 0.147956i
$$343$$ −19.9723 −1.07840
$$344$$ −3.56232 + 6.17012i −0.192067 + 0.332670i
$$345$$ 0 0
$$346$$ 1.05780 + 1.83216i 0.0568675 + 0.0984975i
$$347$$ 7.38162 12.7853i 0.396266 0.686353i −0.596996 0.802244i $$-0.703639\pi$$
0.993262 + 0.115891i $$0.0369724\pi$$
$$348$$ −2.93831 5.08931i −0.157510 0.272816i
$$349$$ 14.8315 0.793913 0.396956 0.917837i $$-0.370066\pi$$
0.396956 + 0.917837i $$0.370066\pi$$
$$350$$ 0 0
$$351$$ 2.41572 + 4.18415i 0.128942 + 0.223333i
$$352$$ 3.19690 + 5.53719i 0.170395 + 0.295133i
$$353$$ 26.8115 1.42703 0.713516 0.700639i $$-0.247102\pi$$
0.713516 + 0.700639i $$0.247102\pi$$
$$354$$ −8.22537 −0.437173
$$355$$ 0 0
$$356$$ −5.64947 + 9.78517i −0.299421 + 0.518613i
$$357$$ 7.26080 + 12.5761i 0.384282 + 0.665596i
$$358$$ −4.93969 + 8.55579i −0.261071 + 0.452188i
$$359$$ −0.197846 + 0.342680i −0.0104419 + 0.0180859i −0.871199 0.490930i $$-0.836657\pi$$
0.860757 + 0.509016i $$0.169990\pi$$
$$360$$ 0 0
$$361$$ 9.15178 16.6507i 0.481673 0.876351i
$$362$$ −15.0795 −0.792560
$$363$$ 19.8597 34.3979i 1.04236 1.80542i
$$364$$ 1.00000 1.73205i 0.0524142 0.0907841i
$$365$$ 0 0
$$366$$ 5.33085 9.23330i 0.278648 0.482632i
$$367$$ −3.49227 6.04879i −0.182295 0.315744i 0.760367 0.649494i $$-0.225019\pi$$
−0.942662 + 0.333750i $$0.891686\pi$$
$$368$$ 3.47063 0.180919
$$369$$ −4.55011 −0.236870
$$370$$ 0 0
$$371$$ −7.22758 12.5185i −0.375237 0.649930i
$$372$$ 10.9697 0.568751
$$373$$ 2.52621 0.130802 0.0654012 0.997859i $$-0.479167\pi$$
0.0654012 + 0.997859i $$0.479167\pi$$
$$374$$ 14.9938 + 25.9701i 0.775313 + 1.34288i
$$375$$ 0 0
$$376$$ 3.59684 + 6.22992i 0.185493 + 0.321283i
$$377$$ −1.89801 + 3.28744i −0.0977523 + 0.169312i
$$378$$ 6.55321 11.3505i 0.337061 0.583807i
$$379$$ −29.3075 −1.50543 −0.752713 0.658349i $$-0.771255\pi$$
−0.752713 + 0.658349i $$0.771255\pi$$
$$380$$ 0 0
$$381$$ −19.0071 −0.973765
$$382$$ 4.42096 7.65733i 0.226196 0.391783i
$$383$$ −3.11717 + 5.39911i −0.159280 + 0.275881i −0.934609 0.355676i $$-0.884251\pi$$
0.775329 + 0.631557i $$0.217584\pi$$
$$384$$ −0.664633 1.15118i −0.0339169 0.0587458i
$$385$$ 0 0
$$386$$ 9.34642 + 16.1885i 0.475720 + 0.823971i
$$387$$ 8.78506 0.446570
$$388$$ 11.3500 0.576209
$$389$$ −13.2183 22.8947i −0.670193 1.16081i −0.977849 0.209311i $$-0.932878\pi$$
0.307656 0.951498i $$-0.400455\pi$$
$$390$$ 0 0
$$391$$ 16.2776 0.823196
$$392$$ 1.57452 0.0795254
$$393$$ 1.58112 + 2.73857i 0.0797567 + 0.138143i
$$394$$ 8.15847 14.1309i 0.411018 0.711903i
$$395$$ 0 0
$$396$$ 3.94195 6.82766i 0.198090 0.343103i
$$397$$ 4.36575 7.56171i 0.219111 0.379511i −0.735426 0.677606i $$-0.763018\pi$$
0.954536 + 0.298094i $$0.0963510\pi$$
$$398$$ 3.14905 0.157847
$$399$$ −0.141952 13.4953i −0.00710648 0.675611i
$$400$$ 0 0
$$401$$ 1.58356 2.74281i 0.0790794 0.136969i −0.823774 0.566919i $$-0.808135\pi$$
0.902853 + 0.429949i $$0.141469\pi$$
$$402$$ −3.26012 + 5.64669i −0.162600 + 0.281631i
$$403$$ −3.54294 6.13654i −0.176486 0.305683i
$$404$$ −1.11042 + 1.92331i −0.0552457 + 0.0956884i
$$405$$ 0 0
$$406$$ 10.2976 0.511061
$$407$$ −62.4560 −3.09583
$$408$$ −3.11721 5.39916i −0.154325 0.267298i
$$409$$ −8.54431 14.7992i −0.422489 0.731773i 0.573693 0.819070i $$-0.305510\pi$$
−0.996182 + 0.0872978i $$0.972177\pi$$
$$410$$ 0 0
$$411$$ −12.0853 −0.596123
$$412$$ −1.63232 2.82726i −0.0804187 0.139289i
$$413$$ 7.20664 12.4823i 0.354615 0.614212i
$$414$$ −2.13973 3.70613i −0.105162 0.182146i
$$415$$ 0 0
$$416$$ −0.429320 + 0.743604i −0.0210491 + 0.0364582i
$$417$$ 28.0020 1.37127
$$418$$ −0.293136 27.8684i −0.0143378 1.36309i
$$419$$ 7.80296 0.381200 0.190600 0.981668i $$-0.438957\pi$$
0.190600 + 0.981668i $$0.438957\pi$$
$$420$$ 0 0
$$421$$ −16.9845 + 29.4180i −0.827773 + 1.43374i 0.0720091 + 0.997404i $$0.477059\pi$$
−0.899782 + 0.436340i $$0.856274\pi$$
$$422$$ −3.95415 6.84879i −0.192485 0.333394i
$$423$$ 4.43510 7.68182i 0.215642 0.373503i
$$424$$ 3.10295 + 5.37446i 0.150692 + 0.261007i
$$425$$ 0 0
$$426$$ 2.92453 0.141694
$$427$$ 9.34122 + 16.1795i 0.452053 + 0.782979i
$$428$$ −5.00000 8.66025i −0.241684 0.418609i
$$429$$ 7.29763 0.352333
$$430$$ 0 0
$$431$$ −9.07565 15.7195i −0.437158 0.757181i 0.560311 0.828283i $$-0.310682\pi$$
−0.997469 + 0.0711019i $$0.977348\pi$$
$$432$$ −2.81343 + 4.87300i −0.135361 + 0.234452i
$$433$$ 0.157154 + 0.272199i 0.00755234 + 0.0130810i 0.869777 0.493445i $$-0.164263\pi$$
−0.862225 + 0.506526i $$0.830929\pi$$
$$434$$ −9.61106 + 16.6468i −0.461346 + 0.799074i
$$435$$ 0 0
$$436$$ −3.03434 −0.145319
$$437$$ −13.1802 7.42583i −0.630492 0.355226i
$$438$$ 6.19062 0.295799
$$439$$ −4.33220 + 7.50359i −0.206765 + 0.358127i −0.950694 0.310132i $$-0.899627\pi$$
0.743929 + 0.668259i $$0.232960\pi$$
$$440$$ 0 0
$$441$$ −0.970736 1.68136i −0.0462255 0.0800650i
$$442$$ −2.01356 + 3.48759i −0.0957753 + 0.165888i
$$443$$ −1.94419 3.36744i −0.0923714 0.159992i 0.816137 0.577858i $$-0.196111\pi$$
−0.908509 + 0.417866i $$0.862778\pi$$
$$444$$ 12.9845 0.616219
$$445$$ 0 0
$$446$$ −4.16463 7.21336i −0.197201 0.341562i
$$447$$ −4.22559 7.31894i −0.199864 0.346174i
$$448$$ 2.32927 0.110047
$$449$$ 32.9375 1.55442 0.777208 0.629243i $$-0.216635\pi$$
0.777208 + 0.629243i $$0.216635\pi$$
$$450$$ 0 0
$$451$$ −11.7969 + 20.4329i −0.555496 + 0.962147i
$$452$$ −2.48710 4.30778i −0.116983 0.202621i
$$453$$ −2.03084 + 3.51752i −0.0954174 + 0.165268i
$$454$$ 5.68402 9.84500i 0.266764 0.462049i
$$455$$ 0 0
$$456$$ 0.0609427 + 5.79381i 0.00285390 + 0.271320i
$$457$$ −1.22533 −0.0573184 −0.0286592 0.999589i $$-0.509124\pi$$
−0.0286592 + 0.999589i $$0.509124\pi$$
$$458$$ −1.12780 + 1.95341i −0.0526986 + 0.0912766i
$$459$$ −13.1953 + 22.8549i −0.615904 + 1.06678i
$$460$$ 0 0
$$461$$ 19.5927 33.9356i 0.912524 1.58054i 0.102038 0.994781i $$-0.467464\pi$$
0.810486 0.585758i $$-0.199203\pi$$
$$462$$ −9.89827 17.1443i −0.460509 0.797626i
$$463$$ 32.5754 1.51391 0.756953 0.653469i $$-0.226687\pi$$
0.756953 + 0.653469i $$0.226687\pi$$
$$464$$ −4.42096 −0.205238
$$465$$ 0 0
$$466$$ 7.96900 + 13.8027i 0.369157 + 0.639398i
$$467$$ 16.9079 0.782406 0.391203 0.920304i $$-0.372059\pi$$
0.391203 + 0.920304i $$0.372059\pi$$
$$468$$ 1.05875 0.0489407
$$469$$ −5.71269 9.89467i −0.263788 0.456894i
$$470$$ 0 0
$$471$$ 5.41192 + 9.37371i 0.249368 + 0.431918i
$$472$$ −3.09395 + 5.35888i −0.142411 + 0.246663i
$$473$$ 22.7767 39.4505i 1.04728 1.81394i
$$474$$ 15.3970 0.707206
$$475$$ 0 0
$$476$$ 10.9245 0.500725
$$477$$ 3.82610 6.62700i 0.175185 0.303429i
$$478$$ 3.31706 5.74532i 0.151719 0.262785i
$$479$$ −1.82570 3.16220i −0.0834181 0.144484i 0.821298 0.570500i $$-0.193250\pi$$
−0.904716 + 0.426015i $$0.859917\pi$$
$$480$$ 0 0
$$481$$ −4.19369 7.26368i −0.191216 0.331195i
$$482$$ 22.0794 1.00569
$$483$$ −10.7458 −0.488950
$$484$$ −14.9403 25.8774i −0.679106 1.17625i
$$485$$ 0 0
$$486$$ 11.8554 0.537771
$$487$$ 13.7416 0.622691 0.311346 0.950297i $$-0.399220\pi$$
0.311346 + 0.950297i $$0.399220\pi$$
$$488$$ −4.01037 6.94616i −0.181541 0.314438i
$$489$$ −8.91274 + 15.4373i −0.403048 + 0.698099i
$$490$$ 0 0
$$491$$ 17.3839 30.1098i 0.784525 1.35884i −0.144758 0.989467i $$-0.546240\pi$$
0.929283 0.369369i $$-0.120426\pi$$
$$492$$ 2.45257 4.24798i 0.110571 0.191514i
$$493$$ −20.7348 −0.933849
$$494$$ 3.22143 1.90535i 0.144939 0.0857258i
$$495$$ 0 0
$$496$$ 4.12622 7.14682i 0.185273 0.320902i
$$497$$ −2.56232 + 4.43807i −0.114936 + 0.199075i
$$498$$ 4.03970 + 6.99696i 0.181023 + 0.313541i
$$499$$ −8.31410 + 14.4005i −0.372190 + 0.644653i −0.989902 0.141752i $$-0.954726\pi$$
0.617712 + 0.786405i $$0.288060\pi$$
$$500$$ 0 0
$$501$$ 17.2600 0.771121
$$502$$ −9.45115 −0.421825
$$503$$ 2.37970 + 4.12176i 0.106106 + 0.183780i 0.914189 0.405287i $$-0.132829\pi$$
−0.808084 + 0.589068i $$0.799495\pi$$
$$504$$ −1.43605 2.48732i −0.0639670 0.110794i
$$505$$ 0 0
$$506$$ −22.1905 −0.986487
$$507$$ −8.15022 14.1166i −0.361964 0.626940i
$$508$$ −7.14949 + 12.3833i −0.317207 + 0.549419i
$$509$$ 1.41576 + 2.45217i 0.0627524 + 0.108690i 0.895695 0.444669i $$-0.146679\pi$$
−0.832942 + 0.553360i $$0.813345\pi$$
$$510$$ 0 0
$$511$$ −5.42390 + 9.39446i −0.239939 + 0.415587i
$$512$$ −1.00000 −0.0441942
$$513$$ 21.1107 12.4862i 0.932062 0.551278i
$$514$$ −26.7890 −1.18161
$$515$$ 0 0
$$516$$ −4.73527 + 8.20172i −0.208459 + 0.361061i
$$517$$ −22.9975 39.8328i −1.01143 1.75185i
$$518$$ −11.3764 + 19.7045i −0.499849 + 0.865764i
$$519$$ 1.40609 + 2.43542i 0.0617206 + 0.106903i
$$520$$ 0 0
$$521$$ 4.92317 0.215688 0.107844 0.994168i $$-0.465605\pi$$
0.107844 + 0.994168i $$0.465605\pi$$
$$522$$ 2.72564 + 4.72095i 0.119298 + 0.206630i
$$523$$ −14.4447 25.0190i −0.631624 1.09400i −0.987220 0.159365i $$-0.949055\pi$$
0.355596 0.934640i $$-0.384278\pi$$
$$524$$ 2.37893 0.103924
$$525$$ 0 0
$$526$$ −7.19364 12.4598i −0.313658 0.543271i
$$527$$ 19.3525 33.5194i 0.843006 1.46013i
$$528$$ 4.24953 + 7.36040i 0.184937 + 0.320320i
$$529$$ 5.47738 9.48710i 0.238147 0.412483i
$$530$$ 0 0
$$531$$ 7.63002 0.331115
$$532$$ −8.84569 4.98375i −0.383509 0.216073i
$$533$$ −3.16848 −0.137242
$$534$$ −7.50965 + 13.0071i −0.324974 + 0.562872i
$$535$$ 0 0
$$536$$ 2.45257 + 4.24798i 0.105935 + 0.183485i
$$537$$ −6.56616 + 11.3729i −0.283351 + 0.490778i
$$538$$ 6.44486 + 11.1628i 0.277858 + 0.481264i
$$539$$ −10.0672 −0.433624
$$540$$ 0 0
$$541$$ −2.30730 3.99637i −0.0991987 0.171817i 0.812154 0.583442i $$-0.198295\pi$$
−0.911353 + 0.411625i $$0.864961\pi$$
$$542$$ 10.0907 + 17.4776i 0.433433 + 0.750727i
$$543$$ −20.0446 −0.860198
$$544$$ −4.69012 −0.201087
$$545$$ 0 0
$$546$$ 1.32927 2.30235i 0.0568873 0.0985317i
$$547$$ 12.1562 + 21.0552i 0.519763 + 0.900255i 0.999736 + 0.0229724i $$0.00731297\pi$$
−0.479973 + 0.877283i $$0.659354\pi$$
$$548$$ −4.54585 + 7.87364i −0.194189 + 0.336345i
$$549$$ −4.94500 + 8.56500i −0.211048 + 0.365545i
$$550$$ 0 0
$$551$$ 16.7892 + 9.45919i 0.715243 + 0.402975i
$$552$$ 4.61338 0.196359
$$553$$ −13.4900 + 23.3654i −0.573654 + 0.993597i
$$554$$ −3.70049 + 6.40943i −0.157219 + 0.272311i
$$555$$ 0 0
$$556$$ 10.5329 18.2435i 0.446694 0.773697i
$$557$$ 12.2154 + 21.1577i 0.517582 + 0.896479i 0.999791 + 0.0204227i $$0.00650119\pi$$
−0.482209 + 0.876056i $$0.660165\pi$$
$$558$$ −10.1757 −0.430772
$$559$$ 6.11750 0.258743
$$560$$ 0 0
$$561$$ 19.9308 + 34.5211i 0.841478 + 1.45748i
$$562$$ −2.72167 −0.114807
$$563$$ 19.7981 0.834390 0.417195 0.908817i $$-0.363013\pi$$
0.417195 + 0.908817i $$0.363013\pi$$
$$564$$ 4.78116 + 8.28121i 0.201323 + 0.348702i
$$565$$ 0 0
$$566$$ 10.2721 + 17.7918i 0.431769 + 0.747845i
$$567$$ 4.40280 7.62587i 0.184900 0.320256i
$$568$$ 1.10005 1.90535i 0.0461573 0.0799467i
$$569$$ −39.9935 −1.67662 −0.838308 0.545197i $$-0.816455\pi$$
−0.838308 + 0.545197i $$0.816455\pi$$
$$570$$ 0 0
$$571$$ −30.3255 −1.26908 −0.634542 0.772889i $$-0.718811\pi$$
−0.634542 + 0.772889i $$0.718811\pi$$
$$572$$ 2.74498 4.75445i 0.114774 0.198794i
$$573$$ 5.87663 10.1786i 0.245500 0.425218i
$$574$$ 4.29763 + 7.44372i 0.179380 + 0.310695i
$$575$$ 0 0
$$576$$ 0.616527 + 1.06786i 0.0256886 + 0.0444940i
$$577$$ −31.8330 −1.32523 −0.662613 0.748962i $$-0.730552\pi$$
−0.662613 + 0.748962i $$0.730552\pi$$
$$578$$ −4.99721 −0.207856
$$579$$ 12.4239 + 21.5188i 0.516318 + 0.894289i
$$580$$ 0 0
$$581$$ −14.1575 −0.587352
$$582$$ 15.0872 0.625383
$$583$$ −19.8396 34.3632i −0.821673 1.42318i
$$584$$ 2.32859 4.03323i 0.0963576 0.166896i
$$585$$ 0 0
$$586$$ −13.3658 + 23.1502i −0.552134 + 0.956324i
$$587$$ 0.530771 0.919322i 0.0219073 0.0379445i −0.854864 0.518852i $$-0.826359\pi$$
0.876771 + 0.480908i $$0.159693\pi$$
$$588$$ 2.09296 0.0863122
$$589$$ −30.9614 + 18.3124i −1.27574 + 0.754551i
$$590$$ 0 0
$$591$$ 10.8448 18.7837i 0.446094 0.772657i
$$592$$ 4.88411 8.45952i 0.200736 0.347684i
$$593$$ −18.7747 32.5188i −0.770985 1.33539i −0.937024 0.349266i $$-0.886431\pi$$
0.166039 0.986119i $$-0.446902\pi$$
$$594$$ 17.9885 31.1570i 0.738076 1.27839i
$$595$$ 0 0
$$596$$ −6.35778 −0.260425
$$597$$ 4.18592 0.171318
$$598$$ −1.49001 2.58077i −0.0609310 0.105536i
$$599$$ 5.02165 + 8.69775i 0.205179 + 0.355380i 0.950190 0.311672i $$-0.100889\pi$$
−0.745011 + 0.667052i $$0.767556\pi$$
$$600$$ 0 0
$$601$$ 7.56630 0.308636 0.154318 0.988021i $$-0.450682\pi$$
0.154318 + 0.988021i $$0.450682\pi$$
$$602$$ −8.29759 14.3718i −0.338184 0.585753i
$$603$$ 3.02415 5.23799i 0.123153 0.213307i
$$604$$ 1.52779 + 2.64622i 0.0621651 + 0.107673i
$$605$$ 0 0
$$606$$ −1.47605 + 2.55659i −0.0599604 + 0.103854i
$$607$$ −30.8174 −1.25084 −0.625420 0.780288i $$-0.715072\pi$$
−0.625420 + 0.780288i $$0.715072\pi$$
$$608$$ 3.79763 + 2.13962i 0.154014 + 0.0867732i
$$609$$ 13.6882 0.554675
$$610$$ 0 0
$$611$$ 3.08839 5.34925i 0.124943 0.216408i
$$612$$ 2.89158 + 5.00837i 0.116885 + 0.202451i
$$613$$ 9.36510 16.2208i 0.378253 0.655153i −0.612555 0.790428i $$-0.709858\pi$$
0.990808 + 0.135275i $$0.0431916\pi$$
$$614$$ 6.38026 + 11.0509i 0.257486 + 0.445980i
$$615$$ 0 0
$$616$$ −14.8928 −0.600050
$$617$$ 23.1741 + 40.1386i 0.932952 + 1.61592i 0.778245 + 0.627960i $$0.216110\pi$$
0.154707 + 0.987960i $$0.450557\pi$$
$$618$$ −2.16979 3.75818i −0.0872816 0.151176i
$$619$$ 11.5591 0.464600 0.232300 0.972644i $$-0.425375\pi$$
0.232300 + 0.972644i $$0.425375\pi$$
$$620$$ 0 0
$$621$$ −9.76435 16.9123i −0.391830 0.678669i
$$622$$ −3.48323 + 6.03313i −0.139665 + 0.241906i
$$623$$ −13.1591 22.7923i −0.527209 0.913153i
$$624$$ −0.570680 + 0.988447i −0.0228455 + 0.0395695i
$$625$$ 0 0
$$626$$ 26.1692 1.04593
$$627$$ −0.389655 37.0445i −0.0155613 1.47941i
$$628$$ 8.14272 0.324930
$$629$$ 22.9070 39.6761i 0.913363 1.58199i
$$630$$ 0 0
$$631$$ −22.4567 38.8962i −0.893989 1.54843i −0.835051 0.550173i $$-0.814562\pi$$
−0.0589383 0.998262i $$-0.518772\pi$$
$$632$$ 5.79153 10.0312i 0.230375 0.399021i
$$633$$ −5.25612 9.10386i −0.208912 0.361846i
$$634$$ 8.75740 0.347801
$$635$$ 0 0
$$636$$ 4.12464 + 7.14408i 0.163553 + 0.283281i
$$637$$ −0.675974 1.17082i −0.0267831 0.0463897i
$$638$$ 28.2667 1.11909
$$639$$ −2.71285 −0.107319
$$640$$ 0 0
$$641$$ 17.3522 30.0549i 0.685371 1.18710i −0.287949 0.957646i $$-0.592973\pi$$
0.973320 0.229451i $$-0.0736932\pi$$
$$642$$ −6.64633 11.5118i −0.262310 0.454333i
$$643$$ −18.7485 + 32.4734i −0.739369 + 1.28062i 0.213411 + 0.976963i $$0.431543\pi$$
−0.952780 + 0.303662i $$0.901791\pi$$
$$644$$ −4.04200 + 7.00096i −0.159277 + 0.275876i
$$645$$ 0 0
$$646$$ 17.8113 + 10.0351i 0.700778 + 0.394825i
$$647$$ 22.6592 0.890823 0.445412 0.895326i $$-0.353057\pi$$
0.445412 + 0.895326i $$0.353057\pi$$
$$648$$ −1.89021 + 3.27394i −0.0742544 + 0.128612i
$$649$$ 19.7821 34.2636i 0.776516 1.34496i
$$650$$ 0 0
$$651$$ −12.7756 + 22.1281i −0.500717 + 0.867267i
$$652$$ 6.70501 + 11.6134i 0.262588 + 0.454817i
$$653$$ 17.7667 0.695266 0.347633 0.937631i $$-0.386986\pi$$
0.347633 + 0.937631i $$0.386986\pi$$
$$654$$ −4.03344 −0.157720
$$655$$ 0 0
$$656$$ −1.84506 3.19574i −0.0720375 0.124773i
$$657$$ −5.74255 −0.224038
$$658$$ −16.7560 −0.653217
$$659$$ −0.991869 1.71797i −0.0386377 0.0669225i 0.846060 0.533088i $$-0.178969\pi$$
−0.884698 + 0.466165i $$0.845635\pi$$
$$660$$ 0 0
$$661$$ −13.1253 22.7337i −0.510515 0.884237i −0.999926 0.0121841i $$-0.996122\pi$$
0.489411 0.872053i $$-0.337212\pi$$
$$662$$ −4.67369 + 8.09507i −0.181648 + 0.314624i
$$663$$ −2.67656 + 4.63593i −0.103949 + 0.180045i
$$664$$ 6.07809 0.235876
$$665$$ 0 0
$$666$$ −12.0447 −0.466724
$$667$$ 7.67175 13.2879i 0.297051 0.514508i
$$668$$ 6.49232 11.2450i 0.251195 0.435083i
$$669$$ −5.53590 9.58846i −0.214030 0.370711i
$$670$$ 0 0
$$671$$ 25.6415 + 44.4124i 0.989879 + 1.71452i
$$672$$ 3.09621 0.119439
$$673$$ 16.0432 0.618418 0.309209 0.950994i $$-0.399936\pi$$
0.309209 + 0.950994i $$0.399936\pi$$
$$674$$ −4.87376 8.44159i −0.187730 0.325158i
$$675$$ 0 0
$$676$$ −12.2627 −0.471644
$$677$$ 48.5483 1.86586 0.932931 0.360056i $$-0.117243\pi$$
0.932931 + 0.360056i $$0.117243\pi$$
$$678$$ −3.30601 5.72618i −0.126967 0.219913i
$$679$$ −13.2186 + 22.8953i −0.507283 + 0.878640i
$$680$$ 0 0
$$681$$ 7.55556 13.0866i 0.289530 0.501480i
$$682$$ −26.3822 + 45.6953i −1.01023 + 1.74976i
$$683$$ 13.3802 0.511981 0.255990 0.966679i $$-0.417598\pi$$
0.255990 + 0.966679i $$0.417598\pi$$
$$684$$ −0.0565317 5.37446i −0.00216155 0.205498i
$$685$$ 0 0
$$686$$ −9.98617 + 17.2966i −0.381274 + 0.660385i
$$687$$ −1.49914 + 2.59659i −0.0571959 + 0.0990662i
$$688$$ 3.56232 + 6.17012i 0.135812 + 0.235234i
$$689$$ 2.66431 4.61473i 0.101502 0.175807i
$$690$$ 0 0
$$691$$ −25.8354 −0.982825 −0.491413 0.870927i $$-0.663519\pi$$
−0.491413 + 0.870927i $$0.663519\pi$$
$$692$$ 2.11559 0.0804228
$$693$$ 9.18184 + 15.9034i 0.348789 + 0.604121i
$$694$$ −7.38162 12.7853i −0.280202 0.485325i
$$695$$ 0 0
$$696$$ −5.87663 −0.222753
$$697$$ −8.65354 14.9884i −0.327776 0.567725i
$$698$$ 7.41576 12.8445i 0.280691 0.486170i
$$699$$ 10.5929 + 18.3475i 0.400661 + 0.693965i
$$700$$ 0 0
$$701$$ −24.6167 + 42.6373i −0.929758 + 1.61039i −0.146034 + 0.989280i $$0.546651\pi$$
−0.783724 + 0.621109i $$0.786682\pi$$
$$702$$ 4.83144 0.182351
$$703$$ −36.6482 + 21.6760i −1.38221 + 0.817525i
$$704$$ 6.39380 0.240975
$$705$$ 0 0
$$706$$ 13.4058 23.2194i 0.504532 0.873875i
$$707$$ −2.58647 4.47990i −0.0972744 0.168484i
$$708$$ −4.11268 + 7.12338i −0.154564 + 0.267713i
$$709$$ −5.44796 9.43614i −0.204602 0.354382i 0.745404 0.666613i $$-0.232257\pi$$
−0.950006 + 0.312232i $$0.898923\pi$$
$$710$$ 0 0
$$711$$ −14.2825 −0.535637
$$712$$ 5.64947 + 9.78517i 0.211723 + 0.366715i
$$713$$ 14.3206 + 24.8039i 0.536309 + 0.928915i
$$714$$ 14.5216 0.543457
$$715$$ 0 0
$$716$$ 4.93969 + 8.55579i 0.184605 + 0.319745i
$$717$$ 4.40925 7.63705i 0.164667 0.285211i
$$718$$ 0.197846 + 0.342680i 0.00738355 + 0.0127887i
$$719$$ 16.9141 29.2961i 0.630789 1.09256i −0.356602 0.934257i $$-0.616065\pi$$
0.987391 0.158302i $$-0.0506020\pi$$
$$720$$ 0 0
$$721$$ 7.60422 0.283196
$$722$$ −9.84402 16.2510i −0.366356 0.604800i
$$723$$ 29.3494 1.09152
$$724$$ −7.53974 + 13.0592i −0.280212 + 0.485342i
$$725$$ 0 0
$$726$$ −19.8597 34.3979i −0.737061 1.27663i
$$727$$ −25.4674 + 44.1108i −0.944533 + 1.63598i −0.187848 + 0.982198i $$0.560151\pi$$
−0.756684 + 0.653780i $$0.773182\pi$$
$$728$$ −1.00000 1.73205i −0.0370625 0.0641941i
$$729$$ 27.1002 1.00371
$$730$$ 0 0
$$731$$ 16.7077 + 28.9386i 0.617957 + 1.07033i
$$732$$ −5.33085 9.23330i −0.197034 0.341272i
$$733$$ 30.8270 1.13862 0.569310 0.822123i $$-0.307210\pi$$
0.569310 + 0.822123i $$0.307210\pi$$
$$734$$ −6.98454 −0.257804
$$735$$ 0 0
$$736$$ 1.73531 3.00565i 0.0639645 0.110790i
$$737$$ −15.6813 27.1607i −0.577626 1.00048i
$$738$$ −2.27506 + 3.94052i −0.0837460 + 0.145052i
$$739$$ 18.8645 32.6742i 0.693941 1.20194i −0.276596 0.960986i $$-0.589206\pi$$
0.970536 0.240954i $$-0.0774604\pi$$
$$740$$ 0 0
$$741$$ 4.28214 2.53272i 0.157308 0.0930417i
$$742$$ −14.4552 −0.530666
$$743$$ −16.3990 + 28.4038i −0.601619 + 1.04204i 0.390957 + 0.920409i $$0.372144\pi$$
−0.992576 + 0.121626i $$0.961189\pi$$
$$744$$ 5.48484 9.50002i 0.201084 0.348288i
$$745$$ 0 0
$$746$$ 1.26311 2.18777i 0.0462456 0.0800998i
$$747$$ −3.74731 6.49053i −0.137107 0.237476i
$$748$$ 29.9877 1.09646
$$749$$ 23.2927 0.851095
$$750$$ 0 0
$$751$$ −2.19685 3.80505i −0.0801641 0.138848i 0.823156 0.567815i $$-0.192211\pi$$
−0.903320 + 0.428967i $$0.858878\pi$$
$$752$$ 7.19369 0.262327
$$753$$ −12.5631 −0.457824
$$754$$ 1.89801 + 3.28744i 0.0691213 + 0.119722i
$$755$$ 0 0
$$756$$ −6.55321 11.3505i −0.238338 0.412814i
$$757$$ −25.4884 + 44.1472i −0.926391 + 1.60456i −0.137082 + 0.990560i $$0.543773\pi$$
−0.789309 + 0.613997i $$0.789561\pi$$
$$758$$ −14.6538 + 25.3811i −0.532248 + 0.921881i
$$759$$ −29.4970 −1.07067
$$760$$ 0 0
$$761$$ 10.5364 0.381945 0.190973 0.981595i $$-0.438836\pi$$
0.190973 + 0.981595i $$0.438836\pi$$
$$762$$ −9.50357 + 16.4607i −0.344278 + 0.596307i
$$763$$ 3.53389 6.12088i 0.127935 0.221591i
$$764$$ −4.42096 7.65733i −0.159945 0.277032i
$$765$$ 0 0
$$766$$ 3.11717 + 5.39911i 0.112628 + 0.195078i
$$767$$ 5.31318 0.191848
$$768$$ −1.32927 −0.0479657
$$769$$ 22.2243 + 38.4936i 0.801429 + 1.38812i 0.918676 + 0.395013i $$0.129260\pi$$
−0.117246 + 0.993103i $$0.537407\pi$$
$$770$$ 0 0
$$771$$ −35.6096 −1.28245
$$772$$ 18.6928 0.672770
$$773$$ 23.1902 + 40.1667i 0.834095 + 1.44469i 0.894766 + 0.446536i $$0.147343\pi$$
−0.0606710 + 0.998158i $$0.519324\pi$$
$$774$$ 4.39253 7.60809i 0.157886 0.273467i
$$775$$ 0 0
$$776$$ 5.67500 9.82939i 0.203721 0.352855i
$$777$$ −15.1222 + 26.1925i −0.542507 + 0.939649i
$$778$$ −26.4365 −0.947796
$$779$$ 0.169181 + 16.0840i 0.00606152 + 0.576268i
$$780$$ 0 0
$$781$$ −7.03353 + 12.1824i −0.251679 + 0.435921i
$$782$$ 8.13882 14.0969i 0.291044 0.504102i
$$783$$ 12.4380 + 21.5433i 0.444499 + 0.769895i
$$784$$ 0.787262 1.36358i 0.0281165 0.0486992i
$$785$$ 0 0
$$786$$ 3.16223 0.112793