# Properties

 Label 300.2.h.b.299.5 Level $300$ Weight $2$ Character 300.299 Analytic conductor $2.396$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 300.h (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.39551206064$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.342102016.5 Defining polynomial: $$x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: no (minimal twist has level 60) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 299.5 Root $$0.599676 + 1.28078i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.299 Dual form 300.2.h.b.299.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.28078 - 0.599676i) q^{2} +(-1.66757 + 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} +0.936426 q^{7} +(0.719224 - 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +O(q^{10})$$ $$q+(1.28078 - 0.599676i) q^{2} +(-1.66757 + 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} +0.936426 q^{7} +(0.719224 - 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +4.27156 q^{11} +(-1.41656 + 3.16123i) q^{12} -3.12311i q^{13} +(1.19935 - 0.561553i) q^{14} +(-0.719224 - 3.93481i) q^{16} -2.00000 q^{17} +(2.34435 - 3.53610i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(5.47091 - 2.56155i) q^{22} +7.60669i q^{23} +(0.0814236 + 4.89830i) q^{24} +(-1.87285 - 4.00000i) q^{26} +(-3.54042 + 3.80335i) q^{27} +(1.19935 - 1.43845i) q^{28} +5.12311i q^{29} +2.39871i q^{31} +(-3.28078 - 4.60831i) q^{32} +(-7.12311 + 2.00000i) q^{33} +(-2.56155 + 1.19935i) q^{34} +(0.882071 - 5.93481i) q^{36} -3.12311i q^{37} +(-2.56155 - 5.47091i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(-1.73707 + 1.49798i) q^{42} -1.46228 q^{43} +(5.47091 - 6.56155i) q^{44} +(4.56155 + 9.74247i) q^{46} +0.936426i q^{47} +(3.04168 + 6.22480i) q^{48} -6.12311 q^{49} +(3.33513 - 0.936426i) q^{51} +(-4.79741 - 4.00000i) q^{52} +4.24621 q^{53} +(-2.25371 + 6.99434i) q^{54} +(0.673500 - 2.56155i) q^{56} +(2.00000 + 7.12311i) q^{57} +(3.07221 + 6.56155i) q^{58} -7.19612 q^{59} -5.12311 q^{61} +(1.43845 + 3.07221i) q^{62} +(2.39871 - 1.46228i) q^{63} +(-6.96543 - 3.93481i) q^{64} +(-7.92375 + 6.83311i) q^{66} +5.20798 q^{67} +(-2.56155 + 3.07221i) q^{68} +(-3.56155 - 12.6847i) q^{69} -6.67026 q^{71} +(-2.42923 - 8.13012i) q^{72} +8.24621i q^{73} +(-1.87285 - 4.00000i) q^{74} +(-6.56155 - 5.47091i) q^{76} +4.00000 q^{77} +(4.99596 + 5.79337i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(4.27156 + 9.12311i) q^{82} -4.68213i q^{83} +(-1.32650 + 2.96026i) q^{84} +(-1.87285 + 0.876894i) q^{86} +(-2.39871 - 8.54312i) q^{87} +(3.07221 - 11.6847i) q^{88} +6.24621i q^{89} -2.92456i q^{91} +(11.6847 + 9.74247i) q^{92} +(-1.12311 - 4.00000i) q^{93} +(0.561553 + 1.19935i) q^{94} +(7.62858 + 6.14856i) q^{96} -6.00000i q^{97} +(-7.84233 + 3.67188i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 2q^{2} + 2q^{4} - 6q^{6} + 14q^{8} + 4q^{9} + O(q^{10})$$ $$8q + 2q^{2} + 2q^{4} - 6q^{6} + 14q^{8} + 4q^{9} + 14q^{12} - 14q^{16} - 16q^{17} + 18q^{18} + 4q^{21} + 2q^{24} - 18q^{32} - 24q^{33} - 4q^{34} + 18q^{36} - 4q^{38} - 16q^{42} + 20q^{46} - 10q^{48} - 16q^{49} - 32q^{53} + 10q^{54} + 16q^{57} - 8q^{61} + 28q^{62} + 2q^{64} - 40q^{66} - 4q^{68} - 12q^{69} - 10q^{72} - 36q^{76} + 32q^{77} - 8q^{78} - 16q^{84} + 44q^{92} + 24q^{93} - 12q^{94} + 42q^{96} - 38q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.28078 0.599676i 0.905646 0.424035i
$$3$$ −1.66757 + 0.468213i −0.962770 + 0.270323i
$$4$$ 1.28078 1.53610i 0.640388 0.768051i
$$5$$ 0 0
$$6$$ −1.85500 + 1.59968i −0.757302 + 0.653065i
$$7$$ 0.936426 0.353936 0.176968 0.984217i $$-0.443371\pi$$
0.176968 + 0.984217i $$0.443371\pi$$
$$8$$ 0.719224 2.73546i 0.254284 0.967130i
$$9$$ 2.56155 1.56155i 0.853851 0.520518i
$$10$$ 0 0
$$11$$ 4.27156 1.28792 0.643962 0.765058i $$-0.277290\pi$$
0.643962 + 0.765058i $$0.277290\pi$$
$$12$$ −1.41656 + 3.16123i −0.408924 + 0.912568i
$$13$$ 3.12311i 0.866194i −0.901347 0.433097i $$-0.857421\pi$$
0.901347 0.433097i $$-0.142579\pi$$
$$14$$ 1.19935 0.561553i 0.320541 0.150081i
$$15$$ 0 0
$$16$$ −0.719224 3.93481i −0.179806 0.983702i
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 2.34435 3.53610i 0.552569 0.833467i
$$19$$ 4.27156i 0.979963i −0.871733 0.489981i $$-0.837004\pi$$
0.871733 0.489981i $$-0.162996\pi$$
$$20$$ 0 0
$$21$$ −1.56155 + 0.438447i −0.340759 + 0.0956770i
$$22$$ 5.47091 2.56155i 1.16640 0.546125i
$$23$$ 7.60669i 1.58610i 0.609154 + 0.793052i $$0.291509\pi$$
−0.609154 + 0.793052i $$0.708491\pi$$
$$24$$ 0.0814236 + 4.89830i 0.0166205 + 0.999862i
$$25$$ 0 0
$$26$$ −1.87285 4.00000i −0.367297 0.784465i
$$27$$ −3.54042 + 3.80335i −0.681354 + 0.731954i
$$28$$ 1.19935 1.43845i 0.226656 0.271841i
$$29$$ 5.12311i 0.951337i 0.879625 + 0.475668i $$0.157794\pi$$
−0.879625 + 0.475668i $$0.842206\pi$$
$$30$$ 0 0
$$31$$ 2.39871i 0.430820i 0.976524 + 0.215410i $$0.0691088\pi$$
−0.976524 + 0.215410i $$0.930891\pi$$
$$32$$ −3.28078 4.60831i −0.579965 0.814642i
$$33$$ −7.12311 + 2.00000i −1.23997 + 0.348155i
$$34$$ −2.56155 + 1.19935i −0.439303 + 0.205687i
$$35$$ 0 0
$$36$$ 0.882071 5.93481i 0.147012 0.989135i
$$37$$ 3.12311i 0.513435i −0.966486 0.256718i $$-0.917359\pi$$
0.966486 0.256718i $$-0.0826411\pi$$
$$38$$ −2.56155 5.47091i −0.415539 0.887499i
$$39$$ 1.46228 + 5.20798i 0.234152 + 0.833945i
$$40$$ 0 0
$$41$$ 7.12311i 1.11244i 0.831034 + 0.556221i $$0.187749\pi$$
−0.831034 + 0.556221i $$0.812251\pi$$
$$42$$ −1.73707 + 1.49798i −0.268036 + 0.231143i
$$43$$ −1.46228 −0.222995 −0.111498 0.993765i $$-0.535565\pi$$
−0.111498 + 0.993765i $$0.535565\pi$$
$$44$$ 5.47091 6.56155i 0.824771 0.989191i
$$45$$ 0 0
$$46$$ 4.56155 + 9.74247i 0.672564 + 1.43645i
$$47$$ 0.936426i 0.136592i 0.997665 + 0.0682959i $$0.0217562\pi$$
−0.997665 + 0.0682959i $$0.978244\pi$$
$$48$$ 3.04168 + 6.22480i 0.439029 + 0.898473i
$$49$$ −6.12311 −0.874729
$$50$$ 0 0
$$51$$ 3.33513 0.936426i 0.467012 0.131126i
$$52$$ −4.79741 4.00000i −0.665281 0.554700i
$$53$$ 4.24621 0.583262 0.291631 0.956531i $$-0.405802\pi$$
0.291631 + 0.956531i $$0.405802\pi$$
$$54$$ −2.25371 + 6.99434i −0.306691 + 0.951809i
$$55$$ 0 0
$$56$$ 0.673500 2.56155i 0.0900002 0.342302i
$$57$$ 2.00000 + 7.12311i 0.264906 + 0.943478i
$$58$$ 3.07221 + 6.56155i 0.403400 + 0.861574i
$$59$$ −7.19612 −0.936855 −0.468427 0.883502i $$-0.655179\pi$$
−0.468427 + 0.883502i $$0.655179\pi$$
$$60$$ 0 0
$$61$$ −5.12311 −0.655946 −0.327973 0.944687i $$-0.606366\pi$$
−0.327973 + 0.944687i $$0.606366\pi$$
$$62$$ 1.43845 + 3.07221i 0.182683 + 0.390171i
$$63$$ 2.39871 1.46228i 0.302209 0.184230i
$$64$$ −6.96543 3.93481i −0.870679 0.491851i
$$65$$ 0 0
$$66$$ −7.92375 + 6.83311i −0.975347 + 0.841098i
$$67$$ 5.20798 0.636257 0.318128 0.948048i $$-0.396946\pi$$
0.318128 + 0.948048i $$0.396946\pi$$
$$68$$ −2.56155 + 3.07221i −0.310634 + 0.372560i
$$69$$ −3.56155 12.6847i −0.428761 1.52705i
$$70$$ 0 0
$$71$$ −6.67026 −0.791615 −0.395807 0.918334i $$-0.629535\pi$$
−0.395807 + 0.918334i $$0.629535\pi$$
$$72$$ −2.42923 8.13012i −0.286287 0.958144i
$$73$$ 8.24621i 0.965146i 0.875856 + 0.482573i $$0.160298\pi$$
−0.875856 + 0.482573i $$0.839702\pi$$
$$74$$ −1.87285 4.00000i −0.217715 0.464991i
$$75$$ 0 0
$$76$$ −6.56155 5.47091i −0.752662 0.627557i
$$77$$ 4.00000 0.455842
$$78$$ 4.99596 + 5.79337i 0.565681 + 0.655970i
$$79$$ 9.06897i 1.02034i 0.860074 + 0.510169i $$0.170417\pi$$
−0.860074 + 0.510169i $$0.829583\pi$$
$$80$$ 0 0
$$81$$ 4.12311 8.00000i 0.458123 0.888889i
$$82$$ 4.27156 + 9.12311i 0.471715 + 1.00748i
$$83$$ 4.68213i 0.513931i −0.966421 0.256965i $$-0.917277\pi$$
0.966421 0.256965i $$-0.0827226\pi$$
$$84$$ −1.32650 + 2.96026i −0.144733 + 0.322991i
$$85$$ 0 0
$$86$$ −1.87285 + 0.876894i −0.201955 + 0.0945580i
$$87$$ −2.39871 8.54312i −0.257168 0.915918i
$$88$$ 3.07221 11.6847i 0.327498 1.24559i
$$89$$ 6.24621i 0.662097i 0.943614 + 0.331049i $$0.107402\pi$$
−0.943614 + 0.331049i $$0.892598\pi$$
$$90$$ 0 0
$$91$$ 2.92456i 0.306577i
$$92$$ 11.6847 + 9.74247i 1.21821 + 1.01572i
$$93$$ −1.12311 4.00000i −0.116461 0.414781i
$$94$$ 0.561553 + 1.19935i 0.0579198 + 0.123704i
$$95$$ 0 0
$$96$$ 7.62858 + 6.14856i 0.778589 + 0.627534i
$$97$$ 6.00000i 0.609208i −0.952479 0.304604i $$-0.901476\pi$$
0.952479 0.304604i $$-0.0985241\pi$$
$$98$$ −7.84233 + 3.67188i −0.792195 + 0.370916i
$$99$$ 10.9418 6.67026i 1.09969 0.670387i
$$100$$ 0 0
$$101$$ 9.12311i 0.907783i −0.891057 0.453891i $$-0.850035\pi$$
0.891057 0.453891i $$-0.149965\pi$$
$$102$$ 3.71001 3.19935i 0.367345 0.316783i
$$103$$ 12.4041 1.22221 0.611106 0.791549i $$-0.290725\pi$$
0.611106 + 0.791549i $$0.290725\pi$$
$$104$$ −8.54312 2.24621i −0.837722 0.220259i
$$105$$ 0 0
$$106$$ 5.43845 2.54635i 0.528229 0.247324i
$$107$$ 0.936426i 0.0905278i −0.998975 0.0452639i $$-0.985587\pi$$
0.998975 0.0452639i $$-0.0144129\pi$$
$$108$$ 1.30784 + 10.3097i 0.125847 + 0.992050i
$$109$$ 9.12311 0.873835 0.436918 0.899502i $$-0.356070\pi$$
0.436918 + 0.899502i $$0.356070\pi$$
$$110$$ 0 0
$$111$$ 1.46228 + 5.20798i 0.138793 + 0.494320i
$$112$$ −0.673500 3.68466i −0.0636398 0.348167i
$$113$$ 14.0000 1.31701 0.658505 0.752577i $$-0.271189\pi$$
0.658505 + 0.752577i $$0.271189\pi$$
$$114$$ 6.83311 + 7.92375i 0.639980 + 0.742127i
$$115$$ 0 0
$$116$$ 7.86962 + 6.56155i 0.730676 + 0.609225i
$$117$$ −4.87689 8.00000i −0.450869 0.739600i
$$118$$ −9.21662 + 4.31534i −0.848458 + 0.397259i
$$119$$ −1.87285 −0.171684
$$120$$ 0 0
$$121$$ 7.24621 0.658746
$$122$$ −6.56155 + 3.07221i −0.594055 + 0.278144i
$$123$$ −3.33513 11.8782i −0.300719 1.07103i
$$124$$ 3.68466 + 3.07221i 0.330892 + 0.275892i
$$125$$ 0 0
$$126$$ 2.19531 3.31130i 0.195574 0.294994i
$$127$$ −4.68213 −0.415472 −0.207736 0.978185i $$-0.566609\pi$$
−0.207736 + 0.978185i $$0.566609\pi$$
$$128$$ −11.2808 0.862603i −0.997089 0.0762440i
$$129$$ 2.43845 0.684658i 0.214693 0.0602808i
$$130$$ 0 0
$$131$$ −17.6121 −1.53878 −0.769388 0.638782i $$-0.779438\pi$$
−0.769388 + 0.638782i $$0.779438\pi$$
$$132$$ −6.05090 + 13.5034i −0.526663 + 1.17532i
$$133$$ 4.00000i 0.346844i
$$134$$ 6.67026 3.12311i 0.576223 0.269795i
$$135$$ 0 0
$$136$$ −1.43845 + 5.47091i −0.123346 + 0.469127i
$$137$$ −8.24621 −0.704521 −0.352261 0.935902i $$-0.614587\pi$$
−0.352261 + 0.935902i $$0.614587\pi$$
$$138$$ −12.1682 14.1104i −1.03583 1.20116i
$$139$$ 13.8664i 1.17613i −0.808813 0.588066i $$-0.799890\pi$$
0.808813 0.588066i $$-0.200110\pi$$
$$140$$ 0 0
$$141$$ −0.438447 1.56155i −0.0369239 0.131506i
$$142$$ −8.54312 + 4.00000i −0.716922 + 0.335673i
$$143$$ 13.3405i 1.11559i
$$144$$ −7.98674 8.95611i −0.665562 0.746343i
$$145$$ 0 0
$$146$$ 4.94506 + 10.5616i 0.409256 + 0.874080i
$$147$$ 10.2107 2.86692i 0.842163 0.236459i
$$148$$ −4.79741 4.00000i −0.394345 0.328798i
$$149$$ 14.0000i 1.14692i 0.819232 + 0.573462i $$0.194400\pi$$
−0.819232 + 0.573462i $$0.805600\pi$$
$$150$$ 0 0
$$151$$ 6.14441i 0.500025i −0.968243 0.250013i $$-0.919565\pi$$
0.968243 0.250013i $$-0.0804347\pi$$
$$152$$ −11.6847 3.07221i −0.947751 0.249189i
$$153$$ −5.12311 + 3.12311i −0.414179 + 0.252488i
$$154$$ 5.12311 2.39871i 0.412832 0.193293i
$$155$$ 0 0
$$156$$ 9.87285 + 4.42405i 0.790461 + 0.354208i
$$157$$ 21.3693i 1.70546i 0.522354 + 0.852729i $$0.325054\pi$$
−0.522354 + 0.852729i $$0.674946\pi$$
$$158$$ 5.43845 + 11.6153i 0.432660 + 0.924065i
$$159$$ −7.08084 + 1.98813i −0.561547 + 0.157669i
$$160$$ 0 0
$$161$$ 7.12311i 0.561379i
$$162$$ 0.483365 12.7187i 0.0379768 0.999279i
$$163$$ −24.1671 −1.89291 −0.946456 0.322834i $$-0.895364\pi$$
−0.946456 + 0.322834i $$0.895364\pi$$
$$164$$ 10.9418 + 9.12311i 0.854413 + 0.712395i
$$165$$ 0 0
$$166$$ −2.80776 5.99676i −0.217925 0.465439i
$$167$$ 2.80928i 0.217389i −0.994075 0.108694i $$-0.965333\pi$$
0.994075 0.108694i $$-0.0346670\pi$$
$$168$$ 0.0762472 + 4.58690i 0.00588260 + 0.353887i
$$169$$ 3.24621 0.249709
$$170$$ 0 0
$$171$$ −6.67026 10.9418i −0.510088 0.836742i
$$172$$ −1.87285 + 2.24621i −0.142804 + 0.171272i
$$173$$ 2.00000 0.152057 0.0760286 0.997106i $$-0.475776\pi$$
0.0760286 + 0.997106i $$0.475776\pi$$
$$174$$ −8.19531 9.50338i −0.621285 0.720449i
$$175$$ 0 0
$$176$$ −3.07221 16.8078i −0.231576 1.26693i
$$177$$ 12.0000 3.36932i 0.901975 0.253253i
$$178$$ 3.74571 + 8.00000i 0.280752 + 0.599625i
$$179$$ 14.6875 1.09780 0.548899 0.835889i $$-0.315047\pi$$
0.548899 + 0.835889i $$0.315047\pi$$
$$180$$ 0 0
$$181$$ 4.24621 0.315618 0.157809 0.987470i $$-0.449557\pi$$
0.157809 + 0.987470i $$0.449557\pi$$
$$182$$ −1.75379 3.74571i −0.129999 0.277650i
$$183$$ 8.54312 2.39871i 0.631525 0.177317i
$$184$$ 20.8078 + 5.47091i 1.53397 + 0.403321i
$$185$$ 0 0
$$186$$ −3.83715 4.44961i −0.281354 0.326261i
$$187$$ −8.54312 −0.624735
$$188$$ 1.43845 + 1.19935i 0.104910 + 0.0874718i
$$189$$ −3.31534 + 3.56155i −0.241156 + 0.259065i
$$190$$ 0 0
$$191$$ 7.72197 0.558742 0.279371 0.960183i $$-0.409874\pi$$
0.279371 + 0.960183i $$0.409874\pi$$
$$192$$ 13.4577 + 3.30024i 0.971222 + 0.238175i
$$193$$ 16.2462i 1.16943i −0.811240 0.584714i $$-0.801207\pi$$
0.811240 0.584714i $$-0.198793\pi$$
$$194$$ −3.59806 7.68466i −0.258326 0.551726i
$$195$$ 0 0
$$196$$ −7.84233 + 9.40572i −0.560166 + 0.671837i
$$197$$ 12.2462 0.872506 0.436253 0.899824i $$-0.356305\pi$$
0.436253 + 0.899824i $$0.356305\pi$$
$$198$$ 10.0140 15.1047i 0.711666 1.07344i
$$199$$ 17.6121i 1.24849i 0.781230 + 0.624244i $$0.214593\pi$$
−0.781230 + 0.624244i $$0.785407\pi$$
$$200$$ 0 0
$$201$$ −8.68466 + 2.43845i −0.612569 + 0.171995i
$$202$$ −5.47091 11.6847i −0.384932 0.822130i
$$203$$ 4.79741i 0.336712i
$$204$$ 2.83311 6.32246i 0.198357 0.442661i
$$205$$ 0 0
$$206$$ 15.8869 7.43845i 1.10689 0.518261i
$$207$$ 11.8782 + 19.4849i 0.825595 + 1.35430i
$$208$$ −12.2888 + 2.24621i −0.852077 + 0.155747i
$$209$$ 18.2462i 1.26212i
$$210$$ 0 0
$$211$$ 1.34700i 0.0927313i −0.998925 0.0463656i $$-0.985236\pi$$
0.998925 0.0463656i $$-0.0147639\pi$$
$$212$$ 5.43845 6.52262i 0.373514 0.447975i
$$213$$ 11.1231 3.12311i 0.762143 0.213992i
$$214$$ −0.561553 1.19935i −0.0383870 0.0819861i
$$215$$ 0 0
$$216$$ 7.85753 + 12.4201i 0.534637 + 0.845082i
$$217$$ 2.24621i 0.152483i
$$218$$ 11.6847 5.47091i 0.791385 0.370537i
$$219$$ −3.86098 13.7511i −0.260901 0.929213i
$$220$$ 0 0
$$221$$ 6.24621i 0.420166i
$$222$$ 4.99596 + 5.79337i 0.335307 + 0.388826i
$$223$$ 18.0227 1.20689 0.603443 0.797406i $$-0.293795\pi$$
0.603443 + 0.797406i $$0.293795\pi$$
$$224$$ −3.07221 4.31534i −0.205270 0.288331i
$$225$$ 0 0
$$226$$ 17.9309 8.39547i 1.19274 0.558458i
$$227$$ 8.65840i 0.574678i −0.957829 0.287339i $$-0.907229\pi$$
0.957829 0.287339i $$-0.0927706\pi$$
$$228$$ 13.5034 + 6.05090i 0.894283 + 0.400731i
$$229$$ −0.246211 −0.0162701 −0.00813505 0.999967i $$-0.502589\pi$$
−0.00813505 + 0.999967i $$0.502589\pi$$
$$230$$ 0 0
$$231$$ −6.67026 + 1.87285i −0.438871 + 0.123225i
$$232$$ 14.0140 + 3.68466i 0.920066 + 0.241910i
$$233$$ −10.0000 −0.655122 −0.327561 0.944830i $$-0.606227\pi$$
−0.327561 + 0.944830i $$0.606227\pi$$
$$234$$ −11.0436 7.32165i −0.721944 0.478631i
$$235$$ 0 0
$$236$$ −9.21662 + 11.0540i −0.599951 + 0.719553i
$$237$$ −4.24621 15.1231i −0.275821 0.982351i
$$238$$ −2.39871 + 1.12311i −0.155485 + 0.0728001i
$$239$$ −20.8319 −1.34751 −0.673753 0.738957i $$-0.735319\pi$$
−0.673753 + 0.738957i $$0.735319\pi$$
$$240$$ 0 0
$$241$$ −11.3693 −0.732362 −0.366181 0.930544i $$-0.619335\pi$$
−0.366181 + 0.930544i $$0.619335\pi$$
$$242$$ 9.28078 4.34538i 0.596591 0.279332i
$$243$$ −3.12985 + 15.2710i −0.200780 + 0.979636i
$$244$$ −6.56155 + 7.86962i −0.420060 + 0.503801i
$$245$$ 0 0
$$246$$ −11.3947 13.2134i −0.726497 0.842454i
$$247$$ −13.3405 −0.848837
$$248$$ 6.56155 + 1.72521i 0.416659 + 0.109551i
$$249$$ 2.19224 + 7.80776i 0.138927 + 0.494797i
$$250$$ 0 0
$$251$$ 25.1035 1.58452 0.792259 0.610184i $$-0.208905\pi$$
0.792259 + 0.610184i $$0.208905\pi$$
$$252$$ 0.825994 5.55751i 0.0520328 0.350090i
$$253$$ 32.4924i 2.04278i
$$254$$ −5.99676 + 2.80776i −0.376270 + 0.176175i
$$255$$ 0 0
$$256$$ −14.9654 + 5.66001i −0.935340 + 0.353751i
$$257$$ 2.49242 0.155473 0.0777365 0.996974i $$-0.475231\pi$$
0.0777365 + 0.996974i $$0.475231\pi$$
$$258$$ 2.71253 2.33917i 0.168875 0.145631i
$$259$$ 2.92456i 0.181723i
$$260$$ 0 0
$$261$$ 8.00000 + 13.1231i 0.495188 + 0.812300i
$$262$$ −22.5571 + 10.5616i −1.39359 + 0.652495i
$$263$$ 15.0981i 0.930989i 0.885051 + 0.465494i $$0.154123\pi$$
−0.885051 + 0.465494i $$0.845877\pi$$
$$264$$ 0.347806 + 20.9234i 0.0214060 + 1.28775i
$$265$$ 0 0
$$266$$ −2.39871 5.12311i −0.147074 0.314118i
$$267$$ −2.92456 10.4160i −0.178980 0.637447i
$$268$$ 6.67026 8.00000i 0.407451 0.488678i
$$269$$ 14.0000i 0.853595i −0.904347 0.426798i $$-0.859642\pi$$
0.904347 0.426798i $$-0.140358\pi$$
$$270$$ 0 0
$$271$$ 31.7738i 1.93012i 0.262032 + 0.965059i $$0.415608\pi$$
−0.262032 + 0.965059i $$0.584392\pi$$
$$272$$ 1.43845 + 7.86962i 0.0872187 + 0.477166i
$$273$$ 1.36932 + 4.87689i 0.0828748 + 0.295163i
$$274$$ −10.5616 + 4.94506i −0.638047 + 0.298742i
$$275$$ 0 0
$$276$$ −24.0465 10.7753i −1.44743 0.648597i
$$277$$ 1.36932i 0.0822743i −0.999154 0.0411371i $$-0.986902\pi$$
0.999154 0.0411371i $$-0.0130981\pi$$
$$278$$ −8.31534 17.7597i −0.498721 1.06516i
$$279$$ 3.74571 + 6.14441i 0.224250 + 0.367856i
$$280$$ 0 0
$$281$$ 27.6155i 1.64740i −0.567023 0.823702i $$-0.691905\pi$$
0.567023 0.823702i $$-0.308095\pi$$
$$282$$ −1.49798 1.73707i −0.0892034 0.103441i
$$283$$ −4.38684 −0.260770 −0.130385 0.991463i $$-0.541621\pi$$
−0.130385 + 0.991463i $$0.541621\pi$$
$$284$$ −8.54312 + 10.2462i −0.506941 + 0.608001i
$$285$$ 0 0
$$286$$ −8.00000 17.0862i −0.473050 1.01033i
$$287$$ 6.67026i 0.393733i
$$288$$ −15.6000 6.68132i −0.919239 0.393701i
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 2.80928 + 10.0054i 0.164683 + 0.586527i
$$292$$ 12.6670 + 10.5616i 0.741282 + 0.618068i
$$293$$ −30.4924 −1.78139 −0.890693 0.454605i $$-0.849780\pi$$
−0.890693 + 0.454605i $$0.849780\pi$$
$$294$$ 11.3584 9.79499i 0.662434 0.571255i
$$295$$ 0 0
$$296$$ −8.54312 2.24621i −0.496559 0.130558i
$$297$$ −15.1231 + 16.2462i −0.877532 + 0.942701i
$$298$$ 8.39547 + 17.9309i 0.486337 + 1.03871i
$$299$$ 23.7565 1.37387
$$300$$ 0 0
$$301$$ −1.36932 −0.0789261
$$302$$ −3.68466 7.86962i −0.212028 0.452846i
$$303$$ 4.27156 + 15.2134i 0.245395 + 0.873986i
$$304$$ −16.8078 + 3.07221i −0.963991 + 0.176203i
$$305$$ 0 0
$$306$$ −4.68870 + 7.07221i −0.268035 + 0.404291i
$$307$$ 8.13254 0.464149 0.232074 0.972698i $$-0.425449\pi$$
0.232074 + 0.972698i $$0.425449\pi$$
$$308$$ 5.12311 6.14441i 0.291916 0.350110i
$$309$$ −20.6847 + 5.80776i −1.17671 + 0.330392i
$$310$$ 0 0
$$311$$ 14.1617 0.803035 0.401517 0.915851i $$-0.368483\pi$$
0.401517 + 0.915851i $$0.368483\pi$$
$$312$$ 15.2979 0.254294i 0.866074 0.0143966i
$$313$$ 10.4924i 0.593067i −0.955022 0.296533i $$-0.904169\pi$$
0.955022 0.296533i $$-0.0958306\pi$$
$$314$$ 12.8147 + 27.3693i 0.723174 + 1.54454i
$$315$$ 0 0
$$316$$ 13.9309 + 11.6153i 0.783673 + 0.653413i
$$317$$ −32.7386 −1.83878 −0.919392 0.393342i $$-0.871319\pi$$
−0.919392 + 0.393342i $$0.871319\pi$$
$$318$$ −7.87673 + 6.79256i −0.441705 + 0.380908i
$$319$$ 21.8836i 1.22525i
$$320$$ 0 0
$$321$$ 0.438447 + 1.56155i 0.0244717 + 0.0871574i
$$322$$ 4.27156 + 9.12311i 0.238045 + 0.508411i
$$323$$ 8.54312i 0.475352i
$$324$$ −7.00805 16.5797i −0.389336 0.921096i
$$325$$ 0 0
$$326$$ −30.9526 + 14.4924i −1.71431 + 0.802661i
$$327$$ −15.2134 + 4.27156i −0.841302 + 0.236218i
$$328$$ 19.4849 + 5.12311i 1.07588 + 0.282876i
$$329$$ 0.876894i 0.0483448i
$$330$$ 0 0
$$331$$ 28.0281i 1.54056i −0.637705 0.770281i $$-0.720116\pi$$
0.637705 0.770281i $$-0.279884\pi$$
$$332$$ −7.19224 5.99676i −0.394725 0.329115i
$$333$$ −4.87689 8.00000i −0.267252 0.438397i
$$334$$ −1.68466 3.59806i −0.0921804 0.196877i
$$335$$ 0 0
$$336$$ 2.84831 + 5.82907i 0.155388 + 0.318002i
$$337$$ 34.4924i 1.87892i −0.342656 0.939461i $$-0.611326\pi$$
0.342656 0.939461i $$-0.388674\pi$$
$$338$$ 4.15767 1.94668i 0.226147 0.105885i
$$339$$ −23.3459 + 6.55498i −1.26798 + 0.356018i
$$340$$ 0 0
$$341$$ 10.2462i 0.554863i
$$342$$ −15.1047 10.0140i −0.816767 0.541497i
$$343$$ −12.2888 −0.663534
$$344$$ −1.05171 + 4.00000i −0.0567042 + 0.215666i
$$345$$ 0 0
$$346$$ 2.56155 1.19935i 0.137710 0.0644776i
$$347$$ 23.8718i 1.28150i 0.767748 + 0.640752i $$0.221377\pi$$
−0.767748 + 0.640752i $$0.778623\pi$$
$$348$$ −16.1953 7.25716i −0.868160 0.389025i
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 11.8782 + 11.0571i 0.634014 + 0.590184i
$$352$$ −14.0140 19.6847i −0.746950 1.04920i
$$353$$ −3.75379 −0.199794 −0.0998970 0.994998i $$-0.531851\pi$$
−0.0998970 + 0.994998i $$0.531851\pi$$
$$354$$ 13.3488 11.5115i 0.709482 0.611827i
$$355$$ 0 0
$$356$$ 9.59482 + 8.00000i 0.508525 + 0.423999i
$$357$$ 3.12311 0.876894i 0.165292 0.0464102i
$$358$$ 18.8114 8.80776i 0.994215 0.465505i
$$359$$ 1.05171 0.0555069 0.0277535 0.999615i $$-0.491165\pi$$
0.0277535 + 0.999615i $$0.491165\pi$$
$$360$$ 0 0
$$361$$ 0.753789 0.0396731
$$362$$ 5.43845 2.54635i 0.285838 0.133833i
$$363$$ −12.0835 + 3.39277i −0.634221 + 0.178074i
$$364$$ −4.49242 3.74571i −0.235467 0.196328i
$$365$$ 0 0
$$366$$ 9.50338 8.19531i 0.496749 0.428376i
$$367$$ 26.5658 1.38672 0.693361 0.720590i $$-0.256129\pi$$
0.693361 + 0.720590i $$0.256129\pi$$
$$368$$ 29.9309 5.47091i 1.56025 0.285191i
$$369$$ 11.1231 + 18.2462i 0.579046 + 0.949860i
$$370$$ 0 0
$$371$$ 3.97626 0.206437
$$372$$ −7.58286 3.39790i −0.393153 0.176173i
$$373$$ 0.876894i 0.0454039i 0.999742 + 0.0227019i $$0.00722687\pi$$
−0.999742 + 0.0227019i $$0.992773\pi$$
$$374$$ −10.9418 + 5.12311i −0.565788 + 0.264909i
$$375$$ 0 0
$$376$$ 2.56155 + 0.673500i 0.132102 + 0.0347331i
$$377$$ 16.0000 0.824042
$$378$$ −2.11043 + 6.54968i −0.108549 + 0.336879i
$$379$$ 25.1035i 1.28948i −0.764402 0.644740i $$-0.776966\pi$$
0.764402 0.644740i $$-0.223034\pi$$
$$380$$ 0 0
$$381$$ 7.80776 2.19224i 0.400004 0.112312i
$$382$$ 9.89012 4.63068i 0.506022 0.236926i
$$383$$ 4.68213i 0.239246i 0.992819 + 0.119623i $$0.0381685\pi$$
−0.992819 + 0.119623i $$0.961831\pi$$
$$384$$ 19.2153 3.84336i 0.980578 0.196131i
$$385$$ 0 0
$$386$$ −9.74247 20.8078i −0.495879 1.05909i
$$387$$ −3.74571 + 2.28343i −0.190405 + 0.116073i
$$388$$ −9.21662 7.68466i −0.467903 0.390129i
$$389$$ 28.7386i 1.45711i −0.684989 0.728553i $$-0.740193\pi$$
0.684989 0.728553i $$-0.259807\pi$$
$$390$$ 0 0
$$391$$ 15.2134i 0.769374i
$$392$$ −4.40388 + 16.7495i −0.222430 + 0.845977i
$$393$$ 29.3693 8.24621i 1.48149 0.415966i
$$394$$ 15.6847 7.34376i 0.790182 0.369973i
$$395$$ 0 0
$$396$$ 3.76782 25.3509i 0.189340 1.27393i
$$397$$ 23.1231i 1.16052i 0.814433 + 0.580258i $$0.197048\pi$$
−0.814433 + 0.580258i $$0.802952\pi$$
$$398$$ 10.5616 + 22.5571i 0.529403 + 1.13069i
$$399$$ 1.87285 + 6.67026i 0.0937599 + 0.333931i
$$400$$ 0 0
$$401$$ 24.0000i 1.19850i 0.800561 + 0.599251i $$0.204535\pi$$
−0.800561 + 0.599251i $$0.795465\pi$$
$$402$$ −9.66083 + 8.33109i −0.481838 + 0.415517i
$$403$$ 7.49141 0.373174
$$404$$ −14.0140 11.6847i −0.697224 0.581333i
$$405$$ 0 0
$$406$$ 2.87689 + 6.14441i 0.142778 + 0.304942i
$$407$$ 13.3405i 0.661265i
$$408$$ −0.162847 9.79661i −0.00806214 0.485004i
$$409$$ −0.630683 −0.0311853 −0.0155926 0.999878i $$-0.504963\pi$$
−0.0155926 + 0.999878i $$0.504963\pi$$
$$410$$ 0 0
$$411$$ 13.7511 3.86098i 0.678292 0.190448i
$$412$$ 15.8869 19.0540i 0.782690 0.938722i
$$413$$ −6.73863 −0.331586
$$414$$ 26.8980 + 17.8327i 1.32197 + 0.876432i
$$415$$ 0 0
$$416$$ −14.3922 + 10.2462i −0.705637 + 0.502362i
$$417$$ 6.49242 + 23.1231i 0.317935 + 1.13234i
$$418$$ −10.9418 23.3693i −0.535182 1.14303i
$$419$$ −6.14441 −0.300174 −0.150087 0.988673i $$-0.547955\pi$$
−0.150087 + 0.988673i $$0.547955\pi$$
$$420$$ 0 0
$$421$$ −0.630683 −0.0307376 −0.0153688 0.999882i $$-0.504892\pi$$
−0.0153688 + 0.999882i $$0.504892\pi$$
$$422$$ −0.807764 1.72521i −0.0393213 0.0839817i
$$423$$ 1.46228 + 2.39871i 0.0710985 + 0.116629i
$$424$$ 3.05398 11.6153i 0.148314 0.564090i
$$425$$ 0 0
$$426$$ 12.3734 10.6703i 0.599491 0.516976i
$$427$$ −4.79741 −0.232163
$$428$$ −1.43845 1.19935i −0.0695300 0.0579729i
$$429$$ 6.24621 + 22.2462i 0.301570 + 1.07406i
$$430$$ 0 0
$$431$$ −36.0453 −1.73624 −0.868121 0.496353i $$-0.834672\pi$$
−0.868121 + 0.496353i $$0.834672\pi$$
$$432$$ 17.5118 + 11.1954i 0.842536 + 0.538640i
$$433$$ 18.0000i 0.865025i −0.901628 0.432512i $$-0.857627\pi$$
0.901628 0.432512i $$-0.142373\pi$$
$$434$$ 1.34700 + 2.87689i 0.0646581 + 0.138095i
$$435$$ 0 0
$$436$$ 11.6847 14.0140i 0.559594 0.671150i
$$437$$ 32.4924 1.55432
$$438$$ −13.1913 15.2967i −0.630303 0.730907i
$$439$$ 29.9009i 1.42709i −0.700608 0.713546i $$-0.747088\pi$$
0.700608 0.713546i $$-0.252912\pi$$
$$440$$ 0 0
$$441$$ −15.6847 + 9.56155i −0.746888 + 0.455312i
$$442$$ 3.74571 + 8.00000i 0.178165 + 0.380521i
$$443$$ 25.7446i 1.22316i −0.791181 0.611582i $$-0.790533\pi$$
0.791181 0.611582i $$-0.209467\pi$$
$$444$$ 9.87285 + 4.42405i 0.468545 + 0.209956i
$$445$$ 0 0
$$446$$ 23.0830 10.8078i 1.09301 0.511762i
$$447$$ −6.55498 23.3459i −0.310040 1.10422i
$$448$$ −6.52262 3.68466i −0.308165 0.174084i
$$449$$ 2.63068i 0.124150i 0.998071 + 0.0620748i $$0.0197717\pi$$
−0.998071 + 0.0620748i $$0.980228\pi$$
$$450$$ 0 0
$$451$$ 30.4268i 1.43274i
$$452$$ 17.9309 21.5054i 0.843397 1.01153i
$$453$$ 2.87689 + 10.2462i 0.135168 + 0.481409i
$$454$$ −5.19224 11.0895i −0.243684 0.520455i
$$455$$ 0 0
$$456$$ 20.9234 0.347806i 0.979827 0.0162875i
$$457$$ 10.0000i 0.467780i −0.972263 0.233890i $$-0.924854\pi$$
0.972263 0.233890i $$-0.0751456\pi$$
$$458$$ −0.315342 + 0.147647i −0.0147349 + 0.00689909i
$$459$$ 7.08084 7.60669i 0.330505 0.355050i
$$460$$ 0 0
$$461$$ 15.8617i 0.738755i −0.929279 0.369377i $$-0.879571\pi$$
0.929279 0.369377i $$-0.120429\pi$$
$$462$$ −7.42001 + 6.39871i −0.345210 + 0.297695i
$$463$$ 0.936426 0.0435194 0.0217597 0.999763i $$-0.493073\pi$$
0.0217597 + 0.999763i $$0.493073\pi$$
$$464$$ 20.1584 3.68466i 0.935832 0.171056i
$$465$$ 0 0
$$466$$ −12.8078 + 5.99676i −0.593308 + 0.277795i
$$467$$ 16.1498i 0.747324i 0.927565 + 0.373662i $$0.121898\pi$$
−0.927565 + 0.373662i $$0.878102\pi$$
$$468$$ −18.5350 2.75480i −0.856782 0.127341i
$$469$$ 4.87689 0.225194
$$470$$ 0 0
$$471$$ −10.0054 35.6347i −0.461024 1.64196i
$$472$$ −5.17562 + 19.6847i −0.238227 + 0.906060i
$$473$$ −6.24621 −0.287201
$$474$$ −14.5074 16.8230i −0.666348 0.772704i
$$475$$ 0 0
$$476$$ −2.39871 + 2.87689i −0.109944 + 0.131862i
$$477$$ 10.8769 6.63068i 0.498019 0.303598i
$$478$$ −26.6811 + 12.4924i −1.22036 + 0.571390i
$$479$$ 22.9354 1.04794 0.523971 0.851736i $$-0.324450\pi$$
0.523971 + 0.851736i $$0.324450\pi$$
$$480$$ 0 0
$$481$$ −9.75379 −0.444734
$$482$$ −14.5616 + 6.81791i −0.663261 + 0.310547i
$$483$$ −3.33513 11.8782i −0.151754 0.540479i
$$484$$ 9.28078 11.1309i 0.421853 0.505951i
$$485$$ 0 0
$$486$$ 5.14904 + 21.4357i 0.233565 + 0.972341i
$$487$$ −15.3287 −0.694608 −0.347304 0.937753i $$-0.612903\pi$$
−0.347304 + 0.937753i $$0.612903\pi$$
$$488$$ −3.68466 + 14.0140i −0.166797 + 0.634385i
$$489$$ 40.3002 11.3153i 1.82244 0.511697i
$$490$$ 0 0
$$491$$ −18.6638 −0.842285 −0.421143 0.906994i $$-0.638371\pi$$
−0.421143 + 0.906994i $$0.638371\pi$$
$$492$$ −22.5178 10.0903i −1.01518 0.454905i
$$493$$ 10.2462i 0.461466i
$$494$$ −17.0862 + 8.00000i −0.768746 + 0.359937i
$$495$$ 0 0
$$496$$ 9.43845 1.72521i 0.423799 0.0774640i
$$497$$ −6.24621 −0.280181
$$498$$ 7.48990 + 8.68537i 0.335630 + 0.389201i
$$499$$ 1.57756i 0.0706212i 0.999376 + 0.0353106i $$0.0112421\pi$$
−0.999376 + 0.0353106i $$0.988758\pi$$
$$500$$ 0 0
$$501$$ 1.31534 + 4.68466i 0.0587651 + 0.209295i
$$502$$ 32.1520 15.0540i 1.43501 0.671892i
$$503$$ 19.8955i 0.887097i −0.896250 0.443549i $$-0.853719\pi$$
0.896250 0.443549i $$-0.146281\pi$$
$$504$$ −2.27479 7.61326i −0.101327 0.339121i
$$505$$ 0 0
$$506$$ 19.4849 + 41.6155i 0.866211 + 1.85004i
$$507$$ −5.41327 + 1.51992i −0.240412 + 0.0675020i
$$508$$ −5.99676 + 7.19224i −0.266063 + 0.319104i
$$509$$ 2.87689i 0.127516i −0.997965 0.0637581i $$-0.979691\pi$$
0.997965 0.0637581i $$-0.0203086\pi$$
$$510$$ 0 0
$$511$$ 7.72197i 0.341600i
$$512$$ −15.7732 + 16.2236i −0.697083 + 0.716990i
$$513$$ 16.2462 + 15.1231i 0.717288 + 0.667701i
$$514$$ 3.19224 1.49465i 0.140803 0.0659261i
$$515$$ 0 0
$$516$$ 2.07140 4.62260i 0.0911883 0.203499i
$$517$$ 4.00000i 0.175920i
$$518$$ −1.75379 3.74571i −0.0770571 0.164577i
$$519$$ −3.33513 + 0.936426i −0.146396 + 0.0411046i
$$520$$ 0 0
$$521$$ 21.7538i 0.953051i −0.879161 0.476525i $$-0.841896\pi$$
0.879161 0.476525i $$-0.158104\pi$$
$$522$$ 18.1158 + 12.0104i 0.792908 + 0.525679i
$$523$$ 0.641132 0.0280348 0.0140174 0.999902i $$-0.495538\pi$$
0.0140174 + 0.999902i $$0.495538\pi$$
$$524$$ −22.5571 + 27.0540i −0.985413 + 1.18186i
$$525$$ 0 0
$$526$$ 9.05398 + 19.3373i 0.394772 + 0.843146i
$$527$$ 4.79741i 0.208979i
$$528$$ 12.9927 + 26.5896i 0.565436 + 1.15716i
$$529$$ −34.8617 −1.51573
$$530$$ 0 0
$$531$$ −18.4332 + 11.2371i −0.799934 + 0.487649i
$$532$$ −6.14441 5.12311i −0.266394 0.222115i
$$533$$ 22.2462 0.963590
$$534$$ −9.99192 11.5867i −0.432393 0.501407i
$$535$$ 0 0
$$536$$ 3.74571 14.2462i 0.161790 0.615343i
$$537$$ −24.4924 + 6.87689i −1.05693 + 0.296760i
$$538$$ −8.39547 17.9309i −0.361954 0.773055i
$$539$$ −26.1552 −1.12658
$$540$$ 0 0
$$541$$ 38.9848 1.67609 0.838045 0.545602i $$-0.183699\pi$$
0.838045 + 0.545602i $$0.183699\pi$$
$$542$$ 19.0540 + 40.6951i 0.818438 + 1.74800i
$$543$$ −7.08084 + 1.98813i −0.303868 + 0.0853189i
$$544$$ 6.56155 + 9.21662i 0.281324 + 0.395159i
$$545$$ 0 0
$$546$$ 4.67835 + 5.42506i 0.200215 + 0.232171i
$$547$$ 25.2188 1.07828 0.539139 0.842217i $$-0.318750\pi$$
0.539139 + 0.842217i $$0.318750\pi$$
$$548$$ −10.5616 + 12.6670i −0.451167 + 0.541109i
$$549$$ −13.1231 + 8.00000i −0.560080 + 0.341432i
$$550$$ 0 0
$$551$$ 21.8836 0.932275
$$552$$ −37.2599 + 0.619364i −1.58589 + 0.0263619i
$$553$$ 8.49242i 0.361135i
$$554$$ −0.821147 1.75379i −0.0348872 0.0745113i
$$555$$ 0 0
$$556$$ −21.3002 17.7597i −0.903329 0.753180i
$$557$$ −19.7538 −0.836995 −0.418497 0.908218i $$-0.637443\pi$$
−0.418497 + 0.908218i $$0.637443\pi$$
$$558$$ 8.48207 + 5.62341i 0.359075 + 0.238058i
$$559$$ 4.56685i 0.193157i
$$560$$ 0 0
$$561$$ 14.2462 4.00000i 0.601476 0.168880i
$$562$$ −16.5604 35.3693i −0.698558 1.49196i
$$563$$ 36.1606i 1.52399i −0.647584 0.761994i $$-0.724221\pi$$
0.647584 0.761994i $$-0.275779\pi$$
$$564$$ −2.96026 1.32650i −0.124649 0.0558557i
$$565$$ 0 0
$$566$$ −5.61856 + 2.63068i −0.236166 + 0.110576i
$$567$$ 3.86098 7.49141i 0.162146 0.314610i
$$568$$ −4.79741 + 18.2462i −0.201295 + 0.765594i
$$569$$ 4.87689i 0.204450i 0.994761 + 0.102225i $$0.0325962\pi$$
−0.994761 + 0.102225i $$0.967404\pi$$
$$570$$ 0 0
$$571$$ 16.7909i 0.702679i −0.936248 0.351339i $$-0.885726\pi$$
0.936248 0.351339i $$-0.114274\pi$$
$$572$$ −20.4924 17.0862i −0.856831 0.714411i
$$573$$ −12.8769 + 3.61553i −0.537940 + 0.151041i
$$574$$ 4.00000 + 8.54312i 0.166957 + 0.356583i
$$575$$ 0 0
$$576$$ −23.9867 + 0.797675i −0.999448 + 0.0332364i
$$577$$ 15.7538i 0.655839i −0.944706 0.327919i $$-0.893653\pi$$
0.944706 0.327919i $$-0.106347\pi$$
$$578$$ −16.6501 + 7.79579i −0.692553 + 0.324262i
$$579$$ 7.60669 + 27.0916i 0.316123 + 1.12589i
$$580$$ 0 0
$$581$$ 4.38447i 0.181899i
$$582$$ 9.59806 + 11.1300i 0.397852 + 0.461354i
$$583$$ 18.1379 0.751197
$$584$$ 22.5571 + 5.93087i 0.933421 + 0.245421i
$$585$$ 0 0
$$586$$ −39.0540 + 18.2856i −1.61330 + 0.755371i
$$587$$ 38.0335i 1.56981i −0.619617 0.784904i $$-0.712712\pi$$
0.619617 0.784904i $$-0.287288\pi$$
$$588$$ 8.67372 19.3565i 0.357698 0.798250i
$$589$$ 10.2462 0.422188
$$590$$ 0 0
$$591$$ −20.4214 + 5.73384i −0.840023 + 0.235859i
$$592$$ −12.2888 + 2.24621i −0.505067 + 0.0923187i
$$593$$ −8.24621 −0.338631 −0.169316 0.985562i $$-0.554156\pi$$
−0.169316 + 0.985562i $$0.554156\pi$$
$$594$$ −9.62685 + 29.8767i −0.394994 + 1.22586i
$$595$$ 0 0
$$596$$ 21.5054 + 17.9309i 0.880897 + 0.734477i
$$597$$ −8.24621 29.3693i −0.337495 1.20201i
$$598$$ 30.4268 14.2462i 1.24424 0.582571i
$$599$$ 36.8665 1.50632 0.753162 0.657836i $$-0.228528\pi$$
0.753162 + 0.657836i $$0.228528\pi$$
$$600$$ 0 0
$$601$$ 14.8769 0.606841 0.303421 0.952857i $$-0.401871\pi$$
0.303421 + 0.952857i $$0.401871\pi$$
$$602$$ −1.75379 + 0.821147i −0.0714791 + 0.0334675i
$$603$$ 13.3405 8.13254i 0.543268 0.331183i
$$604$$ −9.43845 7.86962i −0.384045 0.320210i
$$605$$ 0 0
$$606$$ 14.5940 + 16.9234i 0.592841 + 0.687466i
$$607$$ 29.4903 1.19698 0.598488 0.801132i $$-0.295768\pi$$
0.598488 + 0.801132i $$0.295768\pi$$
$$608$$ −19.6847 + 14.0140i −0.798318 + 0.568344i
$$609$$ −2.24621 8.00000i −0.0910211 0.324176i
$$610$$ 0 0
$$611$$ 2.92456 0.118315
$$612$$ −1.76414 + 11.8696i −0.0713112 + 0.479801i
$$613$$ 0.876894i 0.0354174i −0.999843 0.0177087i $$-0.994363\pi$$
0.999843 0.0177087i $$-0.00563715\pi$$
$$614$$ 10.4160 4.87689i 0.420354 0.196815i
$$615$$ 0 0
$$616$$ 2.87689 10.9418i 0.115913 0.440859i
$$617$$ 14.0000 0.563619 0.281809 0.959470i $$-0.409065\pi$$
0.281809 + 0.959470i $$0.409065\pi$$
$$618$$ −23.0096 + 19.8425i −0.925584 + 0.798184i
$$619$$ 20.3061i 0.816171i 0.912944 + 0.408085i $$0.133803\pi$$
−0.912944 + 0.408085i $$0.866197\pi$$
$$620$$ 0 0
$$621$$ −28.9309 26.9309i −1.16096 1.08070i
$$622$$ 18.1379 8.49242i 0.727265 0.340515i
$$623$$ 5.84912i 0.234340i
$$624$$ 19.4407 9.49949i 0.778252 0.380284i
$$625$$ 0 0
$$626$$ −6.29206 13.4384i −0.251481 0.537108i
$$627$$ 8.54312 + 30.4268i 0.341179 + 1.21513i
$$628$$ 32.8255 + 27.3693i 1.30988 + 1.09215i
$$629$$ 6.24621i 0.249053i
$$630$$ 0 0
$$631$$ 30.1315i 1.19951i −0.800182 0.599757i $$-0.795264\pi$$
0.800182 0.599757i $$-0.204736\pi$$
$$632$$ 24.8078 + 6.52262i 0.986800 + 0.259456i
$$633$$ 0.630683 + 2.24621i 0.0250674 + 0.0892789i
$$634$$ −41.9309 + 19.6326i −1.66529 + 0.779710i
$$635$$ 0 0
$$636$$ −6.01499 + 13.4232i −0.238510 + 0.532266i
$$637$$ 19.1231i 0.757685i
$$638$$ 13.1231 + 28.0281i 0.519549 + 1.10964i
$$639$$ −17.0862 + 10.4160i −0.675921 + 0.412049i
$$640$$ 0 0
$$641$$ 47.6155i 1.88070i −0.340208 0.940350i $$-0.610498\pi$$
0.340208 0.940350i $$-0.389502\pi$$
$$642$$ 1.49798 + 1.73707i 0.0591205 + 0.0685568i
$$643$$ 20.4214 0.805340 0.402670 0.915345i $$-0.368082\pi$$
0.402670 + 0.915345i $$0.368082\pi$$
$$644$$ 10.9418 + 9.12311i 0.431168 + 0.359501i
$$645$$ 0 0
$$646$$ 5.12311 + 10.9418i 0.201566 + 0.430500i
$$647$$ 3.63043i 0.142727i −0.997450 0.0713634i $$-0.977265\pi$$
0.997450 0.0713634i $$-0.0227350\pi$$
$$648$$ −18.9182 17.0324i −0.743177 0.669094i
$$649$$ −30.7386 −1.20660
$$650$$ 0 0
$$651$$ −1.05171 3.74571i −0.0412196 0.146806i
$$652$$ −30.9526 + 37.1231i −1.21220 + 1.45385i
$$653$$ 26.9848 1.05600 0.527999 0.849245i $$-0.322942\pi$$
0.527999 + 0.849245i $$0.322942\pi$$
$$654$$ −16.9234 + 14.5940i −0.661757 + 0.570671i
$$655$$ 0 0
$$656$$ 28.0281 5.12311i 1.09431 0.200024i
$$657$$ 12.8769 + 21.1231i 0.502375 + 0.824091i
$$658$$ 0.525853 + 1.12311i 0.0204999 + 0.0437832i
$$659$$ −26.9764 −1.05085 −0.525425 0.850840i $$-0.676094\pi$$
−0.525425 + 0.850840i $$0.676094\pi$$
$$660$$ 0 0
$$661$$ −46.1080 −1.79339 −0.896696 0.442647i $$-0.854039\pi$$
−0.896696 + 0.442647i $$0.854039\pi$$
$$662$$ −16.8078 35.8977i −0.653252 1.39520i
$$663$$ −2.92456 10.4160i −0.113580 0.404523i
$$664$$ −12.8078 3.36750i −0.497038 0.130684i
$$665$$ 0 0
$$666$$ −11.0436 7.32165i −0.427932 0.283708i
$$667$$ −38.9699 −1.50892
$$668$$ −4.31534 3.59806i −0.166966 0.139213i
$$669$$ −30.0540 + 8.43845i −1.16195 + 0.326249i
$$670$$ 0 0
$$671$$ −21.8836 −0.844809
$$672$$ 7.14361 + 5.75767i 0.275571 + 0.222107i
$$673$$ 10.4924i 0.404453i 0.979339 + 0.202227i $$0.0648177\pi$$
−0.979339 + 0.202227i $$0.935182\pi$$
$$674$$ −20.6843 44.1771i −0.796729 1.70164i
$$675$$ 0 0
$$676$$ 4.15767 4.98651i 0.159910 0.191789i
$$677$$ −34.4924 −1.32565 −0.662826 0.748774i $$-0.730643\pi$$
−0.662826 + 0.748774i $$0.730643\pi$$
$$678$$ −25.9700 + 22.3955i −0.997373 + 0.860093i
$$679$$ 5.61856i 0.215620i
$$680$$ 0 0
$$681$$ 4.05398 + 14.4384i 0.155349 + 0.553282i
$$682$$ 6.14441 + 13.1231i 0.235282 + 0.502510i
$$683$$ 36.1606i 1.38365i 0.722067 + 0.691823i $$0.243192\pi$$
−0.722067 + 0.691823i $$0.756808\pi$$
$$684$$ −25.3509 3.76782i −0.969315 0.144066i
$$685$$ 0 0
$$686$$ −15.7392 + 7.36932i −0.600927 + 0.281362i
$$687$$ 0.410574 0.115279i 0.0156644 0.00439818i
$$688$$ 1.05171 + 5.75379i 0.0400959 + 0.219361i
$$689$$ 13.2614i 0.505218i
$$690$$ 0 0
$$691$$ 29.0798i 1.10625i 0.833100 + 0.553123i $$0.186564\pi$$
−0.833100 + 0.553123i $$0.813436\pi$$
$$692$$ 2.56155 3.07221i 0.0973756 0.116788i
$$693$$ 10.2462 6.24621i 0.389221 0.237274i
$$694$$ 14.3153 + 30.5744i 0.543403 + 1.16059i
$$695$$ 0 0
$$696$$ −25.0945 + 0.417142i −0.951205 + 0.0158117i
$$697$$ 14.2462i 0.539614i
$$698$$ 17.9309 8.39547i 0.678693 0.317773i
$$699$$ 16.6757 4.68213i 0.630731 0.177094i
$$700$$ 0 0
$$701$$ 50.4924i 1.90707i 0.301278 + 0.953536i $$0.402587\pi$$
−0.301278 + 0.953536i $$0.597413\pi$$
$$702$$ 21.8441 + 7.03857i 0.824451 + 0.265654i
$$703$$ −13.3405 −0.503148
$$704$$ −29.7533 16.8078i −1.12137 0.633466i
$$705$$ 0 0
$$706$$ −4.80776 + 2.25106i −0.180943 + 0.0847197i
$$707$$ 8.54312i 0.321297i
$$708$$ 10.1937 22.7486i 0.383103 0.854944i
$$709$$ 26.4924 0.994944 0.497472 0.867480i $$-0.334262\pi$$
0.497472 + 0.867480i $$0.334262\pi$$
$$710$$ 0 0
$$711$$ 14.1617 + 23.2306i 0.531104 + 0.871217i
$$712$$ 17.0862 + 4.49242i 0.640334 + 0.168361i
$$713$$ −18.2462 −0.683326
$$714$$ 3.47415 2.99596i 0.130017 0.112121i
$$715$$ 0 0
$$716$$ 18.8114 22.5616i 0.703016 0.843165i
$$717$$ 34.7386 9.75379i 1.29734 0.364262i
$$718$$ 1.34700 0.630683i 0.0502696 0.0235369i
$$719$$ −5.84912 −0.218135 −0.109068 0.994034i $$-0.534787\pi$$
−0.109068 + 0.994034i $$0.534787\pi$$
$$720$$ 0 0
$$721$$ 11.6155 0.432585
$$722$$ 0.965435 0.452029i 0.0359298 0.0168228i
$$723$$ 18.9591 5.32326i 0.705096 0.197974i
$$724$$ 5.43845 6.52262i 0.202118 0.242411i
$$725$$ 0 0
$$726$$ −13.4417 + 11.5916i −0.498870 + 0.430204i
$$727$$ −26.5658 −0.985270 −0.492635 0.870236i $$-0.663966\pi$$
−0.492635 + 0.870236i $$0.663966\pi$$
$$728$$ −8.00000 2.10341i −0.296500 0.0779576i
$$729$$ −1.93087 26.9309i −0.0715137 0.997440i
$$730$$ 0 0
$$731$$ 2.92456 0.108169
$$732$$ 7.25716 16.1953i 0.268233 0.598596i
$$733$$ 35.1231i 1.29730i 0.761086 + 0.648651i $$0.224666\pi$$
−0.761086 + 0.648651i $$0.775334\pi$$
$$734$$ 34.0248 15.9309i 1.25588 0.588019i
$$735$$ 0 0
$$736$$ 35.0540 24.9559i 1.29211 0.919885i
$$737$$ 22.2462 0.819450
$$738$$ 25.1880 + 16.6991i 0.927184 + 0.614701i
$$739$$ 18.6638i 0.686559i 0.939233 + 0.343279i $$0.111538\pi$$
−0.939233 + 0.343279i $$0.888462\pi$$
$$740$$ 0 0
$$741$$ 22.2462 6.24621i 0.817235 0.229460i
$$742$$ 5.09271 2.38447i 0.186959 0.0875367i
$$743$$ 12.4041i 0.455062i −0.973771 0.227531i $$-0.926935\pi$$
0.973771 0.227531i $$-0.0730654\pi$$
$$744$$ −11.7496 + 0.195311i −0.430761 + 0.00716046i
$$745$$ 0 0
$$746$$ 0.525853 + 1.12311i 0.0192528 + 0.0411198i
$$747$$ −7.31140 11.9935i −0.267510 0.438820i
$$748$$ −10.9418 + 13.1231i −0.400073 + 0.479828i
$$749$$ 0.876894i 0.0320410i
$$750$$ 0 0
$$751$$ 15.7392i 0.574333i 0.957881 + 0.287166i $$0.0927133\pi$$
−0.957881 + 0.287166i $$0.907287\pi$$
$$752$$ 3.68466 0.673500i 0.134366 0.0245600i
$$753$$ −41.8617 + 11.7538i −1.52553 + 0.428332i
$$754$$ 20.4924 9.59482i 0.746290 0.349423i
$$755$$ 0 0
$$756$$ 1.22470 + 9.65426i 0.0445419 + 0.351122i
$$757$$ 19.1231i 0.695041i 0.937672 + 0.347521i $$0.112976\pi$$
−0.937672 + 0.347521i $$0.887024\pi$$
$$758$$ −15.0540 32.1520i −0.546785 1.16781i
$$759$$ −15.2134 54.1833i −0.552211 1.96673i
$$760$$ 0 0
$$761$$ 51.2311i 1.85712i 0.371177 + 0.928562i $$0.378954\pi$$
−0.371177 + 0.928562i $$0.621046\pi$$
$$762$$ 8.68537 7.48990i 0.314638 0.271330i
$$763$$ 8.54312 0.309282
$$764$$ 9.89012 11.8617i 0.357812 0.429143i
$$765$$ 0 0
$$766$$ 2.80776 + 5.99676i 0.101449 + 0.216672i
$$767$$ 22.4742i 0.811498i
$$768$$ 22.3058 16.4455i 0.804890 0.593424i
$$769$$ 26.9848 0.973098 0.486549 0.873653i $$-0.338255\pi$$
0.486549 + 0.873653i $$0.338255\pi$$
$$770$$ 0 0
$$771$$ −4.15628 + 1.16699i −0.149685 + 0.0420279i
$$772$$ −24.9559 20.8078i −0.898181 0.748888i
$$773$$ 16.2462 0.584336 0.292168 0.956367i $$-0.405623\pi$$
0.292168 + 0.956367i $$0.405623\pi$$
$$774$$ −3.42809 + 5.17077i −0.123220 + 0.185859i
$$775$$ 0 0
$$776$$ −16.4127 4.31534i −0.589183 0.154912i
$$777$$ 1.36932 + 4.87689i 0.0491240 + 0.174958i
$$778$$ −17.2339 36.8078i −0.617865 1.31962i
$$779$$ 30.4268 1.09015
$$780$$ 0 0
$$781$$ −28.4924 −1.01954
$$782$$ −9.12311 19.4849i −0.326242 0.696780i
$$783$$ −19.4849 18.1379i −0.696335 0.648197i
$$784$$ 4.40388 + 24.0932i 0.157282 + 0.860473i
$$785$$ 0