# Properties

 Label 1680.2.bg.t.961.1 Level $1680$ Weight $2$ Character 1680.961 Analytic conductor $13.415$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.bg (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 420) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$-0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1680.961 Dual form 1680.2.bg.t.1201.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} +3.24264 q^{13} +1.00000 q^{15} +(-2.12132 - 3.67423i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(1.00000 - 2.44949i) q^{21} +(-2.12132 + 3.67423i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -1.75736 q^{29} +(-4.74264 - 8.21449i) q^{31} +(2.12132 - 3.67423i) q^{33} +(-2.62132 + 0.358719i) q^{35} +(-1.62132 + 2.80821i) q^{37} +(1.62132 + 2.80821i) q^{39} -4.24264 q^{41} -3.24264 q^{43} +(0.500000 + 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(2.12132 - 3.67423i) q^{51} +(-4.24264 - 7.34847i) q^{53} -4.24264 q^{55} -7.00000 q^{57} +(-5.12132 - 8.87039i) q^{59} +(-2.24264 + 3.88437i) q^{61} +(2.62132 - 0.358719i) q^{63} +(1.62132 - 2.80821i) q^{65} +(-2.62132 - 4.54026i) q^{67} -4.24264 q^{69} +12.7279 q^{71} +(-4.62132 - 8.00436i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-4.24264 + 10.3923i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +10.2426 q^{83} -4.24264 q^{85} +(-0.878680 - 1.52192i) q^{87} +(5.12132 - 8.87039i) q^{89} +(-5.25736 - 6.77962i) q^{91} +(4.74264 - 8.21449i) q^{93} +(3.50000 + 6.06218i) q^{95} -0.485281 q^{97} +4.24264 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9}+O(q^{10})$$ 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9 $$4 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 2 q^{9} - 4 q^{13} + 4 q^{15} - 14 q^{19} + 4 q^{21} - 2 q^{25} - 4 q^{27} - 24 q^{29} - 2 q^{31} - 2 q^{35} + 2 q^{37} - 2 q^{39} + 4 q^{43} + 2 q^{45} - 12 q^{47} + 10 q^{49} - 28 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{63} - 2 q^{65} - 2 q^{67} - 10 q^{73} + 2 q^{75} + 22 q^{79} - 2 q^{81} + 24 q^{83} - 12 q^{87} + 12 q^{89} - 38 q^{91} + 2 q^{93} + 14 q^{95} + 32 q^{97}+O(q^{100})$$ 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 2 * q^9 - 4 * q^13 + 4 * q^15 - 14 * q^19 + 4 * q^21 - 2 * q^25 - 4 * q^27 - 24 * q^29 - 2 * q^31 - 2 * q^35 + 2 * q^37 - 2 * q^39 + 4 * q^43 + 2 * q^45 - 12 * q^47 + 10 * q^49 - 28 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^63 - 2 * q^65 - 2 * q^67 - 10 * q^73 + 2 * q^75 + 22 * q^79 - 2 * q^81 + 24 * q^83 - 12 * q^87 + 12 * q^89 - 38 * q^91 + 2 * q^93 + 14 * q^95 + 32 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0 0
$$7$$ −1.62132 2.09077i −0.612801 0.790237i
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −2.12132 3.67423i −0.639602 1.10782i −0.985520 0.169559i $$-0.945766\pi$$
0.345918 0.938265i $$-0.387568\pi$$
$$12$$ 0 0
$$13$$ 3.24264 0.899347 0.449673 0.893193i $$-0.351540\pi$$
0.449673 + 0.893193i $$0.351540\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 0 0
$$17$$ −2.12132 3.67423i −0.514496 0.891133i −0.999859 0.0168199i $$-0.994646\pi$$
0.485363 0.874313i $$-0.338688\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 1.00000 2.44949i 0.218218 0.534522i
$$22$$ 0 0
$$23$$ −2.12132 + 3.67423i −0.442326 + 0.766131i −0.997862 0.0653618i $$-0.979180\pi$$
0.555536 + 0.831493i $$0.312513\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −1.75736 −0.326333 −0.163167 0.986599i $$-0.552171\pi$$
−0.163167 + 0.986599i $$0.552171\pi$$
$$30$$ 0 0
$$31$$ −4.74264 8.21449i −0.851803 1.47537i −0.879579 0.475753i $$-0.842176\pi$$
0.0277757 0.999614i $$-0.491158\pi$$
$$32$$ 0 0
$$33$$ 2.12132 3.67423i 0.369274 0.639602i
$$34$$ 0 0
$$35$$ −2.62132 + 0.358719i −0.443084 + 0.0606347i
$$36$$ 0 0
$$37$$ −1.62132 + 2.80821i −0.266543 + 0.461667i −0.967967 0.251078i $$-0.919215\pi$$
0.701423 + 0.712745i $$0.252548\pi$$
$$38$$ 0 0
$$39$$ 1.62132 + 2.80821i 0.259619 + 0.449673i
$$40$$ 0 0
$$41$$ −4.24264 −0.662589 −0.331295 0.943527i $$-0.607485\pi$$
−0.331295 + 0.943527i $$0.607485\pi$$
$$42$$ 0 0
$$43$$ −3.24264 −0.494498 −0.247249 0.968952i $$-0.579527\pi$$
−0.247249 + 0.968952i $$0.579527\pi$$
$$44$$ 0 0
$$45$$ 0.500000 + 0.866025i 0.0745356 + 0.129099i
$$46$$ 0 0
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −1.74264 + 6.77962i −0.248949 + 0.968517i
$$50$$ 0 0
$$51$$ 2.12132 3.67423i 0.297044 0.514496i
$$52$$ 0 0
$$53$$ −4.24264 7.34847i −0.582772 1.00939i −0.995149 0.0983769i $$-0.968635\pi$$
0.412378 0.911013i $$-0.364698\pi$$
$$54$$ 0 0
$$55$$ −4.24264 −0.572078
$$56$$ 0 0
$$57$$ −7.00000 −0.927173
$$58$$ 0 0
$$59$$ −5.12132 8.87039i −0.666739 1.15483i −0.978811 0.204767i $$-0.934356\pi$$
0.312072 0.950059i $$-0.398977\pi$$
$$60$$ 0 0
$$61$$ −2.24264 + 3.88437i −0.287141 + 0.497342i −0.973126 0.230273i $$-0.926038\pi$$
0.685985 + 0.727615i $$0.259371\pi$$
$$62$$ 0 0
$$63$$ 2.62132 0.358719i 0.330255 0.0451944i
$$64$$ 0 0
$$65$$ 1.62132 2.80821i 0.201100 0.348315i
$$66$$ 0 0
$$67$$ −2.62132 4.54026i −0.320245 0.554681i 0.660293 0.751008i $$-0.270432\pi$$
−0.980539 + 0.196327i $$0.937099\pi$$
$$68$$ 0 0
$$69$$ −4.24264 −0.510754
$$70$$ 0 0
$$71$$ 12.7279 1.51053 0.755263 0.655422i $$-0.227509\pi$$
0.755263 + 0.655422i $$0.227509\pi$$
$$72$$ 0 0
$$73$$ −4.62132 8.00436i −0.540885 0.936840i −0.998854 0.0478714i $$-0.984756\pi$$
0.457969 0.888968i $$-0.348577\pi$$
$$74$$ 0 0
$$75$$ 0.500000 0.866025i 0.0577350 0.100000i
$$76$$ 0 0
$$77$$ −4.24264 + 10.3923i −0.483494 + 1.18431i
$$78$$ 0 0
$$79$$ 5.50000 9.52628i 0.618798 1.07179i −0.370907 0.928670i $$-0.620953\pi$$
0.989705 0.143120i $$-0.0457135\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 10.2426 1.12428 0.562138 0.827043i $$-0.309979\pi$$
0.562138 + 0.827043i $$0.309979\pi$$
$$84$$ 0 0
$$85$$ −4.24264 −0.460179
$$86$$ 0 0
$$87$$ −0.878680 1.52192i −0.0942043 0.163167i
$$88$$ 0 0
$$89$$ 5.12132 8.87039i 0.542859 0.940259i −0.455879 0.890042i $$-0.650675\pi$$
0.998738 0.0502176i $$-0.0159915\pi$$
$$90$$ 0 0
$$91$$ −5.25736 6.77962i −0.551121 0.710697i
$$92$$ 0 0
$$93$$ 4.74264 8.21449i 0.491789 0.851803i
$$94$$ 0 0
$$95$$ 3.50000 + 6.06218i 0.359092 + 0.621966i
$$96$$ 0 0
$$97$$ −0.485281 −0.0492729 −0.0246364 0.999696i $$-0.507843\pi$$
−0.0246364 + 0.999696i $$0.507843\pi$$
$$98$$ 0 0
$$99$$ 4.24264 0.426401
$$100$$ 0 0
$$101$$ 3.87868 + 6.71807i 0.385943 + 0.668473i 0.991900 0.127025i $$-0.0405428\pi$$
−0.605956 + 0.795498i $$0.707209\pi$$
$$102$$ 0 0
$$103$$ −8.62132 + 14.9326i −0.849484 + 1.47135i 0.0321856 + 0.999482i $$0.489753\pi$$
−0.881670 + 0.471867i $$0.843580\pi$$
$$104$$ 0 0
$$105$$ −1.62132 2.09077i −0.158225 0.204038i
$$106$$ 0 0
$$107$$ 6.36396 11.0227i 0.615227 1.06561i −0.375117 0.926977i $$-0.622398\pi$$
0.990345 0.138628i $$-0.0442691\pi$$
$$108$$ 0 0
$$109$$ 4.74264 + 8.21449i 0.454263 + 0.786806i 0.998645 0.0520310i $$-0.0165695\pi$$
−0.544383 + 0.838837i $$0.683236\pi$$
$$110$$ 0 0
$$111$$ −3.24264 −0.307778
$$112$$ 0 0
$$113$$ −18.0000 −1.69330 −0.846649 0.532152i $$-0.821383\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 0 0
$$115$$ 2.12132 + 3.67423i 0.197814 + 0.342624i
$$116$$ 0 0
$$117$$ −1.62132 + 2.80821i −0.149891 + 0.259619i
$$118$$ 0 0
$$119$$ −4.24264 + 10.3923i −0.388922 + 0.952661i
$$120$$ 0 0
$$121$$ −3.50000 + 6.06218i −0.318182 + 0.551107i
$$122$$ 0 0
$$123$$ −2.12132 3.67423i −0.191273 0.331295i
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.75736 0.244676 0.122338 0.992488i $$-0.460961\pi$$
0.122338 + 0.992488i $$0.460961\pi$$
$$128$$ 0 0
$$129$$ −1.62132 2.80821i −0.142749 0.247249i
$$130$$ 0 0
$$131$$ 7.24264 12.5446i 0.632792 1.09603i −0.354186 0.935175i $$-0.615242\pi$$
0.986978 0.160854i $$-0.0514247\pi$$
$$132$$ 0 0
$$133$$ 18.3492 2.51104i 1.59108 0.217734i
$$134$$ 0 0
$$135$$ −0.500000 + 0.866025i −0.0430331 + 0.0745356i
$$136$$ 0 0
$$137$$ −2.12132 3.67423i −0.181237 0.313911i 0.761065 0.648675i $$-0.224677\pi$$
−0.942302 + 0.334764i $$0.891343\pi$$
$$138$$ 0 0
$$139$$ 15.4853 1.31344 0.656722 0.754133i $$-0.271942\pi$$
0.656722 + 0.754133i $$0.271942\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 0 0
$$143$$ −6.87868 11.9142i −0.575224 0.996317i
$$144$$ 0 0
$$145$$ −0.878680 + 1.52192i −0.0729704 + 0.126388i
$$146$$ 0 0
$$147$$ −6.74264 + 1.88064i −0.556124 + 0.155112i
$$148$$ 0 0
$$149$$ 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i $$-0.669768\pi$$
0.999953 + 0.00974235i $$0.00310113\pi$$
$$150$$ 0 0
$$151$$ 11.2426 + 19.4728i 0.914913 + 1.58468i 0.807028 + 0.590513i $$0.201074\pi$$
0.107885 + 0.994163i $$0.465592\pi$$
$$152$$ 0 0
$$153$$ 4.24264 0.342997
$$154$$ 0 0
$$155$$ −9.48528 −0.761876
$$156$$ 0 0
$$157$$ 3.24264 + 5.61642i 0.258791 + 0.448239i 0.965918 0.258847i $$-0.0833426\pi$$
−0.707127 + 0.707086i $$0.750009\pi$$
$$158$$ 0 0
$$159$$ 4.24264 7.34847i 0.336463 0.582772i
$$160$$ 0 0
$$161$$ 11.1213 1.52192i 0.876483 0.119944i
$$162$$ 0 0
$$163$$ 4.00000 6.92820i 0.313304 0.542659i −0.665771 0.746156i $$-0.731897\pi$$
0.979076 + 0.203497i $$0.0652307\pi$$
$$164$$ 0 0
$$165$$ −2.12132 3.67423i −0.165145 0.286039i
$$166$$ 0 0
$$167$$ −18.7279 −1.44921 −0.724605 0.689164i $$-0.757978\pi$$
−0.724605 + 0.689164i $$0.757978\pi$$
$$168$$ 0 0
$$169$$ −2.48528 −0.191175
$$170$$ 0 0
$$171$$ −3.50000 6.06218i −0.267652 0.463586i
$$172$$ 0 0
$$173$$ 10.2426 17.7408i 0.778734 1.34881i −0.153938 0.988080i $$-0.549196\pi$$
0.932672 0.360726i $$-0.117471\pi$$
$$174$$ 0 0
$$175$$ −1.00000 + 2.44949i −0.0755929 + 0.185164i
$$176$$ 0 0
$$177$$ 5.12132 8.87039i 0.384942 0.666739i
$$178$$ 0 0
$$179$$ −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i $$-0.238654\pi$$
−0.956088 + 0.293079i $$0.905320\pi$$
$$180$$ 0 0
$$181$$ −13.0000 −0.966282 −0.483141 0.875542i $$-0.660504\pi$$
−0.483141 + 0.875542i $$0.660504\pi$$
$$182$$ 0 0
$$183$$ −4.48528 −0.331562
$$184$$ 0 0
$$185$$ 1.62132 + 2.80821i 0.119202 + 0.206464i
$$186$$ 0 0
$$187$$ −9.00000 + 15.5885i −0.658145 + 1.13994i
$$188$$ 0 0
$$189$$ 1.62132 + 2.09077i 0.117934 + 0.152081i
$$190$$ 0 0
$$191$$ 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i $$-0.763683\pi$$
0.953912 + 0.300088i $$0.0970159\pi$$
$$192$$ 0 0
$$193$$ −3.37868 5.85204i −0.243203 0.421239i 0.718422 0.695607i $$-0.244865\pi$$
−0.961625 + 0.274368i $$0.911531\pi$$
$$194$$ 0 0
$$195$$ 3.24264 0.232210
$$196$$ 0 0
$$197$$ −16.2426 −1.15724 −0.578620 0.815597i $$-0.696409\pi$$
−0.578620 + 0.815597i $$0.696409\pi$$
$$198$$ 0 0
$$199$$ 5.24264 + 9.08052i 0.371641 + 0.643701i 0.989818 0.142338i $$-0.0454619\pi$$
−0.618177 + 0.786039i $$0.712129\pi$$
$$200$$ 0 0
$$201$$ 2.62132 4.54026i 0.184894 0.320245i
$$202$$ 0 0
$$203$$ 2.84924 + 3.67423i 0.199978 + 0.257881i
$$204$$ 0 0
$$205$$ −2.12132 + 3.67423i −0.148159 + 0.256620i
$$206$$ 0 0
$$207$$ −2.12132 3.67423i −0.147442 0.255377i
$$208$$ 0 0
$$209$$ 29.6985 2.05429
$$210$$ 0 0
$$211$$ −22.4853 −1.54795 −0.773975 0.633216i $$-0.781735\pi$$
−0.773975 + 0.633216i $$0.781735\pi$$
$$212$$ 0 0
$$213$$ 6.36396 + 11.0227i 0.436051 + 0.755263i
$$214$$ 0 0
$$215$$ −1.62132 + 2.80821i −0.110573 + 0.191518i
$$216$$ 0 0
$$217$$ −9.48528 + 23.2341i −0.643903 + 1.57723i
$$218$$ 0 0
$$219$$ 4.62132 8.00436i 0.312280 0.540885i
$$220$$ 0 0
$$221$$ −6.87868 11.9142i −0.462710 0.801437i
$$222$$ 0 0
$$223$$ 7.51472 0.503223 0.251611 0.967828i $$-0.419040\pi$$
0.251611 + 0.967828i $$0.419040\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ −7.60660 13.1750i −0.504868 0.874457i −0.999984 0.00563010i $$-0.998208\pi$$
0.495116 0.868827i $$-0.335125\pi$$
$$228$$ 0 0
$$229$$ 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i $$-0.759040\pi$$
0.958187 + 0.286143i $$0.0923732\pi$$
$$230$$ 0 0
$$231$$ −11.1213 + 1.52192i −0.731729 + 0.100135i
$$232$$ 0 0
$$233$$ −7.24264 + 12.5446i −0.474481 + 0.821825i −0.999573 0.0292201i $$-0.990698\pi$$
0.525092 + 0.851046i $$0.324031\pi$$
$$234$$ 0 0
$$235$$ 3.00000 + 5.19615i 0.195698 + 0.338960i
$$236$$ 0 0
$$237$$ 11.0000 0.714527
$$238$$ 0 0
$$239$$ −10.9706 −0.709627 −0.354813 0.934937i $$-0.615456\pi$$
−0.354813 + 0.934937i $$0.615456\pi$$
$$240$$ 0 0
$$241$$ 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i $$-0.125544\pi$$
−0.794393 + 0.607404i $$0.792211\pi$$
$$242$$ 0 0
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 5.00000 + 4.89898i 0.319438 + 0.312984i
$$246$$ 0 0
$$247$$ −11.3492 + 19.6575i −0.722135 + 1.25077i
$$248$$ 0 0
$$249$$ 5.12132 + 8.87039i 0.324550 + 0.562138i
$$250$$ 0 0
$$251$$ 18.7279 1.18210 0.591048 0.806636i $$-0.298714\pi$$
0.591048 + 0.806636i $$0.298714\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 0 0
$$255$$ −2.12132 3.67423i −0.132842 0.230089i
$$256$$ 0 0
$$257$$ −5.12132 + 8.87039i −0.319459 + 0.553320i −0.980375 0.197140i $$-0.936835\pi$$
0.660916 + 0.750460i $$0.270168\pi$$
$$258$$ 0 0
$$259$$ 8.50000 1.16320i 0.528164 0.0722776i
$$260$$ 0 0
$$261$$ 0.878680 1.52192i 0.0543889 0.0942043i
$$262$$ 0 0
$$263$$ −4.24264 7.34847i −0.261612 0.453126i 0.705058 0.709150i $$-0.250921\pi$$
−0.966671 + 0.256023i $$0.917588\pi$$
$$264$$ 0 0
$$265$$ −8.48528 −0.521247
$$266$$ 0 0
$$267$$ 10.2426 0.626839
$$268$$ 0 0
$$269$$ 1.24264 + 2.15232i 0.0757651 + 0.131229i 0.901419 0.432948i $$-0.142527\pi$$
−0.825654 + 0.564177i $$0.809193\pi$$
$$270$$ 0 0
$$271$$ −11.7279 + 20.3134i −0.712421 + 1.23395i 0.251525 + 0.967851i $$0.419068\pi$$
−0.963946 + 0.266098i $$0.914266\pi$$
$$272$$ 0 0
$$273$$ 3.24264 7.94282i 0.196254 0.480721i
$$274$$ 0 0
$$275$$ −2.12132 + 3.67423i −0.127920 + 0.221565i
$$276$$ 0 0
$$277$$ −8.86396 15.3528i −0.532584 0.922462i −0.999276 0.0380425i $$-0.987888\pi$$
0.466692 0.884420i $$-0.345446\pi$$
$$278$$ 0 0
$$279$$ 9.48528 0.567869
$$280$$ 0 0
$$281$$ 28.9706 1.72824 0.864119 0.503287i $$-0.167876\pi$$
0.864119 + 0.503287i $$0.167876\pi$$
$$282$$ 0 0
$$283$$ 11.8640 + 20.5490i 0.705239 + 1.22151i 0.966605 + 0.256270i $$0.0824938\pi$$
−0.261366 + 0.965240i $$0.584173\pi$$
$$284$$ 0 0
$$285$$ −3.50000 + 6.06218i −0.207322 + 0.359092i
$$286$$ 0 0
$$287$$ 6.87868 + 8.87039i 0.406036 + 0.523602i
$$288$$ 0 0
$$289$$ −0.500000 + 0.866025i −0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ −0.242641 0.420266i −0.0142238 0.0246364i
$$292$$ 0 0
$$293$$ −4.97056 −0.290383 −0.145192 0.989404i $$-0.546380\pi$$
−0.145192 + 0.989404i $$0.546380\pi$$
$$294$$ 0 0
$$295$$ −10.2426 −0.596350
$$296$$ 0 0
$$297$$ 2.12132 + 3.67423i 0.123091 + 0.213201i
$$298$$ 0 0
$$299$$ −6.87868 + 11.9142i −0.397804 + 0.689017i
$$300$$ 0 0
$$301$$ 5.25736 + 6.77962i 0.303029 + 0.390771i
$$302$$ 0 0
$$303$$ −3.87868 + 6.71807i −0.222824 + 0.385943i
$$304$$ 0 0
$$305$$ 2.24264 + 3.88437i 0.128413 + 0.222418i
$$306$$ 0 0
$$307$$ −3.24264 −0.185067 −0.0925336 0.995710i $$-0.529497\pi$$
−0.0925336 + 0.995710i $$0.529497\pi$$
$$308$$ 0 0
$$309$$ −17.2426 −0.980900
$$310$$ 0 0
$$311$$ 10.6066 + 18.3712i 0.601445 + 1.04173i 0.992602 + 0.121410i $$0.0387415\pi$$
−0.391157 + 0.920324i $$0.627925\pi$$
$$312$$ 0 0
$$313$$ −11.8640 + 20.5490i −0.670591 + 1.16150i 0.307146 + 0.951662i $$0.400626\pi$$
−0.977737 + 0.209835i $$0.932707\pi$$
$$314$$ 0 0
$$315$$ 1.00000 2.44949i 0.0563436 0.138013i
$$316$$ 0 0
$$317$$ 12.3640 21.4150i 0.694429 1.20279i −0.275943 0.961174i $$-0.588990\pi$$
0.970373 0.241613i $$-0.0776764\pi$$
$$318$$ 0 0
$$319$$ 3.72792 + 6.45695i 0.208724 + 0.361520i
$$320$$ 0 0
$$321$$ 12.7279 0.710403
$$322$$ 0 0
$$323$$ 29.6985 1.65247
$$324$$ 0 0
$$325$$ −1.62132 2.80821i −0.0899347 0.155771i
$$326$$ 0 0
$$327$$ −4.74264 + 8.21449i −0.262269 + 0.454263i
$$328$$ 0 0
$$329$$ 15.7279 2.15232i 0.867108 0.118661i
$$330$$ 0 0
$$331$$ 8.50000 14.7224i 0.467202 0.809218i −0.532096 0.846684i $$-0.678595\pi$$
0.999298 + 0.0374662i $$0.0119287\pi$$
$$332$$ 0 0
$$333$$ −1.62132 2.80821i −0.0888478 0.153889i
$$334$$ 0 0
$$335$$ −5.24264 −0.286436
$$336$$ 0 0
$$337$$ −13.7279 −0.747808 −0.373904 0.927467i $$-0.621981\pi$$
−0.373904 + 0.927467i $$0.621981\pi$$
$$338$$ 0 0
$$339$$ −9.00000 15.5885i −0.488813 0.846649i
$$340$$ 0 0
$$341$$ −20.1213 + 34.8511i −1.08963 + 1.88730i
$$342$$ 0 0
$$343$$ 17.0000 7.34847i 0.917914 0.396780i
$$344$$ 0 0
$$345$$ −2.12132 + 3.67423i −0.114208 + 0.197814i
$$346$$ 0 0
$$347$$ −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i $$-0.943860\pi$$
0.340293 0.940319i $$-0.389474\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ 0 0
$$351$$ −3.24264 −0.173079
$$352$$ 0 0
$$353$$ 5.12132 + 8.87039i 0.272580 + 0.472123i 0.969522 0.245005i $$-0.0787896\pi$$
−0.696941 + 0.717128i $$0.745456\pi$$
$$354$$ 0 0
$$355$$ 6.36396 11.0227i 0.337764 0.585024i
$$356$$ 0 0
$$357$$ −11.1213 + 1.52192i −0.588603 + 0.0805484i
$$358$$ 0 0
$$359$$ 0.878680 1.52192i 0.0463749 0.0803237i −0.841906 0.539624i $$-0.818566\pi$$
0.888281 + 0.459300i $$0.151900\pi$$
$$360$$ 0 0
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ 0 0
$$363$$ −7.00000 −0.367405
$$364$$ 0 0
$$365$$ −9.24264 −0.483782
$$366$$ 0 0
$$367$$ 17.8640 + 30.9413i 0.932491 + 1.61512i 0.779048 + 0.626965i $$0.215703\pi$$
0.153443 + 0.988157i $$0.450964\pi$$
$$368$$ 0 0
$$369$$ 2.12132 3.67423i 0.110432 0.191273i
$$370$$ 0 0
$$371$$ −8.48528 + 20.7846i −0.440534 + 1.07908i
$$372$$ 0 0
$$373$$ −8.86396 + 15.3528i −0.458959 + 0.794939i −0.998906 0.0467591i $$-0.985111\pi$$
0.539948 + 0.841699i $$0.318444\pi$$
$$374$$ 0 0
$$375$$ −0.500000 0.866025i −0.0258199 0.0447214i
$$376$$ 0 0
$$377$$ −5.69848 −0.293487
$$378$$ 0 0
$$379$$ 20.4558 1.05075 0.525373 0.850872i $$-0.323926\pi$$
0.525373 + 0.850872i $$0.323926\pi$$
$$380$$ 0 0
$$381$$ 1.37868 + 2.38794i 0.0706319 + 0.122338i
$$382$$ 0 0
$$383$$ 12.7279 22.0454i 0.650366 1.12647i −0.332668 0.943044i $$-0.607949\pi$$
0.983034 0.183424i $$-0.0587180\pi$$
$$384$$ 0 0
$$385$$ 6.87868 + 8.87039i 0.350570 + 0.452077i
$$386$$ 0 0
$$387$$ 1.62132 2.80821i 0.0824163 0.142749i
$$388$$ 0 0
$$389$$ 10.6066 + 18.3712i 0.537776 + 0.931455i 0.999023 + 0.0441839i $$0.0140687\pi$$
−0.461247 + 0.887272i $$0.652598\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ 0 0
$$393$$ 14.4853 0.730686
$$394$$ 0 0
$$395$$ −5.50000 9.52628i −0.276735 0.479319i
$$396$$ 0 0
$$397$$ 4.37868 7.58410i 0.219760 0.380635i −0.734975 0.678094i $$-0.762806\pi$$
0.954734 + 0.297460i $$0.0961394\pi$$
$$398$$ 0 0
$$399$$ 11.3492 + 14.6354i 0.568173 + 0.732686i
$$400$$ 0 0
$$401$$ 1.75736 3.04384i 0.0877583 0.152002i −0.818805 0.574072i $$-0.805363\pi$$
0.906563 + 0.422070i $$0.138696\pi$$
$$402$$ 0 0
$$403$$ −15.3787 26.6367i −0.766067 1.32687i
$$404$$ 0 0
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 13.7574 0.681927
$$408$$ 0 0
$$409$$ −8.50000 14.7224i −0.420298 0.727977i 0.575670 0.817682i $$-0.304741\pi$$
−0.995968 + 0.0897044i $$0.971408\pi$$
$$410$$ 0 0
$$411$$ 2.12132 3.67423i 0.104637 0.181237i
$$412$$ 0 0
$$413$$ −10.2426 + 25.0892i −0.504007 + 1.23456i
$$414$$ 0 0
$$415$$ 5.12132 8.87039i 0.251396 0.435430i
$$416$$ 0 0
$$417$$ 7.74264 + 13.4106i 0.379159 + 0.656722i
$$418$$ 0 0
$$419$$ 14.4853 0.707652 0.353826 0.935311i $$-0.384880\pi$$
0.353826 + 0.935311i $$0.384880\pi$$
$$420$$ 0 0
$$421$$ 31.4853 1.53450 0.767249 0.641349i $$-0.221625\pi$$
0.767249 + 0.641349i $$0.221625\pi$$
$$422$$ 0 0
$$423$$ −3.00000 5.19615i −0.145865 0.252646i
$$424$$ 0 0
$$425$$ −2.12132 + 3.67423i −0.102899 + 0.178227i
$$426$$ 0 0
$$427$$ 11.7574 1.60896i 0.568978 0.0778629i
$$428$$ 0 0
$$429$$ 6.87868 11.9142i 0.332106 0.575224i
$$430$$ 0 0
$$431$$ 9.72792 + 16.8493i 0.468578 + 0.811600i 0.999355 0.0359112i $$-0.0114333\pi$$
−0.530777 + 0.847511i $$0.678100\pi$$
$$432$$ 0 0
$$433$$ 33.2426 1.59754 0.798770 0.601637i $$-0.205485\pi$$
0.798770 + 0.601637i $$0.205485\pi$$
$$434$$ 0 0
$$435$$ −1.75736 −0.0842589
$$436$$ 0 0
$$437$$ −14.8492 25.7196i −0.710336 1.23034i
$$438$$ 0 0
$$439$$ −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i $$-0.910034\pi$$
0.721686 + 0.692220i $$0.243367\pi$$
$$440$$ 0 0
$$441$$ −5.00000 4.89898i −0.238095 0.233285i
$$442$$ 0 0
$$443$$ 10.2426 17.7408i 0.486643 0.842890i −0.513240 0.858245i $$-0.671555\pi$$
0.999882 + 0.0153558i $$0.00488809\pi$$
$$444$$ 0 0
$$445$$ −5.12132 8.87039i −0.242774 0.420497i
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ −6.00000 −0.283158 −0.141579 0.989927i $$-0.545218\pi$$
−0.141579 + 0.989927i $$0.545218\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ 0 0
$$453$$ −11.2426 + 19.4728i −0.528225 + 0.914913i
$$454$$ 0 0
$$455$$ −8.50000 + 1.16320i −0.398486 + 0.0545316i
$$456$$ 0 0
$$457$$ −16.1066 + 27.8975i −0.753435 + 1.30499i 0.192714 + 0.981255i $$0.438271\pi$$
−0.946149 + 0.323733i $$0.895062\pi$$
$$458$$ 0 0
$$459$$ 2.12132 + 3.67423i 0.0990148 + 0.171499i
$$460$$ 0 0
$$461$$ 18.7279 0.872246 0.436123 0.899887i $$-0.356351\pi$$
0.436123 + 0.899887i $$0.356351\pi$$
$$462$$ 0 0
$$463$$ −10.2721 −0.477384 −0.238692 0.971095i $$-0.576719\pi$$
−0.238692 + 0.971095i $$0.576719\pi$$
$$464$$ 0 0
$$465$$ −4.74264 8.21449i −0.219935 0.380938i
$$466$$ 0 0
$$467$$ −5.48528 + 9.50079i −0.253829 + 0.439644i −0.964577 0.263803i $$-0.915023\pi$$
0.710748 + 0.703447i $$0.248357\pi$$
$$468$$ 0 0
$$469$$ −5.24264 + 12.8418i −0.242083 + 0.592979i
$$470$$ 0 0
$$471$$ −3.24264 + 5.61642i −0.149413 + 0.258791i
$$472$$ 0 0
$$473$$ 6.87868 + 11.9142i 0.316282 + 0.547817i
$$474$$ 0 0
$$475$$ 7.00000 0.321182
$$476$$ 0 0
$$477$$ 8.48528 0.388514
$$478$$ 0 0
$$479$$ 6.00000 + 10.3923i 0.274147 + 0.474837i 0.969920 0.243426i $$-0.0782712\pi$$
−0.695773 + 0.718262i $$0.744938\pi$$
$$480$$ 0 0
$$481$$ −5.25736 + 9.10601i −0.239715 + 0.415198i
$$482$$ 0 0
$$483$$ 6.87868 + 8.87039i 0.312991 + 0.403617i
$$484$$ 0 0
$$485$$ −0.242641 + 0.420266i −0.0110177 + 0.0190833i
$$486$$ 0 0
$$487$$ −18.8640 32.6733i −0.854808 1.48057i −0.876823 0.480813i $$-0.840342\pi$$
0.0220157 0.999758i $$-0.492992\pi$$
$$488$$ 0 0
$$489$$ 8.00000 0.361773
$$490$$ 0 0
$$491$$ −15.5147 −0.700169 −0.350085 0.936718i $$-0.613847\pi$$
−0.350085 + 0.936718i $$0.613847\pi$$
$$492$$ 0 0
$$493$$ 3.72792 + 6.45695i 0.167897 + 0.290806i
$$494$$ 0 0
$$495$$ 2.12132 3.67423i 0.0953463 0.165145i
$$496$$ 0 0
$$497$$ −20.6360 26.6112i −0.925653 1.19367i
$$498$$ 0 0
$$499$$ 9.74264 16.8747i 0.436140 0.755417i −0.561247 0.827648i $$-0.689678\pi$$
0.997388 + 0.0722305i $$0.0230117\pi$$
$$500$$ 0 0
$$501$$ −9.36396 16.2189i −0.418351 0.724605i
$$502$$ 0 0
$$503$$ 26.4853 1.18092 0.590460 0.807067i $$-0.298946\pi$$
0.590460 + 0.807067i $$0.298946\pi$$
$$504$$ 0 0
$$505$$ 7.75736 0.345198
$$506$$ 0 0
$$507$$ −1.24264 2.15232i −0.0551876 0.0955877i
$$508$$ 0 0
$$509$$ 9.72792 16.8493i 0.431183 0.746830i −0.565793 0.824547i $$-0.691430\pi$$
0.996975 + 0.0777173i $$0.0247632\pi$$
$$510$$ 0 0
$$511$$ −9.24264 + 22.6398i −0.408870 + 1.00152i
$$512$$ 0 0
$$513$$ 3.50000 6.06218i 0.154529 0.267652i
$$514$$ 0 0
$$515$$ 8.62132 + 14.9326i 0.379901 + 0.658007i
$$516$$ 0 0
$$517$$ 25.4558 1.11955
$$518$$ 0 0
$$519$$ 20.4853 0.899204
$$520$$ 0 0
$$521$$ 6.72792 + 11.6531i 0.294756 + 0.510532i 0.974928 0.222520i $$-0.0714284\pi$$
−0.680172 + 0.733052i $$0.738095\pi$$
$$522$$ 0 0
$$523$$ −2.62132 + 4.54026i −0.114622 + 0.198532i −0.917629 0.397439i $$-0.869899\pi$$
0.803006 + 0.595970i $$0.203232\pi$$
$$524$$ 0 0
$$525$$ −2.62132 + 0.358719i −0.114404 + 0.0156558i
$$526$$ 0 0
$$527$$ −20.1213 + 34.8511i −0.876498 + 1.51814i
$$528$$ 0 0
$$529$$ 2.50000 + 4.33013i 0.108696 + 0.188266i
$$530$$ 0 0
$$531$$ 10.2426 0.444493
$$532$$ 0 0
$$533$$ −13.7574 −0.595897
$$534$$ 0 0
$$535$$ −6.36396 11.0227i −0.275138 0.476553i
$$536$$ 0 0
$$537$$ 3.00000 5.19615i 0.129460 0.224231i
$$538$$ 0 0
$$539$$ 28.6066 7.97887i 1.23217 0.343674i
$$540$$ 0 0
$$541$$ 20.4706 35.4561i 0.880098 1.52437i 0.0288675 0.999583i $$-0.490810\pi$$
0.851231 0.524792i $$-0.175857\pi$$
$$542$$ 0 0
$$543$$ −6.50000 11.2583i −0.278942 0.483141i
$$544$$ 0 0
$$545$$ 9.48528 0.406305
$$546$$ 0 0
$$547$$ −33.4558 −1.43047 −0.715234 0.698885i $$-0.753680\pi$$
−0.715234 + 0.698885i $$0.753680\pi$$
$$548$$ 0 0
$$549$$ −2.24264 3.88437i −0.0957136 0.165781i
$$550$$ 0 0
$$551$$ 6.15076 10.6534i 0.262031 0.453851i
$$552$$ 0 0
$$553$$ −28.8345 + 3.94591i −1.22617 + 0.167797i
$$554$$ 0 0
$$555$$ −1.62132 + 2.80821i −0.0688212 + 0.119202i
$$556$$ 0 0
$$557$$ 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i $$0.0525683\pi$$
−0.350824 + 0.936442i $$0.614098\pi$$
$$558$$ 0 0
$$559$$ −10.5147 −0.444725
$$560$$ 0 0
$$561$$ −18.0000 −0.759961
$$562$$ 0 0
$$563$$ −3.00000 5.19615i −0.126435 0.218992i 0.795858 0.605483i $$-0.207020\pi$$
−0.922293 + 0.386492i $$0.873687\pi$$
$$564$$ 0 0
$$565$$ −9.00000 + 15.5885i −0.378633 + 0.655811i
$$566$$ 0 0
$$567$$ −1.00000 + 2.44949i −0.0419961 + 0.102869i
$$568$$ 0 0
$$569$$ 20.8492 36.1119i 0.874046 1.51389i 0.0162699 0.999868i $$-0.494821\pi$$
0.857776 0.514024i $$-0.171846\pi$$
$$570$$ 0 0
$$571$$ −14.4706 25.0637i −0.605574 1.04889i −0.991960 0.126548i $$-0.959610\pi$$
0.386386 0.922337i $$-0.373723\pi$$
$$572$$ 0 0
$$573$$ 6.00000 0.250654
$$574$$ 0 0
$$575$$ 4.24264 0.176930
$$576$$ 0 0
$$577$$ −6.37868 11.0482i −0.265548 0.459942i 0.702159 0.712020i $$-0.252220\pi$$
−0.967707 + 0.252078i $$0.918886\pi$$
$$578$$ 0 0
$$579$$ 3.37868 5.85204i 0.140413 0.243203i
$$580$$ 0 0
$$581$$ −16.6066 21.4150i −0.688958 0.888444i
$$582$$ 0 0
$$583$$ −18.0000 + 31.1769i −0.745484 + 1.29122i
$$584$$ 0 0
$$585$$ 1.62132 + 2.80821i 0.0670333 + 0.116105i
$$586$$ 0 0
$$587$$ −45.2132 −1.86615 −0.933074 0.359684i $$-0.882885\pi$$
−0.933074 + 0.359684i $$0.882885\pi$$
$$588$$ 0 0
$$589$$ 66.3970 2.73584
$$590$$ 0 0
$$591$$ −8.12132 14.0665i −0.334066 0.578620i
$$592$$ 0 0
$$593$$ −1.60660 + 2.78272i −0.0659752 + 0.114272i −0.897126 0.441774i $$-0.854349\pi$$
0.831151 + 0.556047i $$0.187682\pi$$
$$594$$ 0 0
$$595$$ 6.87868 + 8.87039i 0.281998 + 0.363650i
$$596$$ 0 0
$$597$$ −5.24264 + 9.08052i −0.214567 + 0.371641i
$$598$$ 0 0
$$599$$ −16.2426 28.1331i −0.663656 1.14949i −0.979648 0.200724i $$-0.935670\pi$$
0.315991 0.948762i $$-0.397663\pi$$
$$600$$ 0 0
$$601$$ −3.48528 −0.142168 −0.0710838 0.997470i $$-0.522646\pi$$
−0.0710838 + 0.997470i $$0.522646\pi$$
$$602$$ 0 0
$$603$$ 5.24264 0.213497
$$604$$ 0 0
$$605$$ 3.50000 + 6.06218i 0.142295 + 0.246463i
$$606$$ 0 0
$$607$$ −14.6213 + 25.3249i −0.593461 + 1.02790i 0.400301 + 0.916384i $$0.368906\pi$$
−0.993762 + 0.111521i $$0.964428\pi$$
$$608$$ 0 0
$$609$$ −1.75736 + 4.30463i −0.0712118 + 0.174433i
$$610$$ 0 0
$$611$$ −9.72792 + 16.8493i −0.393550 + 0.681648i
$$612$$ 0 0
$$613$$ 2.72792 + 4.72490i 0.110180 + 0.190837i 0.915843 0.401537i $$-0.131524\pi$$
−0.805663 + 0.592374i $$0.798191\pi$$
$$614$$ 0 0
$$615$$ −4.24264 −0.171080
$$616$$ 0 0
$$617$$ −26.4853 −1.06626 −0.533129 0.846034i $$-0.678984\pi$$
−0.533129 + 0.846034i $$0.678984\pi$$
$$618$$ 0 0
$$619$$ −5.98528 10.3668i −0.240569 0.416677i 0.720308 0.693655i $$-0.244001\pi$$
−0.960876 + 0.276977i $$0.910667\pi$$
$$620$$ 0 0
$$621$$ 2.12132 3.67423i 0.0851257 0.147442i
$$622$$ 0 0
$$623$$ −26.8492 + 3.67423i −1.07569 + 0.147205i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 14.8492 + 25.7196i 0.593022 + 1.02714i
$$628$$ 0 0
$$629$$ 13.7574 0.548542
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ −11.2426 19.4728i −0.446855 0.773975i
$$634$$ 0 0
$$635$$ 1.37868 2.38794i 0.0547112 0.0947626i
$$636$$ 0 0
$$637$$ −5.65076 + 21.9839i −0.223891 + 0.871032i
$$638$$ 0 0
$$639$$ −6.36396 + 11.0227i −0.251754 + 0.436051i
$$640$$ 0 0
$$641$$ −17.1213 29.6550i −0.676251 1.17130i −0.976101 0.217316i $$-0.930270\pi$$
0.299850 0.953986i $$-0.403063\pi$$
$$642$$ 0 0
$$643$$ 19.7279 0.777993 0.388997 0.921239i $$-0.372822\pi$$
0.388997 + 0.921239i $$0.372822\pi$$
$$644$$ 0 0
$$645$$ −3.24264 −0.127679
$$646$$ 0 0
$$647$$ 5.12132 + 8.87039i 0.201340 + 0.348731i 0.948960 0.315395i $$-0.102137\pi$$
−0.747621 + 0.664126i $$0.768804\pi$$
$$648$$ 0 0
$$649$$ −21.7279 + 37.6339i −0.852896 + 1.47726i
$$650$$ 0 0
$$651$$ −24.8640 + 3.40256i −0.974495 + 0.133357i
$$652$$ 0 0
$$653$$ −5.12132 + 8.87039i −0.200413 + 0.347125i −0.948661 0.316293i $$-0.897562\pi$$
0.748249 + 0.663418i $$0.230895\pi$$
$$654$$ 0 0
$$655$$ −7.24264 12.5446i −0.282993 0.490159i
$$656$$ 0 0
$$657$$ 9.24264 0.360590
$$658$$ 0 0
$$659$$ −40.9706 −1.59599 −0.797993 0.602666i $$-0.794105\pi$$
−0.797993 + 0.602666i $$0.794105\pi$$
$$660$$ 0 0
$$661$$ 1.01472 + 1.75754i 0.0394680 + 0.0683605i 0.885085 0.465430i $$-0.154100\pi$$
−0.845617 + 0.533791i $$0.820767\pi$$
$$662$$ 0 0
$$663$$ 6.87868 11.9142i 0.267146 0.462710i
$$664$$ 0 0
$$665$$ 7.00000 17.1464i 0.271448 0.664910i
$$666$$ 0 0
$$667$$ 3.72792 6.45695i 0.144346 0.250014i
$$668$$ 0 0
$$669$$ 3.75736 + 6.50794i 0.145268 + 0.251611i
$$670$$ 0 0
$$671$$ 19.0294 0.734623
$$672$$ 0 0
$$673$$ 29.7279 1.14593 0.572964 0.819581i $$-0.305794\pi$$
0.572964 + 0.819581i $$0.305794\pi$$
$$674$$ 0 0
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ 0 0
$$677$$ −6.36396 + 11.0227i −0.244587 + 0.423637i −0.962015 0.272995i $$-0.911986\pi$$
0.717428 + 0.696632i $$0.245319\pi$$
$$678$$ 0 0
$$679$$ 0.786797 + 1.01461i 0.0301945 + 0.0389372i
$$680$$ 0 0
$$681$$ 7.60660 13.1750i 0.291486 0.504868i
$$682$$ 0 0
$$683$$ 16.6066 + 28.7635i 0.635434 + 1.10060i 0.986423 + 0.164224i $$0.0525121\pi$$
−0.350989 + 0.936380i $$0.614155\pi$$
$$684$$ 0 0
$$685$$ −4.24264 −0.162103
$$686$$ 0 0
$$687$$ 7.00000 0.267067
$$688$$ 0 0
$$689$$ −13.7574 23.8284i −0.524114 0.907791i
$$690$$ 0 0
$$691$$ 13.4706 23.3317i 0.512444 0.887580i −0.487452 0.873150i $$-0.662073\pi$$
0.999896 0.0144296i $$-0.00459325\pi$$
$$692$$ 0 0
$$693$$ −6.87868 8.87039i −0.261299 0.336958i
$$694$$ 0 0
$$695$$ 7.74264 13.4106i 0.293695 0.508695i
$$696$$ 0 0
$$697$$ 9.00000 + 15.5885i 0.340899 + 0.590455i
$$698$$ 0 0
$$699$$ −14.4853 −0.547884
$$700$$ 0 0
$$701$$ 8.78680 0.331873 0.165936 0.986136i $$-0.446935\pi$$
0.165936 + 0.986136i $$0.446935\pi$$
$$702$$ 0 0
$$703$$ −11.3492 19.6575i −0.428045 0.741395i
$$704$$ 0 0
$$705$$ −3.00000 + 5.19615i −0.112987 + 0.195698i
$$706$$ 0 0
$$707$$ 7.75736 19.0016i 0.291746 0.714628i
$$708$$ 0 0
$$709$$ 18.2426 31.5972i 0.685117 1.18666i −0.288283 0.957545i $$-0.593085\pi$$
0.973400 0.229112i $$-0.0735822\pi$$
$$710$$ 0 0
$$711$$ 5.50000 + 9.52628i 0.206266 + 0.357263i
$$712$$ 0 0
$$713$$ 40.2426 1.50710
$$714$$ 0 0
$$715$$ −13.7574 −0.514496
$$716$$ 0 0
$$717$$ −5.48528 9.50079i −0.204852 0.354813i
$$718$$ 0 0
$$719$$ 13.2426 22.9369i 0.493867 0.855403i −0.506108 0.862470i $$-0.668916\pi$$
0.999975 + 0.00706717i $$0.00224957\pi$$
$$720$$ 0 0
$$721$$ 45.1985 6.18527i 1.68328 0.230352i
$$722$$ 0 0
$$723$$ −2.00000 + 3.46410i −0.0743808 + 0.128831i
$$724$$ 0 0
$$725$$ 0.878680 + 1.52192i 0.0326333 + 0.0565226i
$$726$$ 0 0
$$727$$ −0.757359 −0.0280889 −0.0140445 0.999901i $$-0.504471\pi$$
−0.0140445 + 0.999901i $$0.504471\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 6.87868 + 11.9142i 0.254417 + 0.440663i
$$732$$ 0 0
$$733$$ −0.893398 + 1.54741i −0.0329984 + 0.0571549i −0.882053 0.471150i $$-0.843839\pi$$
0.849055 + 0.528305i $$0.177172\pi$$
$$734$$ 0 0
$$735$$ −1.74264 + 6.77962i −0.0642783 + 0.250070i
$$736$$ 0 0
$$737$$ −11.1213 + 19.2627i −0.409659 + 0.709550i
$$738$$ 0 0
$$739$$ −7.74264 13.4106i −0.284818 0.493319i 0.687747 0.725950i $$-0.258600\pi$$
−0.972565 + 0.232632i $$0.925266\pi$$
$$740$$ 0 0
$$741$$ −22.6985 −0.833850
$$742$$ 0 0
$$743$$ −15.2132 −0.558118 −0.279059 0.960274i $$-0.590023\pi$$
−0.279059 + 0.960274i $$0.590023\pi$$
$$744$$ 0 0
$$745$$ −6.00000 10.3923i −0.219823 0.380745i
$$746$$ 0 0
$$747$$ −5.12132 + 8.87039i −0.187379 + 0.324550i
$$748$$ 0 0
$$749$$ −33.3640 + 4.56575i −1.21909 + 0.166829i
$$750$$ 0 0
$$751$$ 22.4706 38.9202i 0.819962 1.42022i −0.0857467 0.996317i $$-0.527328\pi$$
0.905709 0.423900i $$-0.139339\pi$$
$$752$$ 0 0
$$753$$ 9.36396 + 16.2189i 0.341242 + 0.591048i
$$754$$ 0 0
$$755$$ 22.4853 0.818323
$$756$$ 0 0
$$757$$ 9.02944 0.328180 0.164090 0.986445i $$-0.447531\pi$$
0.164090 + 0.986445i $$0.447531\pi$$
$$758$$ 0 0
$$759$$ 9.00000 + 15.5885i 0.326679 + 0.565825i
$$760$$ 0 0
$$761$$ −23.1213 + 40.0473i −0.838147 + 1.45171i 0.0532948 + 0.998579i $$0.483028\pi$$
−0.891442 + 0.453135i $$0.850306\pi$$
$$762$$ 0 0
$$763$$ 9.48528 23.2341i 0.343390 0.841131i
$$764$$ 0 0
$$765$$ 2.12132 3.67423i 0.0766965 0.132842i
$$766$$ 0 0
$$767$$ −16.6066 28.7635i −0.599630 1.03859i
$$768$$ 0 0
$$769$$ 5.00000 0.180305 0.0901523 0.995928i $$-0.471265\pi$$
0.0901523 + 0.995928i $$0.471265\pi$$
$$770$$ 0 0
$$771$$ −10.2426 −0.368880
$$772$$ 0 0
$$773$$ −5.84924 10.1312i −0.210383 0.364393i 0.741452 0.671006i $$-0.234138\pi$$
−0.951834 + 0.306613i $$0.900804\pi$$
$$774$$ 0 0
$$775$$ −4.74264 + 8.21449i −0.170361 + 0.295073i
$$776$$ 0 0
$$777$$ 5.25736 + 6.77962i 0.188607 + 0.243217i
$$778$$ 0 0
$$779$$ 14.8492 25.7196i 0.532029 0.921502i
$$780$$ 0 0
$$781$$ −27.0000 46.7654i −0.966136 1.67340i
$$782$$ 0 0
$$783$$ 1.75736 0.0628029
$$784$$ 0 0
$$785$$ 6.48528 0.231470
$$786$$ 0 0
$$787$$ 14.2426 + 24.6690i 0.507695 + 0.879354i 0.999960 + 0.00890869i $$0.00283576\pi$$
−0.492265 + 0.870445i $$0.663831\pi$$
$$788$$ 0 0
$$789$$ 4.24264 7.34847i 0.151042 0.261612i
$$790$$ 0 0
$$791$$ 29.1838 + 37.6339i 1.03766 + 1.33811i
$$792$$ 0 0
$$793$$ −7.27208 + 12.5956i −0.258239 + 0.447283i
$$794$$ 0 0
$$795$$ −4.24264 7.34847i −0.150471 0.260623i