# Properties

 Label 456.2.q.f.49.1 Level $456$ Weight $2$ Character 456.49 Analytic conductor $3.641$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$456 = 2^{3} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 456.q (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.64117833217$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{18})$$ Defining polynomial: $$x^{6} - x^{3} + 1$$ x^6 - x^3 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 49.1 Root $$-0.766044 - 0.642788i$$ of defining polynomial Character $$\chi$$ $$=$$ 456.49 Dual form 456.2.q.f.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.53209 + 2.65366i) q^{5} -2.06418 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.53209 + 2.65366i) q^{5} -2.06418 q^{7} +(-0.500000 - 0.866025i) q^{9} -6.45336 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.53209 + 2.65366i) q^{15} +(-0.694593 + 1.20307i) q^{17} +(-3.75877 - 2.20718i) q^{19} +(-1.03209 + 1.78763i) q^{21} +(-1.53209 - 2.65366i) q^{23} +(-2.19459 - 3.80115i) q^{25} -1.00000 q^{27} +(1.75877 + 3.04628i) q^{29} +9.45336 q^{31} +(-3.22668 + 5.58878i) q^{33} +(3.16250 - 5.47762i) q^{35} -2.38919 q^{37} -1.00000 q^{39} +(-5.06418 + 8.77141i) q^{41} +(-3.03209 + 5.25173i) q^{43} +3.06418 q^{45} +(3.00000 + 5.19615i) q^{47} -2.73917 q^{49} +(0.694593 + 1.20307i) q^{51} +(5.29086 + 9.16404i) q^{53} +(9.88713 - 17.1250i) q^{55} +(-3.79086 + 2.15160i) q^{57} +(5.59627 - 9.69302i) q^{59} +(-2.56418 - 4.44129i) q^{61} +(1.03209 + 1.78763i) q^{63} +3.06418 q^{65} +(-1.72668 - 2.99070i) q^{67} -3.06418 q^{69} +(-3.36959 + 5.83629i) q^{71} +(4.56418 - 7.90539i) q^{73} -4.38919 q^{75} +13.3209 q^{77} +(0.790859 - 1.36981i) q^{79} +(-0.500000 + 0.866025i) q^{81} -17.6459 q^{83} +(-2.12836 - 3.68642i) q^{85} +3.51754 q^{87} +(-5.22668 - 9.05288i) q^{89} +(1.03209 + 1.78763i) q^{91} +(4.72668 - 8.18685i) q^{93} +(11.6159 - 6.59289i) q^{95} +(-3.36959 + 5.83629i) q^{97} +(3.22668 + 5.58878i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 3 q^{3} + 6 q^{7} - 3 q^{9}+O(q^{10})$$ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 $$6 q + 3 q^{3} + 6 q^{7} - 3 q^{9} - 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} - 6 q^{27} - 12 q^{29} + 30 q^{31} - 6 q^{33} + 24 q^{35} - 6 q^{37} - 6 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{47} + 12 q^{49} + 9 q^{57} + 6 q^{59} + 3 q^{61} - 3 q^{63} + 3 q^{67} - 6 q^{71} + 9 q^{73} - 18 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 24 q^{83} + 24 q^{85} - 24 q^{87} - 18 q^{89} - 3 q^{91} + 15 q^{93} + 48 q^{95} - 6 q^{97} + 6 q^{99}+O(q^{100})$$ 6 * q + 3 * q^3 + 6 * q^7 - 3 * q^9 - 12 * q^11 - 3 * q^13 + 3 * q^21 - 9 * q^25 - 6 * q^27 - 12 * q^29 + 30 * q^31 - 6 * q^33 + 24 * q^35 - 6 * q^37 - 6 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^47 + 12 * q^49 + 9 * q^57 + 6 * q^59 + 3 * q^61 - 3 * q^63 + 3 * q^67 - 6 * q^71 + 9 * q^73 - 18 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 24 * q^83 + 24 * q^85 - 24 * q^87 - 18 * q^89 - 3 * q^91 + 15 * q^93 + 48 * q^95 - 6 * q^97 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$229$$ $$305$$ $$343$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$1$$

## 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
$$5$$ −1.53209 + 2.65366i −0.685171 + 1.18675i 0.288212 + 0.957567i $$0.406939\pi$$
−0.973383 + 0.229184i $$0.926394\pi$$
$$6$$ 0 0
$$7$$ −2.06418 −0.780186 −0.390093 0.920775i $$-0.627557\pi$$
−0.390093 + 0.920775i $$0.627557\pi$$
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −6.45336 −1.94576 −0.972881 0.231306i $$-0.925700\pi$$
−0.972881 + 0.231306i $$0.925700\pi$$
$$12$$ 0 0
$$13$$ −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i $$-0.210951\pi$$
−0.926995 + 0.375073i $$0.877618\pi$$
$$14$$ 0 0
$$15$$ 1.53209 + 2.65366i 0.395584 + 0.685171i
$$16$$ 0 0
$$17$$ −0.694593 + 1.20307i −0.168463 + 0.291787i −0.937880 0.346960i $$-0.887214\pi$$
0.769416 + 0.638748i $$0.220547\pi$$
$$18$$ 0 0
$$19$$ −3.75877 2.20718i −0.862321 0.506362i
$$20$$ 0 0
$$21$$ −1.03209 + 1.78763i −0.225220 + 0.390093i
$$22$$ 0 0
$$23$$ −1.53209 2.65366i −0.319463 0.553325i 0.660913 0.750462i $$-0.270169\pi$$
−0.980376 + 0.197137i $$0.936836\pi$$
$$24$$ 0 0
$$25$$ −2.19459 3.80115i −0.438919 0.760229i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 1.75877 + 3.04628i 0.326595 + 0.565680i 0.981834 0.189742i $$-0.0607652\pi$$
−0.655238 + 0.755422i $$0.727432\pi$$
$$30$$ 0 0
$$31$$ 9.45336 1.69787 0.848937 0.528494i $$-0.177243\pi$$
0.848937 + 0.528494i $$0.177243\pi$$
$$32$$ 0 0
$$33$$ −3.22668 + 5.58878i −0.561693 + 0.972881i
$$34$$ 0 0
$$35$$ 3.16250 5.47762i 0.534561 0.925886i
$$36$$ 0 0
$$37$$ −2.38919 −0.392780 −0.196390 0.980526i $$-0.562922\pi$$
−0.196390 + 0.980526i $$0.562922\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −5.06418 + 8.77141i −0.790892 + 1.36986i 0.134524 + 0.990910i $$0.457050\pi$$
−0.925415 + 0.378954i $$0.876284\pi$$
$$42$$ 0 0
$$43$$ −3.03209 + 5.25173i −0.462389 + 0.800882i −0.999079 0.0428977i $$-0.986341\pi$$
0.536690 + 0.843779i $$0.319674\pi$$
$$44$$ 0 0
$$45$$ 3.06418 0.456781
$$46$$ 0 0
$$47$$ 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i $$-0.0224970\pi$$
−0.559908 + 0.828554i $$0.689164\pi$$
$$48$$ 0 0
$$49$$ −2.73917 −0.391310
$$50$$ 0 0
$$51$$ 0.694593 + 1.20307i 0.0972624 + 0.168463i
$$52$$ 0 0
$$53$$ 5.29086 + 9.16404i 0.726755 + 1.25878i 0.958247 + 0.285941i $$0.0923060\pi$$
−0.231492 + 0.972837i $$0.574361\pi$$
$$54$$ 0 0
$$55$$ 9.88713 17.1250i 1.33318 2.30914i
$$56$$ 0 0
$$57$$ −3.79086 + 2.15160i −0.502112 + 0.284986i
$$58$$ 0 0
$$59$$ 5.59627 9.69302i 0.728572 1.26192i −0.228915 0.973446i $$-0.573518\pi$$
0.957487 0.288477i $$-0.0931489\pi$$
$$60$$ 0 0
$$61$$ −2.56418 4.44129i −0.328309 0.568648i 0.653867 0.756609i $$-0.273146\pi$$
−0.982177 + 0.187961i $$0.939812\pi$$
$$62$$ 0 0
$$63$$ 1.03209 + 1.78763i 0.130031 + 0.225220i
$$64$$ 0 0
$$65$$ 3.06418 0.380064
$$66$$ 0 0
$$67$$ −1.72668 2.99070i −0.210948 0.365372i 0.741064 0.671435i $$-0.234322\pi$$
−0.952011 + 0.306063i $$0.900988\pi$$
$$68$$ 0 0
$$69$$ −3.06418 −0.368884
$$70$$ 0 0
$$71$$ −3.36959 + 5.83629i −0.399896 + 0.692640i −0.993713 0.111960i $$-0.964287\pi$$
0.593817 + 0.804600i $$0.297620\pi$$
$$72$$ 0 0
$$73$$ 4.56418 7.90539i 0.534197 0.925256i −0.465005 0.885308i $$-0.653948\pi$$
0.999202 0.0399477i $$-0.0127191\pi$$
$$74$$ 0 0
$$75$$ −4.38919 −0.506819
$$76$$ 0 0
$$77$$ 13.3209 1.51806
$$78$$ 0 0
$$79$$ 0.790859 1.36981i 0.0889786 0.154116i −0.818101 0.575075i $$-0.804973\pi$$
0.907080 + 0.420959i $$0.138306\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −17.6459 −1.93689 −0.968444 0.249230i $$-0.919823\pi$$
−0.968444 + 0.249230i $$0.919823\pi$$
$$84$$ 0 0
$$85$$ −2.12836 3.68642i −0.230853 0.399848i
$$86$$ 0 0
$$87$$ 3.51754 0.377120
$$88$$ 0 0
$$89$$ −5.22668 9.05288i −0.554027 0.959603i −0.997979 0.0635523i $$-0.979757\pi$$
0.443951 0.896051i $$-0.353576\pi$$
$$90$$ 0 0
$$91$$ 1.03209 + 1.78763i 0.108192 + 0.187395i
$$92$$ 0 0
$$93$$ 4.72668 8.18685i 0.490134 0.848937i
$$94$$ 0 0
$$95$$ 11.6159 6.59289i 1.19176 0.676416i
$$96$$ 0 0
$$97$$ −3.36959 + 5.83629i −0.342130 + 0.592586i −0.984828 0.173534i $$-0.944481\pi$$
0.642698 + 0.766119i $$0.277815\pi$$
$$98$$ 0 0
$$99$$ 3.22668 + 5.58878i 0.324294 + 0.561693i
$$100$$ 0 0
$$101$$ −0.305407 0.528981i −0.0303892 0.0526356i 0.850431 0.526087i $$-0.176341\pi$$
−0.880820 + 0.473451i $$0.843008\pi$$
$$102$$ 0 0
$$103$$ 0.0641778 0.00632362 0.00316181 0.999995i $$-0.498994\pi$$
0.00316181 + 0.999995i $$0.498994\pi$$
$$104$$ 0 0
$$105$$ −3.16250 5.47762i −0.308629 0.534561i
$$106$$ 0 0
$$107$$ 0.610815 0.0590497 0.0295248 0.999564i $$-0.490601\pi$$
0.0295248 + 0.999564i $$0.490601\pi$$
$$108$$ 0 0
$$109$$ −2.30541 + 3.99308i −0.220818 + 0.382468i −0.955057 0.296424i $$-0.904206\pi$$
0.734239 + 0.678891i $$0.237539\pi$$
$$110$$ 0 0
$$111$$ −1.19459 + 2.06910i −0.113386 + 0.196390i
$$112$$ 0 0
$$113$$ 17.4884 1.64517 0.822587 0.568639i $$-0.192530\pi$$
0.822587 + 0.568639i $$0.192530\pi$$
$$114$$ 0 0
$$115$$ 9.38919 0.875546
$$116$$ 0 0
$$117$$ −0.500000 + 0.866025i −0.0462250 + 0.0800641i
$$118$$ 0 0
$$119$$ 1.43376 2.48335i 0.131433 0.227648i
$$120$$ 0 0
$$121$$ 30.6459 2.78599
$$122$$ 0 0
$$123$$ 5.06418 + 8.77141i 0.456622 + 0.790892i
$$124$$ 0 0
$$125$$ −1.87164 −0.167405
$$126$$ 0 0
$$127$$ −7.06418 12.2355i −0.626844 1.08573i −0.988181 0.153291i $$-0.951013\pi$$
0.361337 0.932435i $$-0.382321\pi$$
$$128$$ 0 0
$$129$$ 3.03209 + 5.25173i 0.266961 + 0.462389i
$$130$$ 0 0
$$131$$ −2.75877 + 4.77833i −0.241035 + 0.417485i −0.961009 0.276516i $$-0.910820\pi$$
0.719974 + 0.694001i $$0.244153\pi$$
$$132$$ 0 0
$$133$$ 7.75877 + 4.55601i 0.672771 + 0.395056i
$$134$$ 0 0
$$135$$ 1.53209 2.65366i 0.131861 0.228390i
$$136$$ 0 0
$$137$$ −8.88713 15.3930i −0.759278 1.31511i −0.943219 0.332171i $$-0.892219\pi$$
0.183941 0.982937i $$-0.441115\pi$$
$$138$$ 0 0
$$139$$ 5.48545 + 9.50108i 0.465270 + 0.805871i 0.999214 0.0396488i $$-0.0126239\pi$$
−0.533944 + 0.845520i $$0.679291\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 0 0
$$143$$ 3.22668 + 5.58878i 0.269829 + 0.467357i
$$144$$ 0 0
$$145$$ −10.7784 −0.895095
$$146$$ 0 0
$$147$$ −1.36959 + 2.37219i −0.112961 + 0.195655i
$$148$$ 0 0
$$149$$ −6.53209 + 11.3139i −0.535130 + 0.926872i 0.464027 + 0.885821i $$0.346404\pi$$
−0.999157 + 0.0410508i $$0.986929\pi$$
$$150$$ 0 0
$$151$$ 4.90673 0.399304 0.199652 0.979867i $$-0.436019\pi$$
0.199652 + 0.979867i $$0.436019\pi$$
$$152$$ 0 0
$$153$$ 1.38919 0.112309
$$154$$ 0 0
$$155$$ −14.4834 + 25.0860i −1.16333 + 2.01495i
$$156$$ 0 0
$$157$$ −5.86959 + 10.1664i −0.468444 + 0.811369i −0.999350 0.0360623i $$-0.988519\pi$$
0.530906 + 0.847431i $$0.321852\pi$$
$$158$$ 0 0
$$159$$ 10.5817 0.839185
$$160$$ 0 0
$$161$$ 3.16250 + 5.47762i 0.249240 + 0.431697i
$$162$$ 0 0
$$163$$ −13.4534 −1.05375 −0.526874 0.849943i $$-0.676636\pi$$
−0.526874 + 0.849943i $$0.676636\pi$$
$$164$$ 0 0
$$165$$ −9.88713 17.1250i −0.769712 1.33318i
$$166$$ 0 0
$$167$$ −6.98545 12.0992i −0.540551 0.936261i −0.998872 0.0474747i $$-0.984883\pi$$
0.458322 0.888786i $$-0.348451\pi$$
$$168$$ 0 0
$$169$$ 6.00000 10.3923i 0.461538 0.799408i
$$170$$ 0 0
$$171$$ −0.0320889 + 4.35878i −0.00245390 + 0.333324i
$$172$$ 0 0
$$173$$ −1.75877 + 3.04628i −0.133717 + 0.231604i −0.925107 0.379708i $$-0.876025\pi$$
0.791390 + 0.611312i $$0.209358\pi$$
$$174$$ 0 0
$$175$$ 4.53003 + 7.84624i 0.342438 + 0.593120i
$$176$$ 0 0
$$177$$ −5.59627 9.69302i −0.420641 0.728572i
$$178$$ 0 0
$$179$$ 11.0642 0.826975 0.413488 0.910510i $$-0.364310\pi$$
0.413488 + 0.910510i $$0.364310\pi$$
$$180$$ 0 0
$$181$$ −10.7588 18.6347i −0.799693 1.38511i −0.919816 0.392350i $$-0.871662\pi$$
0.120123 0.992759i $$-0.461671\pi$$
$$182$$ 0 0
$$183$$ −5.12836 −0.379099
$$184$$ 0 0
$$185$$ 3.66044 6.34008i 0.269121 0.466132i
$$186$$ 0 0
$$187$$ 4.48246 7.76385i 0.327790 0.567749i
$$188$$ 0 0
$$189$$ 2.06418 0.150147
$$190$$ 0 0
$$191$$ −15.2317 −1.10213 −0.551065 0.834462i $$-0.685778\pi$$
−0.551065 + 0.834462i $$0.685778\pi$$
$$192$$ 0 0
$$193$$ −3.13041 + 5.42204i −0.225332 + 0.390287i −0.956419 0.291998i $$-0.905680\pi$$
0.731087 + 0.682284i $$0.239013\pi$$
$$194$$ 0 0
$$195$$ 1.53209 2.65366i 0.109715 0.190032i
$$196$$ 0 0
$$197$$ −6.71007 −0.478073 −0.239036 0.971011i $$-0.576832\pi$$
−0.239036 + 0.971011i $$0.576832\pi$$
$$198$$ 0 0
$$199$$ 12.4659 + 21.5915i 0.883681 + 1.53058i 0.847218 + 0.531245i $$0.178276\pi$$
0.0364626 + 0.999335i $$0.488391\pi$$
$$200$$ 0 0
$$201$$ −3.45336 −0.243581
$$202$$ 0 0
$$203$$ −3.63041 6.28806i −0.254805 0.441336i
$$204$$ 0 0
$$205$$ −15.5175 26.8772i −1.08379 1.87718i
$$206$$ 0 0
$$207$$ −1.53209 + 2.65366i −0.106488 + 0.184442i
$$208$$ 0 0
$$209$$ 24.2567 + 14.2437i 1.67787 + 0.985260i
$$210$$ 0 0
$$211$$ −4.48545 + 7.76903i −0.308791 + 0.534842i −0.978098 0.208144i $$-0.933258\pi$$
0.669307 + 0.742986i $$0.266591\pi$$
$$212$$ 0 0
$$213$$ 3.36959 + 5.83629i 0.230880 + 0.399896i
$$214$$ 0 0
$$215$$ −9.29086 16.0922i −0.633631 1.09748i
$$216$$ 0 0
$$217$$ −19.5134 −1.32466
$$218$$ 0 0
$$219$$ −4.56418 7.90539i −0.308419 0.534197i
$$220$$ 0 0
$$221$$ 1.38919 0.0934467
$$222$$ 0 0
$$223$$ −12.5692 + 21.7705i −0.841698 + 1.45786i 0.0467604 + 0.998906i $$0.485110\pi$$
−0.888458 + 0.458957i $$0.848223\pi$$
$$224$$ 0 0
$$225$$ −2.19459 + 3.80115i −0.146306 + 0.253410i
$$226$$ 0 0
$$227$$ −22.8384 −1.51584 −0.757920 0.652348i $$-0.773784\pi$$
−0.757920 + 0.652348i $$0.773784\pi$$
$$228$$ 0 0
$$229$$ −6.03508 −0.398809 −0.199405 0.979917i $$-0.563901\pi$$
−0.199405 + 0.979917i $$0.563901\pi$$
$$230$$ 0 0
$$231$$ 6.66044 11.5362i 0.438225 0.759028i
$$232$$ 0 0
$$233$$ −2.30541 + 3.99308i −0.151032 + 0.261596i −0.931607 0.363467i $$-0.881593\pi$$
0.780575 + 0.625062i $$0.214926\pi$$
$$234$$ 0 0
$$235$$ −18.3851 −1.19931
$$236$$ 0 0
$$237$$ −0.790859 1.36981i −0.0513718 0.0889786i
$$238$$ 0 0
$$239$$ 9.36009 0.605454 0.302727 0.953077i $$-0.402103\pi$$
0.302727 + 0.953077i $$0.402103\pi$$
$$240$$ 0 0
$$241$$ 10.0817 + 17.4620i 0.649421 + 1.12483i 0.983261 + 0.182200i $$0.0583218\pi$$
−0.333841 + 0.942629i $$0.608345\pi$$
$$242$$ 0 0
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 0 0
$$245$$ 4.19665 7.26881i 0.268114 0.464388i
$$246$$ 0 0
$$247$$ −0.0320889 + 4.35878i −0.00204177 + 0.277343i
$$248$$ 0 0
$$249$$ −8.82295 + 15.2818i −0.559132 + 0.968444i
$$250$$ 0 0
$$251$$ −6.06418 10.5035i −0.382768 0.662973i 0.608689 0.793409i $$-0.291696\pi$$
−0.991457 + 0.130436i $$0.958362\pi$$
$$252$$ 0 0
$$253$$ 9.88713 + 17.1250i 0.621598 + 1.07664i
$$254$$ 0 0
$$255$$ −4.25671 −0.266566
$$256$$ 0 0
$$257$$ −15.4192 26.7069i −0.961824 1.66593i −0.717916 0.696130i $$-0.754904\pi$$
−0.243909 0.969798i $$-0.578430\pi$$
$$258$$ 0 0
$$259$$ 4.93170 0.306441
$$260$$ 0 0
$$261$$ 1.75877 3.04628i 0.108865 0.188560i
$$262$$ 0 0
$$263$$ 5.24123 9.07808i 0.323188 0.559778i −0.657956 0.753056i $$-0.728579\pi$$
0.981144 + 0.193278i $$0.0619120\pi$$
$$264$$ 0 0
$$265$$ −32.4243 −1.99181
$$266$$ 0 0
$$267$$ −10.4534 −0.639735
$$268$$ 0 0
$$269$$ 0.901674 1.56175i 0.0549760 0.0952213i −0.837228 0.546854i $$-0.815825\pi$$
0.892204 + 0.451633i $$0.149158\pi$$
$$270$$ 0 0
$$271$$ −14.1284 + 24.4710i −0.858236 + 1.48651i 0.0153732 + 0.999882i $$0.495106\pi$$
−0.873610 + 0.486627i $$0.838227\pi$$
$$272$$ 0 0
$$273$$ 2.06418 0.124930
$$274$$ 0 0
$$275$$ 14.1625 + 24.5302i 0.854031 + 1.47923i
$$276$$ 0 0
$$277$$ 6.48246 0.389493 0.194747 0.980854i $$-0.437612\pi$$
0.194747 + 0.980854i $$0.437612\pi$$
$$278$$ 0 0
$$279$$ −4.72668 8.18685i −0.282979 0.490134i
$$280$$ 0 0
$$281$$ −2.92127 5.05980i −0.174269 0.301842i 0.765639 0.643270i $$-0.222423\pi$$
−0.939908 + 0.341428i $$0.889089\pi$$
$$282$$ 0 0
$$283$$ −8.12836 + 14.0787i −0.483181 + 0.836893i −0.999813 0.0193137i $$-0.993852\pi$$
0.516633 + 0.856207i $$0.327185\pi$$
$$284$$ 0 0
$$285$$ 0.0983261 13.3561i 0.00582433 0.791146i
$$286$$ 0 0
$$287$$ 10.4534 18.1058i 0.617043 1.06875i
$$288$$ 0 0
$$289$$ 7.53508 + 13.0511i 0.443240 + 0.767714i
$$290$$ 0 0
$$291$$ 3.36959 + 5.83629i 0.197529 + 0.342130i
$$292$$ 0 0
$$293$$ 26.2567 1.53393 0.766967 0.641687i $$-0.221765\pi$$
0.766967 + 0.641687i $$0.221765\pi$$
$$294$$ 0 0
$$295$$ 17.1480 + 29.7011i 0.998393 + 1.72927i
$$296$$ 0 0
$$297$$ 6.45336 0.374462
$$298$$ 0 0
$$299$$ −1.53209 + 2.65366i −0.0886030 + 0.153465i
$$300$$ 0 0
$$301$$ 6.25877 10.8405i 0.360750 0.624837i
$$302$$ 0 0
$$303$$ −0.610815 −0.0350904
$$304$$ 0 0
$$305$$ 15.7142 0.899792
$$306$$ 0 0
$$307$$ −7.14796 + 12.3806i −0.407955 + 0.706599i −0.994661 0.103201i $$-0.967091\pi$$
0.586705 + 0.809801i $$0.300425\pi$$
$$308$$ 0 0
$$309$$ 0.0320889 0.0555796i 0.00182547 0.00316181i
$$310$$ 0 0
$$311$$ 22.2276 1.26041 0.630206 0.776428i $$-0.282970\pi$$
0.630206 + 0.776428i $$0.282970\pi$$
$$312$$ 0 0
$$313$$ −1.56624 2.71280i −0.0885290 0.153337i 0.818361 0.574705i $$-0.194883\pi$$
−0.906890 + 0.421368i $$0.861550\pi$$
$$314$$ 0 0
$$315$$ −6.32501 −0.356374
$$316$$ 0 0
$$317$$ 3.04963 + 5.28211i 0.171284 + 0.296673i 0.938869 0.344274i $$-0.111875\pi$$
−0.767585 + 0.640947i $$0.778542\pi$$
$$318$$ 0 0
$$319$$ −11.3500 19.6588i −0.635477 1.10068i
$$320$$ 0 0
$$321$$ 0.305407 0.528981i 0.0170462 0.0295248i
$$322$$ 0 0
$$323$$ 5.26621 2.98897i 0.293020 0.166311i
$$324$$ 0 0
$$325$$ −2.19459 + 3.80115i −0.121734 + 0.210850i
$$326$$ 0 0
$$327$$ 2.30541 + 3.99308i 0.127489 + 0.220818i
$$328$$ 0 0
$$329$$ −6.19253 10.7258i −0.341405 0.591332i
$$330$$ 0 0
$$331$$ −1.93582 −0.106402 −0.0532012 0.998584i $$-0.516942\pi$$
−0.0532012 + 0.998584i $$0.516942\pi$$
$$332$$ 0 0
$$333$$ 1.19459 + 2.06910i 0.0654633 + 0.113386i
$$334$$ 0 0
$$335$$ 10.5817 0.578141
$$336$$ 0 0
$$337$$ 3.58378 6.20729i 0.195221 0.338132i −0.751752 0.659446i $$-0.770791\pi$$
0.946973 + 0.321313i $$0.104124\pi$$
$$338$$ 0 0
$$339$$ 8.74422 15.1454i 0.474921 0.822587i
$$340$$ 0 0
$$341$$ −61.0060 −3.30366
$$342$$ 0 0
$$343$$ 20.1034 1.08548
$$344$$ 0 0
$$345$$ 4.69459 8.13127i 0.252748 0.437773i
$$346$$ 0 0
$$347$$ 4.80840 8.32839i 0.258128 0.447092i −0.707612 0.706601i $$-0.750228\pi$$
0.965741 + 0.259510i $$0.0835609\pi$$
$$348$$ 0 0
$$349$$ 31.5134 1.68687 0.843437 0.537227i $$-0.180528\pi$$
0.843437 + 0.537227i $$0.180528\pi$$
$$350$$ 0 0
$$351$$ 0.500000 + 0.866025i 0.0266880 + 0.0462250i
$$352$$ 0 0
$$353$$ −25.8425 −1.37546 −0.687730 0.725967i $$-0.741393\pi$$
−0.687730 + 0.725967i $$0.741393\pi$$
$$354$$ 0 0
$$355$$ −10.3250 17.8834i −0.547995 0.949154i
$$356$$ 0 0
$$357$$ −1.43376 2.48335i −0.0758828 0.131433i
$$358$$ 0 0
$$359$$ −16.1284 + 27.9351i −0.851222 + 1.47436i 0.0288840 + 0.999583i $$0.490805\pi$$
−0.880106 + 0.474777i $$0.842529\pi$$
$$360$$ 0 0
$$361$$ 9.25671 + 16.5926i 0.487195 + 0.873293i
$$362$$ 0 0
$$363$$ 15.3229 26.5401i 0.804246 1.39300i
$$364$$ 0 0
$$365$$ 13.9855 + 24.2235i 0.732032 + 1.26792i
$$366$$ 0 0
$$367$$ −14.6334 25.3458i −0.763858 1.32304i −0.940848 0.338828i $$-0.889970\pi$$
0.176991 0.984213i $$-0.443364\pi$$
$$368$$ 0 0
$$369$$ 10.1284 0.527261
$$370$$ 0 0
$$371$$ −10.9213 18.9162i −0.567004 0.982080i
$$372$$ 0 0
$$373$$ 8.03920 0.416254 0.208127 0.978102i $$-0.433263\pi$$
0.208127 + 0.978102i $$0.433263\pi$$
$$374$$ 0 0
$$375$$ −0.935822 + 1.62089i −0.0483257 + 0.0837025i
$$376$$ 0 0
$$377$$ 1.75877 3.04628i 0.0905813 0.156891i
$$378$$ 0 0
$$379$$ 8.19253 0.420822 0.210411 0.977613i $$-0.432520\pi$$
0.210411 + 0.977613i $$0.432520\pi$$
$$380$$ 0 0
$$381$$ −14.1284 −0.723818
$$382$$ 0 0
$$383$$ 2.74422 4.75313i 0.140223 0.242874i −0.787357 0.616497i $$-0.788551\pi$$
0.927581 + 0.373623i $$0.121885\pi$$
$$384$$ 0 0
$$385$$ −20.4088 + 35.3491i −1.04013 + 1.80155i
$$386$$ 0 0
$$387$$ 6.06418 0.308259
$$388$$ 0 0
$$389$$ −4.22668 7.32083i −0.214301 0.371181i 0.738755 0.673974i $$-0.235414\pi$$
−0.953056 + 0.302793i $$0.902081\pi$$
$$390$$ 0 0
$$391$$ 4.25671 0.215271
$$392$$ 0 0
$$393$$ 2.75877 + 4.77833i 0.139162 + 0.241035i
$$394$$ 0 0
$$395$$ 2.42333 + 4.19734i 0.121931 + 0.211191i
$$396$$ 0 0
$$397$$ −12.5351 + 21.7114i −0.629118 + 1.08966i 0.358611 + 0.933487i $$0.383250\pi$$
−0.987729 + 0.156177i $$0.950083\pi$$
$$398$$ 0 0
$$399$$ 7.82501 4.44129i 0.391740 0.222342i
$$400$$ 0 0
$$401$$ 12.8726 22.2960i 0.642826 1.11341i −0.341973 0.939710i $$-0.611095\pi$$
0.984799 0.173697i $$-0.0555715\pi$$
$$402$$ 0 0
$$403$$ −4.72668 8.18685i −0.235453 0.407816i
$$404$$ 0 0
$$405$$ −1.53209 2.65366i −0.0761301 0.131861i
$$406$$ 0 0
$$407$$ 15.4183 0.764256
$$408$$ 0 0
$$409$$ 3.21213 + 5.56358i 0.158830 + 0.275101i 0.934447 0.356102i $$-0.115895\pi$$
−0.775617 + 0.631204i $$0.782561\pi$$
$$410$$ 0 0
$$411$$ −17.7743 −0.876739
$$412$$ 0 0
$$413$$ −11.5517 + 20.0081i −0.568421 + 0.984535i
$$414$$ 0 0
$$415$$ 27.0351 46.8261i 1.32710 2.29860i
$$416$$ 0 0
$$417$$ 10.9709 0.537247
$$418$$ 0 0
$$419$$ 16.2668 0.794686 0.397343 0.917670i $$-0.369932\pi$$
0.397343 + 0.917670i $$0.369932\pi$$
$$420$$ 0 0
$$421$$ 14.7297 25.5125i 0.717880 1.24341i −0.243958 0.969786i $$-0.578446\pi$$
0.961838 0.273619i $$-0.0882209\pi$$
$$422$$ 0 0
$$423$$ 3.00000 5.19615i 0.145865 0.252646i
$$424$$ 0 0
$$425$$ 6.09739 0.295767
$$426$$ 0 0
$$427$$ 5.29292 + 9.16760i 0.256142 + 0.443651i
$$428$$ 0 0
$$429$$ 6.45336 0.311571
$$430$$ 0 0
$$431$$ 8.51754 + 14.7528i 0.410276 + 0.710618i 0.994920 0.100672i $$-0.0320992\pi$$
−0.584644 + 0.811290i $$0.698766\pi$$
$$432$$ 0 0
$$433$$ 6.84049 + 11.8481i 0.328733 + 0.569382i 0.982261 0.187520i $$-0.0600451\pi$$
−0.653528 + 0.756903i $$0.726712\pi$$
$$434$$ 0 0
$$435$$ −5.38919 + 9.33434i −0.258392 + 0.447547i
$$436$$ 0 0
$$437$$ −0.0983261 + 13.3561i −0.00470357 + 0.638908i
$$438$$ 0 0
$$439$$ −0.707081 + 1.22470i −0.0337471 + 0.0584518i −0.882406 0.470489i $$-0.844077\pi$$
0.848659 + 0.528941i $$0.177411\pi$$
$$440$$ 0 0
$$441$$ 1.36959 + 2.37219i 0.0652183 + 0.112961i
$$442$$ 0 0
$$443$$ −0.369585 0.640140i −0.0175595 0.0304140i 0.857112 0.515130i $$-0.172256\pi$$
−0.874672 + 0.484716i $$0.838923\pi$$
$$444$$ 0 0
$$445$$ 32.0310 1.51841
$$446$$ 0 0
$$447$$ 6.53209 + 11.3139i 0.308957 + 0.535130i
$$448$$ 0 0
$$449$$ 7.51754 0.354775 0.177387 0.984141i $$-0.443235\pi$$
0.177387 + 0.984141i $$0.443235\pi$$
$$450$$ 0 0
$$451$$ 32.6810 56.6051i 1.53889 2.66543i
$$452$$ 0 0
$$453$$ 2.45336 4.24935i 0.115269 0.199652i
$$454$$ 0 0
$$455$$ −6.32501 −0.296521
$$456$$ 0 0
$$457$$ −15.6810 −0.733525 −0.366763 0.930315i $$-0.619534\pi$$
−0.366763 + 0.930315i $$0.619534\pi$$
$$458$$ 0 0
$$459$$ 0.694593 1.20307i 0.0324208 0.0561545i
$$460$$ 0 0
$$461$$ −10.7442 + 18.6095i −0.500408 + 0.866733i 0.499592 + 0.866261i $$0.333483\pi$$
−1.00000 0.000471567i $$0.999850\pi$$
$$462$$ 0 0
$$463$$ −9.62092 −0.447122 −0.223561 0.974690i $$-0.571768\pi$$
−0.223561 + 0.974690i $$0.571768\pi$$
$$464$$ 0 0
$$465$$ 14.4834 + 25.0860i 0.671651 + 1.16333i
$$466$$ 0 0
$$467$$ 1.87164 0.0866094 0.0433047 0.999062i $$-0.486211\pi$$
0.0433047 + 0.999062i $$0.486211\pi$$
$$468$$ 0 0
$$469$$ 3.56418 + 6.17334i 0.164578 + 0.285058i
$$470$$ 0 0
$$471$$ 5.86959 + 10.1664i 0.270456 + 0.468444i
$$472$$ 0 0
$$473$$ 19.5672 33.8913i 0.899699 1.55833i
$$474$$ 0 0
$$475$$ −0.140844 + 19.1315i −0.00646237 + 0.877813i
$$476$$ 0 0
$$477$$ 5.29086 9.16404i 0.242252 0.419592i
$$478$$ 0 0
$$479$$ −3.36959 5.83629i −0.153960 0.266667i 0.778720 0.627372i $$-0.215869\pi$$
−0.932680 + 0.360705i $$0.882536\pi$$
$$480$$ 0 0
$$481$$ 1.19459 + 2.06910i 0.0544687 + 0.0943426i
$$482$$ 0 0
$$483$$ 6.32501 0.287798
$$484$$ 0 0
$$485$$ −10.3250 17.8834i −0.468834 0.812045i
$$486$$ 0 0
$$487$$ −2.38507 −0.108078 −0.0540388 0.998539i $$-0.517209\pi$$
−0.0540388 + 0.998539i $$0.517209\pi$$
$$488$$ 0 0
$$489$$ −6.72668 + 11.6510i −0.304191 + 0.526874i
$$490$$ 0 0
$$491$$ 5.36959 9.30039i 0.242326 0.419721i −0.719050 0.694958i $$-0.755423\pi$$
0.961376 + 0.275237i $$0.0887563\pi$$
$$492$$ 0 0
$$493$$ −4.88652 −0.220078
$$494$$ 0 0
$$495$$ −19.7743 −0.888787
$$496$$ 0 0
$$497$$ 6.95542 12.0471i 0.311993 0.540388i
$$498$$ 0 0
$$499$$ −14.2733 + 24.7221i −0.638961 + 1.10671i 0.346700 + 0.937976i $$0.387302\pi$$
−0.985661 + 0.168738i $$0.946031\pi$$
$$500$$ 0 0
$$501$$ −13.9709 −0.624174
$$502$$ 0 0
$$503$$ −1.75877 3.04628i −0.0784197 0.135827i 0.824149 0.566374i $$-0.191654\pi$$
−0.902568 + 0.430547i $$0.858321\pi$$
$$504$$ 0 0
$$505$$ 1.87164 0.0832871
$$506$$ 0 0
$$507$$ −6.00000 10.3923i −0.266469 0.461538i
$$508$$ 0 0
$$509$$ −3.61081 6.25411i −0.160047 0.277209i 0.774839 0.632159i $$-0.217831\pi$$
−0.934885 + 0.354950i $$0.884498\pi$$
$$510$$ 0 0
$$511$$ −9.42127 + 16.3181i −0.416773 + 0.721871i
$$512$$ 0 0
$$513$$ 3.75877 + 2.20718i 0.165954 + 0.0974494i
$$514$$ 0 0
$$515$$ −0.0983261 + 0.170306i −0.00433276 + 0.00750457i
$$516$$ 0 0
$$517$$ −19.3601 33.5327i −0.851456 1.47476i
$$518$$ 0 0
$$519$$ 1.75877 + 3.04628i 0.0772015 + 0.133717i
$$520$$ 0 0
$$521$$ 16.8075 0.736348 0.368174 0.929757i $$-0.379983\pi$$
0.368174 + 0.929757i $$0.379983\pi$$
$$522$$ 0 0
$$523$$ 3.88413 + 6.72752i 0.169841 + 0.294174i 0.938364 0.345649i $$-0.112341\pi$$
−0.768523 + 0.639823i $$0.779008\pi$$
$$524$$ 0 0
$$525$$ 9.06006 0.395413
$$526$$ 0 0
$$527$$ −6.56624 + 11.3731i −0.286030 + 0.495418i
$$528$$ 0 0
$$529$$ 6.80541 11.7873i 0.295887 0.512492i
$$530$$ 0 0
$$531$$ −11.1925 −0.485715
$$532$$ 0 0
$$533$$ 10.1284 0.438708
$$534$$ 0 0
$$535$$ −0.935822 + 1.62089i −0.0404591 + 0.0700773i
$$536$$ 0 0
$$537$$ 5.53209 9.58186i 0.238727 0.413488i
$$538$$ 0 0
$$539$$ 17.6769 0.761396
$$540$$ 0 0
$$541$$ 18.1655 + 31.4636i 0.780996 + 1.35272i 0.931362 + 0.364094i $$0.118621\pi$$
−0.150367 + 0.988630i $$0.548045\pi$$
$$542$$ 0 0
$$543$$ −21.5175 −0.923406
$$544$$ 0 0
$$545$$ −7.06418 12.2355i −0.302596 0.524112i
$$546$$ 0 0
$$547$$ −15.8105 27.3845i −0.676006 1.17088i −0.976174 0.216991i $$-0.930376\pi$$
0.300167 0.953887i $$-0.402958\pi$$
$$548$$ 0 0
$$549$$ −2.56418 + 4.44129i −0.109436 + 0.189549i
$$550$$ 0 0
$$551$$ 0.112874 15.3322i 0.00480859 0.653173i
$$552$$ 0 0
$$553$$ −1.63247 + 2.82753i −0.0694199 + 0.120239i
$$554$$ 0 0
$$555$$ −3.66044 6.34008i −0.155377 0.269121i
$$556$$ 0 0
$$557$$ −2.01960 3.49805i −0.0855732 0.148217i 0.820062 0.572275i $$-0.193939\pi$$
−0.905635 + 0.424057i $$0.860605\pi$$
$$558$$ 0 0
$$559$$ 6.06418 0.256487
$$560$$ 0 0
$$561$$ −4.48246 7.76385i −0.189250 0.327790i
$$562$$ 0 0
$$563$$ −8.61081 −0.362903 −0.181451 0.983400i $$-0.558079\pi$$
−0.181451 + 0.983400i $$0.558079\pi$$
$$564$$ 0 0
$$565$$ −26.7939 + 46.4083i −1.12723 + 1.95241i
$$566$$ 0 0
$$567$$ 1.03209 1.78763i 0.0433437 0.0750734i
$$568$$ 0 0
$$569$$ −27.6851 −1.16062 −0.580310 0.814396i $$-0.697069\pi$$
−0.580310 + 0.814396i $$0.697069\pi$$
$$570$$ 0 0
$$571$$ 24.1533 1.01079 0.505393 0.862889i $$-0.331348\pi$$
0.505393 + 0.862889i $$0.331348\pi$$
$$572$$ 0 0
$$573$$ −7.61587 + 13.1911i −0.318157 + 0.551065i
$$574$$ 0 0
$$575$$ −6.72462 + 11.6474i −0.280436 + 0.485730i
$$576$$ 0 0
$$577$$ 28.8675 1.20177 0.600885 0.799335i $$-0.294815\pi$$
0.600885 + 0.799335i $$0.294815\pi$$
$$578$$ 0 0
$$579$$ 3.13041 + 5.42204i 0.130096 + 0.225332i
$$580$$ 0 0
$$581$$ 36.4243 1.51113
$$582$$ 0 0
$$583$$ −34.1438 59.1389i −1.41409 2.44928i
$$584$$ 0 0
$$585$$ −1.53209 2.65366i −0.0633441 0.109715i
$$586$$ 0 0
$$587$$ −5.14290 + 8.90777i −0.212270 + 0.367663i −0.952425 0.304774i $$-0.901419\pi$$
0.740154 + 0.672437i $$0.234752\pi$$
$$588$$ 0 0
$$589$$ −35.5330 20.8653i −1.46411 0.859739i
$$590$$ 0 0
$$591$$ −3.35504 + 5.81109i −0.138008 + 0.239036i
$$592$$ 0 0
$$593$$ 7.96585 + 13.7973i 0.327118 + 0.566586i 0.981939 0.189199i $$-0.0605891\pi$$
−0.654820 + 0.755784i $$0.727256\pi$$
$$594$$ 0 0
$$595$$ 4.39330 + 7.60943i 0.180108 + 0.311956i
$$596$$ 0 0
$$597$$ 24.9317 1.02039
$$598$$ 0 0
$$599$$ 9.03003 + 15.6405i 0.368957 + 0.639052i 0.989403 0.145197i $$-0.0463816\pi$$
−0.620446 + 0.784249i $$0.713048\pi$$
$$600$$ 0 0
$$601$$ −7.86753 −0.320923 −0.160462 0.987042i $$-0.551298\pi$$
−0.160462 + 0.987042i $$0.551298\pi$$
$$602$$ 0 0
$$603$$ −1.72668 + 2.99070i −0.0703159 + 0.121791i
$$604$$ 0 0
$$605$$ −46.9522 + 81.3237i −1.90888 + 3.30628i
$$606$$ 0 0
$$607$$ −17.2668 −0.700838 −0.350419 0.936593i $$-0.613961\pi$$
−0.350419 + 0.936593i $$0.613961\pi$$
$$608$$ 0 0
$$609$$ −7.26083 −0.294224
$$610$$ 0 0
$$611$$ 3.00000 5.19615i 0.121367 0.210214i
$$612$$ 0 0
$$613$$ 13.7939 23.8917i 0.557128 0.964975i −0.440606 0.897701i $$-0.645236\pi$$
0.997735 0.0672742i $$-0.0214302\pi$$
$$614$$ 0 0
$$615$$ −31.0351 −1.25146
$$616$$ 0 0
$$617$$ −8.24628 14.2830i −0.331983 0.575011i 0.650918 0.759148i $$-0.274384\pi$$
−0.982901 + 0.184137i $$0.941051\pi$$
$$618$$ 0 0
$$619$$ 24.4884 0.984274 0.492137 0.870518i $$-0.336216\pi$$
0.492137 + 0.870518i $$0.336216\pi$$
$$620$$ 0 0
$$621$$ 1.53209 + 2.65366i 0.0614806 + 0.106488i
$$622$$ 0 0
$$623$$ 10.7888 + 18.6867i 0.432244 + 0.748669i
$$624$$ 0 0
$$625$$ 13.8405 23.9724i 0.553620 0.958897i
$$626$$ 0 0
$$627$$ 24.4638 13.8851i 0.976990 0.554516i
$$628$$ 0 0
$$629$$ 1.65951 2.87436i 0.0661690 0.114608i
$$630$$ 0 0
$$631$$ −9.83544 17.0355i −0.391543 0.678172i 0.601111 0.799166i $$-0.294725\pi$$
−0.992653 + 0.120994i $$0.961392\pi$$
$$632$$ 0 0
$$633$$ 4.48545 + 7.76903i 0.178281 + 0.308791i
$$634$$ 0 0
$$635$$ 43.2918 1.71798
$$636$$ 0 0
$$637$$ 1.36959 + 2.37219i 0.0542649 + 0.0939896i
$$638$$ 0 0
$$639$$ 6.73917 0.266597
$$640$$ 0 0
$$641$$ −4.06418 + 7.03936i −0.160525 + 0.278038i −0.935057 0.354497i $$-0.884652\pi$$
0.774532 + 0.632535i $$0.217986\pi$$
$$642$$ 0 0
$$643$$ −3.91921 + 6.78828i −0.154559 + 0.267704i −0.932898 0.360140i $$-0.882729\pi$$
0.778340 + 0.627844i $$0.216062\pi$$
$$644$$ 0 0
$$645$$ −18.5817 −0.731654
$$646$$ 0 0
$$647$$ −39.7743 −1.56369 −0.781844 0.623475i $$-0.785720\pi$$
−0.781844 + 0.623475i $$0.785720\pi$$
$$648$$ 0 0
$$649$$ −36.1147 + 62.5526i −1.41763 + 2.45540i
$$650$$ 0 0
$$651$$ −9.75671 + 16.8991i −0.382396 + 0.662329i
$$652$$ 0 0
$$653$$ 8.94593 0.350081 0.175041 0.984561i $$-0.443994\pi$$
0.175041 + 0.984561i $$0.443994\pi$$
$$654$$ 0 0
$$655$$ −8.45336 14.6417i −0.330300 0.572097i
$$656$$ 0 0
$$657$$ −9.12836 −0.356131
$$658$$ 0 0
$$659$$ 5.93676 + 10.2828i 0.231263 + 0.400560i 0.958180 0.286166i $$-0.0923808\pi$$
−0.726917 + 0.686725i $$0.759047\pi$$
$$660$$ 0 0
$$661$$ −21.9067 37.9436i −0.852073 1.47583i −0.879334 0.476205i $$-0.842012\pi$$
0.0272613 0.999628i $$-0.491321\pi$$
$$662$$ 0 0
$$663$$ 0.694593 1.20307i 0.0269757 0.0467234i
$$664$$ 0 0
$$665$$ −23.9772 + 13.6089i −0.929796 + 0.527730i
$$666$$ 0 0
$$667$$ 5.38919 9.33434i 0.208670 0.361427i
$$668$$ 0 0
$$669$$ 12.5692 + 21.7705i 0.485955 + 0.841698i
$$670$$ 0 0
$$671$$ 16.5476 + 28.6612i 0.638812 + 1.10645i
$$672$$ 0 0
$$673$$ −37.6810 −1.45249 −0.726247 0.687433i $$-0.758737\pi$$
−0.726247 + 0.687433i $$0.758737\pi$$
$$674$$ 0 0
$$675$$ 2.19459 + 3.80115i 0.0844699 + 0.146306i
$$676$$ 0 0
$$677$$ −35.1052 −1.34920 −0.674602 0.738182i $$-0.735685\pi$$
−0.674602 + 0.738182i $$0.735685\pi$$
$$678$$ 0 0
$$679$$ 6.95542 12.0471i 0.266925 0.462327i
$$680$$ 0 0
$$681$$ −11.4192 + 19.7787i −0.437585 + 0.757920i
$$682$$ 0 0
$$683$$ 37.6168 1.43937 0.719683 0.694302i $$-0.244287\pi$$
0.719683 + 0.694302i $$0.244287\pi$$
$$684$$ 0 0
$$685$$ 54.4635 2.08094
$$686$$ 0 0
$$687$$ −3.01754 + 5.22653i −0.115126 + 0.199405i
$$688$$ 0 0
$$689$$ 5.29086 9.16404i 0.201566 0.349122i
$$690$$ 0 0
$$691$$ −2.69997 −0.102712 −0.0513558 0.998680i $$-0.516354\pi$$
−0.0513558 + 0.998680i $$0.516354\pi$$
$$692$$ 0 0
$$693$$ −6.66044 11.5362i −0.253009 0.438225i
$$694$$ 0 0
$$695$$ −33.6168 −1.27516
$$696$$ 0 0
$$697$$ −7.03508 12.1851i −0.266473 0.461544i
$$698$$ 0 0
$$699$$ 2.30541 + 3.99308i 0.0871985 + 0.151032i
$$700$$ 0 0
$$701$$ 10.8821 18.8483i 0.411010 0.711891i −0.583990 0.811761i $$-0.698509\pi$$
0.995000 + 0.0998700i $$0.0318427\pi$$
$$702$$ 0 0
$$703$$ 8.98040 + 5.27336i 0.338702 + 0.198889i
$$704$$ 0 0
$$705$$ −9.19253 + 15.9219i −0.346211 + 0.599655i
$$706$$ 0 0
$$707$$ 0.630415 + 1.09191i 0.0237092 + 0.0410655i
$$708$$ 0 0
$$709$$ 13.3033 + 23.0421i 0.499618 + 0.865363i 1.00000 0.000441366i $$-0.000140491\pi$$
−0.500382 + 0.865805i $$0.666807\pi$$
$$710$$ 0 0
$$711$$ −1.58172 −0.0593191
$$712$$ 0 0
$$713$$ −14.4834 25.0860i −0.542407 0.939477i
$$714$$ 0 0
$$715$$ −19.7743 −0.739515
$$716$$ 0 0
$$717$$ 4.68004 8.10608i 0.174779 0.302727i
$$718$$ 0 0
$$719$$ 3.81790 6.61279i 0.142383 0.246615i −0.786010 0.618214i $$-0.787857\pi$$
0.928394 + 0.371598i $$0.121190\pi$$
$$720$$ 0 0
$$721$$ −0.132474 −0.00493360
$$722$$ 0 0
$$723$$ 20.1634 0.749886
$$724$$ 0 0
$$725$$ 7.71957 13.3707i 0.286698 0.496575i
$$726$$ 0 0
$$727$$ −20.3726 + 35.2863i −0.755577 + 1.30870i 0.189510 + 0.981879i $$0.439310\pi$$
−0.945087 + 0.326819i $$0.894023\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −4.21213 7.29563i −0.155791 0.269839i
$$732$$ 0 0
$$733$$ 48.4742 1.79044 0.895218 0.445628i $$-0.147020\pi$$
0.895218 + 0.445628i $$0.147020\pi$$
$$734$$ 0 0
$$735$$ −4.19665 7.26881i −0.154796 0.268114i
$$736$$ 0 0
$$737$$ 11.1429 + 19.3001i 0.410454 + 0.710927i
$$738$$ 0 0
$$739$$ 5.30840 9.19442i 0.195273 0.338222i −0.751717 0.659486i $$-0.770774\pi$$
0.946990 + 0.321263i $$0.104107\pi$$
$$740$$ 0 0
$$741$$ 3.75877 + 2.20718i 0.138082 + 0.0810828i
$$742$$ 0 0
$$743$$ −23.7793 + 41.1870i −0.872378 + 1.51100i −0.0128483 + 0.999917i $$0.504090\pi$$
−0.859530 + 0.511086i $$0.829243\pi$$
$$744$$ 0 0
$$745$$ −20.0155 34.6678i −0.733311 1.27013i
$$746$$ 0 0
$$747$$ 8.82295 + 15.2818i 0.322815 + 0.559132i
$$748$$ 0 0
$$749$$ −1.26083 −0.0460697
$$750$$ 0 0
$$751$$ 7.96791 + 13.8008i 0.290753 + 0.503599i 0.973988 0.226599i $$-0.0727608\pi$$
−0.683235 + 0.730199i $$0.739427\pi$$
$$752$$ 0 0
$$753$$ −12.1284 −0.441982
$$754$$ 0 0
$$755$$ −7.51754 + 13.0208i −0.273591 + 0.473874i
$$756$$ 0 0
$$757$$ 9.17499 15.8916i 0.333471 0.577588i −0.649719 0.760174i $$-0.725113\pi$$
0.983190 + 0.182586i $$0.0584468\pi$$
$$758$$ 0 0
$$759$$ 19.7743 0.717760
$$760$$ 0 0
$$761$$ −36.7802 −1.33328 −0.666641 0.745379i $$-0.732269\pi$$
−0.666641 + 0.745379i $$0.732269\pi$$
$$762$$ 0 0
$$763$$ 4.75877 8.24243i 0.172279 0.298396i
$$764$$ 0 0
$$765$$ −2.12836 + 3.68642i −0.0769509 + 0.133283i
$$766$$ 0 0
$$767$$ −11.1925 −0.404139
$$768$$ 0 0
$$769$$ −21.0175 36.4034i −0.757912 1.31274i −0.943914 0.330193i $$-0.892886\pi$$
0.186002 0.982549i $$-0.440447\pi$$
$$770$$ 0 0
$$771$$ −30.8384 −1.11062
$$772$$ 0 0
$$773$$ −22.9709 39.7868i −0.826206 1.43103i −0.900994 0.433831i $$-0.857161\pi$$
0.0747881 0.997199i $$-0.476172\pi$$
$$774$$ 0 0
$$775$$ −20.7463 35.9336i −0.745228 1.29077i
$$776$$ 0 0
$$777$$ 2.46585 4.27098i 0.0884619 0.153221i
$$778$$ 0 0
$$779$$ 38.3952 21.7922i 1.37565 0.780786i
$$780$$ 0 0
$$781$$ 21.7452 37.6637i 0.778103 1.34771i
$$782$$ 0 0
$$783$$ −1.75877 3.04628i −0.0628533 0.108865i
$$784$$ 0 0
$$785$$ −17.9855 31.1517i −0.641928 1.11185i
$$786$$ 0 0
$$787$$ −17.3250 −0.617570 −0.308785 0.951132i $$-0.599922\pi$$
−0.308785 + 0.951132i $$0.599922\pi$$
$$788$$ 0 0
$$789$$ −5.24123 9.07808i −0.186593 0.323188i
$$790$$ 0 0
$$791$$ −36.0993 −1.28354
$$792$$ 0 0
$$793$$ −2.56418 + 4.44129i −0.0910566 + 0.157715i
$$794$$ 0 0
$$795$$ −16.2121 + 28.0802i −0.574985 + 0.995903i
$$796$$