# Properties

 Label 420.2.q.d.121.2 Level $420$ Weight $2$ Character 420.121 Analytic conductor $3.354$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$420 = 2^{2} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 420.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.35371688489$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 121.2 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 420.121 Dual form 420.2.q.d.361.2

## $q$-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 $$\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$$.

 $$n$$ $$211$$ $$241$$ $$281$$ $$337$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 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 $$0.0542342\pi$$
−0.345918 + 0.938265i $$0.612432\pi$$
$$12$$ 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 $$-0.536593\pi$$
0.917663 0.397360i $$-0.130073\pi$$
$$20$$ 0 0
$$21$$ 1.00000 2.44949i 0.218218 0.534522i
$$22$$ 0 0
$$23$$ 2.12132 3.67423i 0.442326 0.766131i −0.555536 0.831493i $$-0.687487\pi$$
0.997862 + 0.0653618i $$0.0208201\pi$$
$$24$$ 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 $$0.157824\pi$$
−0.0277757 + 0.999614i $$0.508842\pi$$
$$32$$ 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 $$-0.420473\pi$$
0.247249 + 0.968952i $$0.420473\pi$$
$$44$$ 0 0
$$45$$ 0.500000 + 0.866025i 0.0745356 + 0.129099i
$$46$$ 0 0
$$47$$ 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i $$-0.689164\pi$$
0.997503 + 0.0706177i $$0.0224970\pi$$
$$48$$ 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 $$0.0656438\pi$$
−0.312072 + 0.950059i $$0.601023\pi$$
$$60$$ 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 0.980539 0.196327i $$-0.0629013\pi$$
−0.660293 + 0.751008i $$0.729568\pi$$
$$68$$ 0 0
$$69$$ −4.24264 −0.510754
$$70$$ 0 0
$$71$$ −12.7279 −1.51053 −0.755263 0.655422i $$-0.772491\pi$$
−0.755263 + 0.655422i $$0.772491\pi$$
$$72$$ 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 $$0.379047\pi$$
−0.989705 + 0.143120i $$0.954286\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −10.2426 −1.12428 −0.562138 0.827043i $$-0.690021\pi$$
−0.562138 + 0.827043i $$0.690021\pi$$
$$84$$ 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 $$-0.510247\pi$$
0.881670 0.471867i $$-0.156420\pi$$
$$104$$ 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 $$0.377602\pi$$
−0.990345 + 0.138628i $$0.955731\pi$$
$$108$$ 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 $$-0.539039\pi$$
−0.122338 + 0.992488i $$0.539039\pi$$
$$128$$ 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 $$0.384758\pi$$
−0.986978 + 0.160854i $$0.948575\pi$$
$$132$$ 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 $$-0.728058\pi$$
−0.656722 + 0.754133i $$0.728058\pi$$
$$140$$ 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 $$-0.798926\pi$$
−0.107885 0.994163i $$-0.534408\pi$$
$$152$$ 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 −0.979076 0.203497i $$-0.934769\pi$$
0.665771 + 0.746156i $$0.268103\pi$$
$$164$$ 0 0
$$165$$ −2.12132 3.67423i −0.165145 0.286039i
$$166$$ 0 0
$$167$$ 18.7279 1.44921 0.724605 0.689164i $$-0.242022\pi$$
0.724605 + 0.689164i $$0.242022\pi$$
$$168$$ 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 0.956088 0.293079i $$-0.0946798\pi$$
−0.731858 + 0.681457i $$0.761346\pi$$
$$180$$ 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 −0.953912 0.300088i $$-0.902984\pi$$
0.736839 + 0.676068i $$0.236317\pi$$
$$192$$ 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 0.618177 0.786039i $$-0.287871\pi$$
−0.989818 + 0.142338i $$0.954538\pi$$
$$200$$ 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 $$-0.218265\pi$$
0.773975 + 0.633216i $$0.218265\pi$$
$$212$$ 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 $$-0.580960\pi$$
−0.251611 + 0.967828i $$0.580960\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 0 0
$$227$$ 7.60660 + 13.1750i 0.504868 + 0.874457i 0.999984 + 0.00563010i $$0.00179213\pi$$
−0.495116 + 0.868827i $$0.664875\pi$$
$$228$$ 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 $$-0.384544\pi$$
0.354813 + 0.934937i $$0.384544\pi$$
$$240$$ 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 $$-0.701286\pi$$
−0.591048 + 0.806636i $$0.701286\pi$$
$$252$$ 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 0.966671 0.256023i $$-0.0824124\pi$$
−0.705058 + 0.709150i $$0.749079\pi$$
$$264$$ 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 $$-0.580932\pi$$
0.963946 0.266098i $$-0.0857344\pi$$
$$272$$ 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 $$-0.917506\pi$$
0.261366 0.965240i $$-0.415827\pi$$
$$284$$ 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 $$-0.470503\pi$$
0.0925336 + 0.995710i $$0.470503\pi$$
$$308$$ 0 0
$$309$$ −17.2426 −0.980900
$$310$$ 0 0
$$311$$ −10.6066 18.3712i −0.601445 1.04173i −0.992602 0.121410i $$-0.961258\pi$$
0.391157 0.920324i $$-0.372075\pi$$
$$312$$ 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 −0.999298 0.0374662i $$-0.988071\pi$$
0.532096 + 0.846684i $$0.321405\pi$$
$$332$$ 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 $$0.0561403\pi$$
−0.340293 + 0.940319i $$0.610526\pi$$
$$348$$ 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 −0.888281 0.459300i $$-0.848100\pi$$
0.841906 + 0.539624i $$0.181434\pi$$
$$360$$ 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 $$-0.784297\pi$$
−0.153443 0.988157i $$-0.549036\pi$$
$$368$$ 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 $$-0.676074\pi$$
−0.525373 + 0.850872i $$0.676074\pi$$
$$380$$ 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 $$0.392051\pi$$
−0.983034 + 0.183424i $$0.941282\pi$$
$$384$$ 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 $$-0.615120\pi$$
−0.353826 + 0.935311i $$0.615120\pi$$
$$420$$ 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 0.530777 0.847511i $$-0.321900\pi$$
−0.999355 + 0.0359112i $$0.988567\pi$$
$$432$$ 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 −0.721686 0.692220i $$-0.756633\pi$$
0.960323 + 0.278889i $$0.0899661\pi$$
$$440$$ 0 0
$$441$$ −5.00000 4.89898i −0.238095 0.233285i
$$442$$ 0 0
$$443$$ −10.2426 + 17.7408i −0.486643 + 0.842890i −0.999882 0.0153558i $$-0.995112\pi$$
0.513240 + 0.858245i $$0.328445\pi$$
$$444$$ 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 $$-0.423281\pi$$
0.238692 + 0.971095i $$0.423281\pi$$
$$464$$ 0 0
$$465$$ −4.74264 8.21449i −0.219935 0.380938i
$$466$$ 0 0
$$467$$ 5.48528 9.50079i 0.253829 0.439644i −0.710748 0.703447i $$-0.751643\pi$$
0.964577 + 0.263803i $$0.0849768\pi$$
$$468$$ 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 0.695773 0.718262i $$-0.255062\pi$$
−0.969920 + 0.243426i $$0.921729\pi$$
$$480$$ 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 $$0.159658\pi$$
−0.0220157 + 0.999758i $$0.507008\pi$$
$$488$$ 0 0
$$489$$ 8.00000 0.361773
$$490$$ 0 0
$$491$$ 15.5147 0.700169 0.350085 0.936718i $$-0.386153\pi$$
0.350085 + 0.936718i $$0.386153\pi$$
$$492$$ 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 −0.997388 0.0722305i $$-0.976988\pi$$
0.561247 + 0.827648i $$0.310322\pi$$
$$500$$ 0 0
$$501$$ −9.36396 16.2189i −0.418351 0.724605i
$$502$$ 0 0
$$503$$ −26.4853 −1.18092 −0.590460 0.807067i $$-0.701054\pi$$
−0.590460 + 0.807067i $$0.701054\pi$$
$$504$$ 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 −0.803006 0.595970i $$-0.796768\pi$$
0.917629 + 0.397439i $$0.130101\pi$$
$$524$$ 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 $$-0.246320\pi$$
0.715234 + 0.698885i $$0.246320\pi$$
$$548$$ 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 0.922293 0.386492i $$-0.126313\pi$$
−0.795858 + 0.605483i $$0.792980\pi$$
$$564$$ 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 $$0.0403898\pi$$
−0.386386 + 0.922337i $$0.626277\pi$$
$$572$$ 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 $$-0.117115\pi$$
0.933074 + 0.359684i $$0.117115\pi$$
$$588$$ 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 $$0.0643296\pi$$
−0.315991 + 0.948762i $$0.602337\pi$$
$$600$$ 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 $$-0.631094\pi$$
0.993762 0.111521i $$-0.0355722\pi$$
$$608$$ 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 0.960876 0.276977i $$-0.0893327\pi$$
−0.720308 + 0.693655i $$0.755999\pi$$
$$620$$ 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 $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 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 $$-0.627178\pi$$
−0.388997 + 0.921239i $$0.627178\pi$$
$$644$$ 0 0
$$645$$ −3.24264 −0.127679
$$646$$ 0 0
$$647$$ −5.12132 8.87039i −0.201340 0.348731i 0.747621 0.664126i $$-0.231196\pi$$
−0.948960 + 0.315395i $$0.897863\pi$$
$$648$$ 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 $$-0.205895\pi$$
0.797993 + 0.602666i $$0.205895\pi$$
$$660$$ 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 $$-0.947488\pi$$
0.350989 0.936380i $$-0.385845\pi$$
$$684$$ 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 $$0.337927\pi$$
−0.999896 + 0.0144296i $$0.995407\pi$$
$$692$$ 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 −0.999975 0.00706717i $$-0.997750\pi$$
0.506108 + 0.862470i $$0.331084\pi$$
$$720$$ 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 $$-0.495529\pi$$
0.0140445 + 0.999901i $$0.495529\pi$$
$$728$$ 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 0.972565 0.232632i $$-0.0747336\pi$$
−0.687747 + 0.725950i $$0.741400\pi$$
$$740$$ 0 0
$$741$$ −22.6985 −0.833850
$$742$$ 0 0
$$743$$ 15.2132 0.558118 0.279059 0.960274i $$-0.409977\pi$$
0.279059 + 0.960274i $$0.409977\pi$$
$$744$$ 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 $$0.472672\pi$$
−0.905709 + 0.423900i $$0.860661\pi$$
$$752$$ 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 $$-0.997164\pi$$
0.492265 0.870445i $$-0.336169\pi$$
$$788$$ 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