# Properties

 Label 1950.2.i.z.451.1 Level $1950$ Weight $2$ Character 1950.451 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{17})$$ Defining polynomial: $$x^{4} - x^{3} + 5 x^{2} + 4 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 451.1 Root $$-0.780776 - 1.35234i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.451 Dual form 1950.2.i.z.601.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.280776 - 0.486319i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.78078 + 3.08440i) q^{11} +1.00000 q^{12} +(-3.34233 - 1.35234i) q^{13} +0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.56155 - 4.43674i) q^{17} +1.00000 q^{18} +(3.28078 + 5.68247i) q^{19} +0.561553 q^{21} +(-1.78078 - 3.08440i) q^{22} +(-2.34233 + 4.05703i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(-0.280776 + 0.486319i) q^{28} +(3.56155 - 6.16879i) q^{29} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.78078 - 3.08440i) q^{33} +5.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(1.78078 - 3.08440i) q^{37} -6.56155 q^{38} +(2.84233 - 2.21837i) q^{39} +(-2.56155 + 4.43674i) q^{41} +(-0.280776 + 0.486319i) q^{42} +(-2.28078 - 3.95042i) q^{43} +3.56155 q^{44} +(-2.34233 - 4.05703i) q^{46} +4.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.34233 - 5.78908i) q^{49} +5.12311 q^{51} +(0.500000 + 3.57071i) q^{52} -12.2462 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.280776 - 0.486319i) q^{56} -6.56155 q^{57} +(3.56155 + 6.16879i) q^{58} +(-3.12311 - 5.40938i) q^{59} +(-5.34233 - 9.25319i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-0.280776 + 0.486319i) q^{63} +1.00000 q^{64} +3.56155 q^{66} +(4.40388 - 7.62775i) q^{67} +(-2.56155 + 4.43674i) q^{68} +(-2.34233 - 4.05703i) q^{69} +(-4.21922 - 7.30791i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.00000 q^{73} +(1.78078 + 3.08440i) q^{74} +(3.28078 - 5.68247i) q^{76} +2.00000 q^{77} +(0.500000 + 3.57071i) q^{78} +4.80776 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.56155 - 4.43674i) q^{82} +2.43845 q^{83} +(-0.280776 - 0.486319i) q^{84} +4.56155 q^{86} +(3.56155 + 6.16879i) q^{87} +(-1.78078 + 3.08440i) q^{88} +(3.12311 - 5.40938i) q^{89} +(0.280776 + 2.00514i) q^{91} +4.68466 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(-8.90388 - 15.4220i) q^{97} +(3.34233 + 5.78908i) q^{98} +3.56155 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 3 q^{7} + 4 q^{8} - 2 q^{9} - 3 q^{11} + 4 q^{12} - q^{13} - 6 q^{14} - 2 q^{16} - 2 q^{17} + 4 q^{18} + 9 q^{19} - 6 q^{21} - 3 q^{22} + 3 q^{23} - 2 q^{24} - q^{26} + 4 q^{27} + 3 q^{28} + 6 q^{29} + 16 q^{31} - 2 q^{32} - 3 q^{33} + 4 q^{34} - 2 q^{36} + 3 q^{37} - 18 q^{38} - q^{39} - 2 q^{41} + 3 q^{42} - 5 q^{43} + 6 q^{44} + 3 q^{46} + 16 q^{47} - 2 q^{48} + q^{49} + 4 q^{51} + 2 q^{52} - 16 q^{53} - 2 q^{54} + 3 q^{56} - 18 q^{57} + 6 q^{58} + 4 q^{59} - 9 q^{61} - 8 q^{62} + 3 q^{63} + 4 q^{64} + 6 q^{66} - 3 q^{67} - 2 q^{68} + 3 q^{69} - 21 q^{71} - 2 q^{72} + 36 q^{73} + 3 q^{74} + 9 q^{76} + 8 q^{77} + 2 q^{78} - 22 q^{79} - 2 q^{81} - 2 q^{82} + 18 q^{83} + 3 q^{84} + 10 q^{86} + 6 q^{87} - 3 q^{88} - 4 q^{89} - 3 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} + 4 q^{96} - 15 q^{97} + q^{98} + 6 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ −0.280776 0.486319i −0.106124 0.183811i 0.808073 0.589082i $$-0.200511\pi$$
−0.914197 + 0.405271i $$0.867177\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −1.78078 + 3.08440i −0.536924 + 0.929980i 0.462143 + 0.886805i $$0.347081\pi$$
−0.999068 + 0.0431749i $$0.986253\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −3.34233 1.35234i −0.926995 0.375073i
$$14$$ 0.561553 0.150081
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.56155 4.43674i −0.621268 1.07607i −0.989250 0.146235i $$-0.953285\pi$$
0.367982 0.929833i $$-0.380049\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 3.28078 + 5.68247i 0.752662 + 1.30365i 0.946528 + 0.322620i $$0.104564\pi$$
−0.193867 + 0.981028i $$0.562103\pi$$
$$20$$ 0 0
$$21$$ 0.561553 0.122541
$$22$$ −1.78078 3.08440i −0.379663 0.657595i
$$23$$ −2.34233 + 4.05703i −0.488409 + 0.845950i −0.999911 0.0133324i $$-0.995756\pi$$
0.511502 + 0.859282i $$0.329089\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ 2.84233 2.21837i 0.557427 0.435058i
$$27$$ 1.00000 0.192450
$$28$$ −0.280776 + 0.486319i −0.0530618 + 0.0919057i
$$29$$ 3.56155 6.16879i 0.661364 1.14552i −0.318894 0.947790i $$-0.603311\pi$$
0.980257 0.197725i $$-0.0633554\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ −1.78078 3.08440i −0.309993 0.536924i
$$34$$ 5.12311 0.878605
$$35$$ 0 0
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ 1.78078 3.08440i 0.292758 0.507071i −0.681703 0.731629i $$-0.738760\pi$$
0.974461 + 0.224558i $$0.0720937\pi$$
$$38$$ −6.56155 −1.06442
$$39$$ 2.84233 2.21837i 0.455137 0.355223i
$$40$$ 0 0
$$41$$ −2.56155 + 4.43674i −0.400047 + 0.692902i −0.993731 0.111796i $$-0.964340\pi$$
0.593684 + 0.804698i $$0.297673\pi$$
$$42$$ −0.280776 + 0.486319i −0.0433247 + 0.0750407i
$$43$$ −2.28078 3.95042i −0.347815 0.602433i 0.638046 0.769998i $$-0.279743\pi$$
−0.985861 + 0.167565i $$0.946410\pi$$
$$44$$ 3.56155 0.536924
$$45$$ 0 0
$$46$$ −2.34233 4.05703i −0.345358 0.598177i
$$47$$ 4.00000 0.583460 0.291730 0.956501i $$-0.405769\pi$$
0.291730 + 0.956501i $$0.405769\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ 3.34233 5.78908i 0.477476 0.827012i
$$50$$ 0 0
$$51$$ 5.12311 0.717378
$$52$$ 0.500000 + 3.57071i 0.0693375 + 0.495169i
$$53$$ −12.2462 −1.68215 −0.841073 0.540921i $$-0.818076\pi$$
−0.841073 + 0.540921i $$0.818076\pi$$
$$54$$ −0.500000 + 0.866025i −0.0680414 + 0.117851i
$$55$$ 0 0
$$56$$ −0.280776 0.486319i −0.0375203 0.0649871i
$$57$$ −6.56155 −0.869099
$$58$$ 3.56155 + 6.16879i 0.467655 + 0.810002i
$$59$$ −3.12311 5.40938i −0.406594 0.704241i 0.587912 0.808925i $$-0.299950\pi$$
−0.994506 + 0.104684i $$0.966617\pi$$
$$60$$ 0 0
$$61$$ −5.34233 9.25319i −0.684015 1.18475i −0.973745 0.227641i $$-0.926899\pi$$
0.289730 0.957108i $$-0.406434\pi$$
$$62$$ −2.00000 + 3.46410i −0.254000 + 0.439941i
$$63$$ −0.280776 + 0.486319i −0.0353745 + 0.0612704i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 3.56155 0.438397
$$67$$ 4.40388 7.62775i 0.538020 0.931878i −0.460991 0.887405i $$-0.652506\pi$$
0.999011 0.0444727i $$-0.0141608\pi$$
$$68$$ −2.56155 + 4.43674i −0.310634 + 0.538034i
$$69$$ −2.34233 4.05703i −0.281983 0.488409i
$$70$$ 0 0
$$71$$ −4.21922 7.30791i −0.500730 0.867289i −1.00000 0.000842810i $$-0.999732\pi$$
0.499270 0.866447i $$-0.333602\pi$$
$$72$$ −0.500000 0.866025i −0.0589256 0.102062i
$$73$$ 9.00000 1.05337 0.526685 0.850060i $$-0.323435\pi$$
0.526685 + 0.850060i $$0.323435\pi$$
$$74$$ 1.78078 + 3.08440i 0.207011 + 0.358554i
$$75$$ 0 0
$$76$$ 3.28078 5.68247i 0.376331 0.651824i
$$77$$ 2.00000 0.227921
$$78$$ 0.500000 + 3.57071i 0.0566139 + 0.404304i
$$79$$ 4.80776 0.540916 0.270458 0.962732i $$-0.412825\pi$$
0.270458 + 0.962732i $$0.412825\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −2.56155 4.43674i −0.282876 0.489956i
$$83$$ 2.43845 0.267654 0.133827 0.991005i $$-0.457273\pi$$
0.133827 + 0.991005i $$0.457273\pi$$
$$84$$ −0.280776 0.486319i −0.0306352 0.0530618i
$$85$$ 0 0
$$86$$ 4.56155 0.491885
$$87$$ 3.56155 + 6.16879i 0.381839 + 0.661364i
$$88$$ −1.78078 + 3.08440i −0.189831 + 0.328798i
$$89$$ 3.12311 5.40938i 0.331049 0.573393i −0.651669 0.758503i $$-0.725931\pi$$
0.982718 + 0.185110i $$0.0592643\pi$$
$$90$$ 0 0
$$91$$ 0.280776 + 2.00514i 0.0294334 + 0.210196i
$$92$$ 4.68466 0.488409
$$93$$ −2.00000 + 3.46410i −0.207390 + 0.359211i
$$94$$ −2.00000 + 3.46410i −0.206284 + 0.357295i
$$95$$ 0 0
$$96$$ 1.00000 0.102062
$$97$$ −8.90388 15.4220i −0.904052 1.56586i −0.822184 0.569221i $$-0.807245\pi$$
−0.0818678 0.996643i $$-0.526089\pi$$
$$98$$ 3.34233 + 5.78908i 0.337626 + 0.584786i
$$99$$ 3.56155 0.357950
$$100$$ 0 0
$$101$$ −5.12311 + 8.87348i −0.509768 + 0.882944i 0.490168 + 0.871628i $$0.336935\pi$$
−0.999936 + 0.0113162i $$0.996398\pi$$
$$102$$ −2.56155 + 4.43674i −0.253632 + 0.439303i
$$103$$ −8.56155 −0.843595 −0.421797 0.906690i $$-0.638601\pi$$
−0.421797 + 0.906690i $$0.638601\pi$$
$$104$$ −3.34233 1.35234i −0.327742 0.132608i
$$105$$ 0 0
$$106$$ 6.12311 10.6055i 0.594729 1.03010i
$$107$$ 9.68466 16.7743i 0.936251 1.62163i 0.163864 0.986483i $$-0.447604\pi$$
0.772387 0.635152i $$-0.219062\pi$$
$$108$$ −0.500000 0.866025i −0.0481125 0.0833333i
$$109$$ 17.8078 1.70567 0.852837 0.522177i $$-0.174880\pi$$
0.852837 + 0.522177i $$0.174880\pi$$
$$110$$ 0 0
$$111$$ 1.78078 + 3.08440i 0.169024 + 0.292758i
$$112$$ 0.561553 0.0530618
$$113$$ −2.00000 3.46410i −0.188144 0.325875i 0.756487 0.654008i $$-0.226914\pi$$
−0.944632 + 0.328133i $$0.893581\pi$$
$$114$$ 3.28078 5.68247i 0.307273 0.532212i
$$115$$ 0 0
$$116$$ −7.12311 −0.661364
$$117$$ 0.500000 + 3.57071i 0.0462250 + 0.330113i
$$118$$ 6.24621 0.575010
$$119$$ −1.43845 + 2.49146i −0.131862 + 0.228392i
$$120$$ 0 0
$$121$$ −0.842329 1.45896i −0.0765754 0.132632i
$$122$$ 10.6847 0.967344
$$123$$ −2.56155 4.43674i −0.230967 0.400047i
$$124$$ −2.00000 3.46410i −0.179605 0.311086i
$$125$$ 0 0
$$126$$ −0.280776 0.486319i −0.0250136 0.0433247i
$$127$$ −0.596118 + 1.03251i −0.0528969 + 0.0916201i −0.891261 0.453490i $$-0.850179\pi$$
0.838364 + 0.545110i $$0.183512\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 4.56155 0.401622
$$130$$ 0 0
$$131$$ 9.12311 0.797089 0.398545 0.917149i $$-0.369515\pi$$
0.398545 + 0.917149i $$0.369515\pi$$
$$132$$ −1.78078 + 3.08440i −0.154997 + 0.268462i
$$133$$ 1.84233 3.19101i 0.159750 0.276695i
$$134$$ 4.40388 + 7.62775i 0.380437 + 0.658937i
$$135$$ 0 0
$$136$$ −2.56155 4.43674i −0.219651 0.380447i
$$137$$ 8.24621 + 14.2829i 0.704521 + 1.22027i 0.966864 + 0.255292i $$0.0821716\pi$$
−0.262343 + 0.964975i $$0.584495\pi$$
$$138$$ 4.68466 0.398785
$$139$$ −8.71922 15.1021i −0.739555 1.28095i −0.952696 0.303925i $$-0.901703\pi$$
0.213141 0.977021i $$-0.431631\pi$$
$$140$$ 0 0
$$141$$ −2.00000 + 3.46410i −0.168430 + 0.291730i
$$142$$ 8.43845 0.708139
$$143$$ 10.1231 7.90084i 0.846537 0.660702i
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ −4.50000 + 7.79423i −0.372423 + 0.645055i
$$147$$ 3.34233 + 5.78908i 0.275671 + 0.477476i
$$148$$ −3.56155 −0.292758
$$149$$ −3.12311 5.40938i −0.255855 0.443153i 0.709273 0.704934i $$-0.249024\pi$$
−0.965127 + 0.261781i $$0.915690\pi$$
$$150$$ 0 0
$$151$$ −4.31534 −0.351178 −0.175589 0.984464i $$-0.556183\pi$$
−0.175589 + 0.984464i $$0.556183\pi$$
$$152$$ 3.28078 + 5.68247i 0.266106 + 0.460909i
$$153$$ −2.56155 + 4.43674i −0.207089 + 0.358689i
$$154$$ −1.00000 + 1.73205i −0.0805823 + 0.139573i
$$155$$ 0 0
$$156$$ −3.34233 1.35234i −0.267601 0.108274i
$$157$$ 0.753789 0.0601589 0.0300794 0.999548i $$-0.490424\pi$$
0.0300794 + 0.999548i $$0.490424\pi$$
$$158$$ −2.40388 + 4.16365i −0.191243 + 0.331242i
$$159$$ 6.12311 10.6055i 0.485594 0.841073i
$$160$$ 0 0
$$161$$ 2.63068 0.207327
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ −8.24621 14.2829i −0.645893 1.11872i −0.984094 0.177646i $$-0.943152\pi$$
0.338201 0.941074i $$-0.390182\pi$$
$$164$$ 5.12311 0.400047
$$165$$ 0 0
$$166$$ −1.21922 + 2.11176i −0.0946301 + 0.163904i
$$167$$ −5.65767 + 9.79937i −0.437804 + 0.758298i −0.997520 0.0703862i $$-0.977577\pi$$
0.559716 + 0.828684i $$0.310910\pi$$
$$168$$ 0.561553 0.0433247
$$169$$ 9.34233 + 9.03996i 0.718641 + 0.695382i
$$170$$ 0 0
$$171$$ 3.28078 5.68247i 0.250887 0.434549i
$$172$$ −2.28078 + 3.95042i −0.173908 + 0.301217i
$$173$$ 8.56155 + 14.8290i 0.650923 + 1.12743i 0.982899 + 0.184144i $$0.0589512\pi$$
−0.331977 + 0.943288i $$0.607715\pi$$
$$174$$ −7.12311 −0.540001
$$175$$ 0 0
$$176$$ −1.78078 3.08440i −0.134231 0.232495i
$$177$$ 6.24621 0.469494
$$178$$ 3.12311 + 5.40938i 0.234087 + 0.405450i
$$179$$ 1.65767 2.87117i 0.123900 0.214601i −0.797402 0.603448i $$-0.793793\pi$$
0.921302 + 0.388847i $$0.127126\pi$$
$$180$$ 0 0
$$181$$ 17.4924 1.30020 0.650101 0.759848i $$-0.274727\pi$$
0.650101 + 0.759848i $$0.274727\pi$$
$$182$$ −1.87689 0.759413i −0.139125 0.0562914i
$$183$$ 10.6847 0.789833
$$184$$ −2.34233 + 4.05703i −0.172679 + 0.299088i
$$185$$ 0 0
$$186$$ −2.00000 3.46410i −0.146647 0.254000i
$$187$$ 18.2462 1.33430
$$188$$ −2.00000 3.46410i −0.145865 0.252646i
$$189$$ −0.280776 0.486319i −0.0204235 0.0353745i
$$190$$ 0 0
$$191$$ 6.46543 + 11.1985i 0.467822 + 0.810292i 0.999324 0.0367651i $$-0.0117053\pi$$
−0.531501 + 0.847057i $$0.678372\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −1.50000 + 2.59808i −0.107972 + 0.187014i −0.914949 0.403570i $$-0.867769\pi$$
0.806976 + 0.590584i $$0.201102\pi$$
$$194$$ 17.8078 1.27852
$$195$$ 0 0
$$196$$ −6.68466 −0.477476
$$197$$ 1.56155 2.70469i 0.111256 0.192701i −0.805021 0.593246i $$-0.797846\pi$$
0.916277 + 0.400545i $$0.131179\pi$$
$$198$$ −1.78078 + 3.08440i −0.126554 + 0.219198i
$$199$$ 4.28078 + 7.41452i 0.303456 + 0.525602i 0.976916 0.213622i $$-0.0685261\pi$$
−0.673460 + 0.739223i $$0.735193\pi$$
$$200$$ 0 0
$$201$$ 4.40388 + 7.62775i 0.310626 + 0.538020i
$$202$$ −5.12311 8.87348i −0.360460 0.624336i
$$203$$ −4.00000 −0.280745
$$204$$ −2.56155 4.43674i −0.179345 0.310634i
$$205$$ 0 0
$$206$$ 4.28078 7.41452i 0.298256 0.516594i
$$207$$ 4.68466 0.325606
$$208$$ 2.84233 2.21837i 0.197080 0.153816i
$$209$$ −23.3693 −1.61649
$$210$$ 0 0
$$211$$ 3.56155 6.16879i 0.245187 0.424677i −0.716997 0.697076i $$-0.754484\pi$$
0.962184 + 0.272399i $$0.0878172\pi$$
$$212$$ 6.12311 + 10.6055i 0.420537 + 0.728391i
$$213$$ 8.43845 0.578193
$$214$$ 9.68466 + 16.7743i 0.662030 + 1.14667i
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ −1.12311 1.94528i −0.0762414 0.132054i
$$218$$ −8.90388 + 15.4220i −0.603047 + 1.04451i
$$219$$ −4.50000 + 7.79423i −0.304082 + 0.526685i
$$220$$ 0 0
$$221$$ 2.56155 + 18.2931i 0.172309 + 1.23053i
$$222$$ −3.56155 −0.239036
$$223$$ 2.28078 3.95042i 0.152732 0.264540i −0.779499 0.626404i $$-0.784526\pi$$
0.932231 + 0.361864i $$0.117860\pi$$
$$224$$ −0.280776 + 0.486319i −0.0187602 + 0.0324936i
$$225$$ 0 0
$$226$$ 4.00000 0.266076
$$227$$ −8.65767 14.9955i −0.574630 0.995288i −0.996082 0.0884373i $$-0.971813\pi$$
0.421452 0.906851i $$-0.361521\pi$$
$$228$$ 3.28078 + 5.68247i 0.217275 + 0.376331i
$$229$$ −23.4924 −1.55242 −0.776211 0.630473i $$-0.782861\pi$$
−0.776211 + 0.630473i $$0.782861\pi$$
$$230$$ 0 0
$$231$$ −1.00000 + 1.73205i −0.0657952 + 0.113961i
$$232$$ 3.56155 6.16879i 0.233827 0.405001i
$$233$$ −0.630683 −0.0413174 −0.0206587 0.999787i $$-0.506576\pi$$
−0.0206587 + 0.999787i $$0.506576\pi$$
$$234$$ −3.34233 1.35234i −0.218495 0.0884055i
$$235$$ 0 0
$$236$$ −3.12311 + 5.40938i −0.203297 + 0.352120i
$$237$$ −2.40388 + 4.16365i −0.156149 + 0.270458i
$$238$$ −1.43845 2.49146i −0.0932407 0.161498i
$$239$$ −10.0540 −0.650338 −0.325169 0.945656i $$-0.605421\pi$$
−0.325169 + 0.945656i $$0.605421\pi$$
$$240$$ 0 0
$$241$$ −5.71922 9.90599i −0.368408 0.638101i 0.620909 0.783883i $$-0.286764\pi$$
−0.989317 + 0.145782i $$0.953430\pi$$
$$242$$ 1.68466 0.108294
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ −5.34233 + 9.25319i −0.342008 + 0.592375i
$$245$$ 0 0
$$246$$ 5.12311 0.326637
$$247$$ −3.28078 23.4294i −0.208751 1.49078i
$$248$$ 4.00000 0.254000
$$249$$ −1.21922 + 2.11176i −0.0772652 + 0.133827i
$$250$$ 0 0
$$251$$ 2.46543 + 4.27026i 0.155617 + 0.269536i 0.933283 0.359141i $$-0.116930\pi$$
−0.777667 + 0.628677i $$0.783597\pi$$
$$252$$ 0.561553 0.0353745
$$253$$ −8.34233 14.4493i −0.524478 0.908422i
$$254$$ −0.596118 1.03251i −0.0374038 0.0647852i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −13.8078 + 23.9157i −0.861305 + 1.49182i 0.00936553 + 0.999956i $$0.497019\pi$$
−0.870670 + 0.491867i $$0.836315\pi$$
$$258$$ −2.28078 + 3.95042i −0.141995 + 0.245942i
$$259$$ −2.00000 −0.124274
$$260$$ 0 0
$$261$$ −7.12311 −0.440909
$$262$$ −4.56155 + 7.90084i −0.281814 + 0.488116i
$$263$$ −9.34233 + 16.1814i −0.576073 + 0.997787i 0.419851 + 0.907593i $$0.362082\pi$$
−0.995924 + 0.0901944i $$0.971251\pi$$
$$264$$ −1.78078 3.08440i −0.109599 0.189831i
$$265$$ 0 0
$$266$$ 1.84233 + 3.19101i 0.112960 + 0.195653i
$$267$$ 3.12311 + 5.40938i 0.191131 + 0.331049i
$$268$$ −8.80776 −0.538020
$$269$$ −10.6847 18.5064i −0.651455 1.12835i −0.982770 0.184833i $$-0.940826\pi$$
0.331315 0.943520i $$-0.392508\pi$$
$$270$$ 0 0
$$271$$ 9.96543 17.2606i 0.605357 1.04851i −0.386638 0.922232i $$-0.626364\pi$$
0.991995 0.126278i $$-0.0403030\pi$$
$$272$$ 5.12311 0.310634
$$273$$ −1.87689 0.759413i −0.113595 0.0459618i
$$274$$ −16.4924 −0.996344
$$275$$ 0 0
$$276$$ −2.34233 + 4.05703i −0.140992 + 0.244205i
$$277$$ −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i $$-0.214662\pi$$
−0.931305 + 0.364241i $$0.881328\pi$$
$$278$$ 17.4384 1.04589
$$279$$ −2.00000 3.46410i −0.119737 0.207390i
$$280$$ 0 0
$$281$$ −18.2462 −1.08848 −0.544239 0.838930i $$-0.683181\pi$$
−0.544239 + 0.838930i $$0.683181\pi$$
$$282$$ −2.00000 3.46410i −0.119098 0.206284i
$$283$$ 5.80776 10.0593i 0.345236 0.597966i −0.640161 0.768241i $$-0.721132\pi$$
0.985397 + 0.170275i $$0.0544656\pi$$
$$284$$ −4.21922 + 7.30791i −0.250365 + 0.433645i
$$285$$ 0 0
$$286$$ 1.78078 + 12.7173i 0.105300 + 0.751989i
$$287$$ 2.87689 0.169818
$$288$$ −0.500000 + 0.866025i −0.0294628 + 0.0510310i
$$289$$ −4.62311 + 8.00745i −0.271947 + 0.471027i
$$290$$ 0 0
$$291$$ 17.8078 1.04391
$$292$$ −4.50000 7.79423i −0.263343 0.456123i
$$293$$ −1.87689 3.25088i −0.109649 0.189918i 0.805979 0.591944i $$-0.201639\pi$$
−0.915628 + 0.402026i $$0.868306\pi$$
$$294$$ −6.68466 −0.389857
$$295$$ 0 0
$$296$$ 1.78078 3.08440i 0.103506 0.179277i
$$297$$ −1.78078 + 3.08440i −0.103331 + 0.178975i
$$298$$ 6.24621 0.361833
$$299$$ 13.3153 10.3923i 0.770046 0.601003i
$$300$$ 0 0
$$301$$ −1.28078 + 2.21837i −0.0738227 + 0.127865i
$$302$$ 2.15767 3.73720i 0.124160 0.215051i
$$303$$ −5.12311 8.87348i −0.294315 0.509768i
$$304$$ −6.56155 −0.376331
$$305$$ 0 0
$$306$$ −2.56155 4.43674i −0.146434 0.253632i
$$307$$ 5.75379 0.328386 0.164193 0.986428i $$-0.447498\pi$$
0.164193 + 0.986428i $$0.447498\pi$$
$$308$$ −1.00000 1.73205i −0.0569803 0.0986928i
$$309$$ 4.28078 7.41452i 0.243525 0.421797i
$$310$$ 0 0
$$311$$ −22.6847 −1.28633 −0.643164 0.765728i $$-0.722379\pi$$
−0.643164 + 0.765728i $$0.722379\pi$$
$$312$$ 2.84233 2.21837i 0.160915 0.125590i
$$313$$ 31.0000 1.75222 0.876112 0.482108i $$-0.160129\pi$$
0.876112 + 0.482108i $$0.160129\pi$$
$$314$$ −0.376894 + 0.652800i −0.0212694 + 0.0368396i
$$315$$ 0 0
$$316$$ −2.40388 4.16365i −0.135229 0.234223i
$$317$$ −0.246211 −0.0138286 −0.00691430 0.999976i $$-0.502201\pi$$
−0.00691430 + 0.999976i $$0.502201\pi$$
$$318$$ 6.12311 + 10.6055i 0.343367 + 0.594729i
$$319$$ 12.6847 + 21.9705i 0.710205 + 1.23011i
$$320$$ 0 0
$$321$$ 9.68466 + 16.7743i 0.540545 + 0.936251i
$$322$$ −1.31534 + 2.27824i −0.0733011 + 0.126961i
$$323$$ 16.8078 29.1119i 0.935209 1.61983i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 16.4924 0.913431
$$327$$ −8.90388 + 15.4220i −0.492386 + 0.852837i
$$328$$ −2.56155 + 4.43674i −0.141438 + 0.244978i
$$329$$ −1.12311 1.94528i −0.0619188 0.107247i
$$330$$ 0 0
$$331$$ 2.15767 + 3.73720i 0.118596 + 0.205415i 0.919212 0.393764i $$-0.128827\pi$$
−0.800615 + 0.599179i $$0.795494\pi$$
$$332$$ −1.21922 2.11176i −0.0669136 0.115898i
$$333$$ −3.56155 −0.195172
$$334$$ −5.65767 9.79937i −0.309574 0.536198i
$$335$$ 0 0
$$336$$ −0.280776 + 0.486319i −0.0153176 + 0.0265309i
$$337$$ −29.0540 −1.58267 −0.791335 0.611382i $$-0.790614\pi$$
−0.791335 + 0.611382i $$0.790614\pi$$
$$338$$ −12.5000 + 3.57071i −0.679910 + 0.194221i
$$339$$ 4.00000 0.217250
$$340$$ 0 0
$$341$$ −7.12311 + 12.3376i −0.385738 + 0.668117i
$$342$$ 3.28078 + 5.68247i 0.177404 + 0.307273i
$$343$$ −7.68466 −0.414933
$$344$$ −2.28078 3.95042i −0.122971 0.212992i
$$345$$ 0 0
$$346$$ −17.1231 −0.920544
$$347$$ 2.09612 + 3.63058i 0.112526 + 0.194900i 0.916788 0.399374i $$-0.130773\pi$$
−0.804262 + 0.594274i $$0.797439\pi$$
$$348$$ 3.56155 6.16879i 0.190919 0.330682i
$$349$$ 1.37689 2.38485i 0.0737035 0.127658i −0.826818 0.562469i $$-0.809851\pi$$
0.900522 + 0.434811i $$0.143185\pi$$
$$350$$ 0 0
$$351$$ −3.34233 1.35234i −0.178400 0.0721828i
$$352$$ 3.56155 0.189831
$$353$$ 7.12311 12.3376i 0.379125 0.656663i −0.611810 0.791004i $$-0.709558\pi$$
0.990935 + 0.134341i $$0.0428918\pi$$
$$354$$ −3.12311 + 5.40938i −0.165991 + 0.287505i
$$355$$ 0 0
$$356$$ −6.24621 −0.331049
$$357$$ −1.43845 2.49146i −0.0761307 0.131862i
$$358$$ 1.65767 + 2.87117i 0.0876106 + 0.151746i
$$359$$ −13.1231 −0.692611 −0.346306 0.938122i $$-0.612564\pi$$
−0.346306 + 0.938122i $$0.612564\pi$$
$$360$$ 0 0
$$361$$ −12.0270 + 20.8314i −0.632999 + 1.09639i
$$362$$ −8.74621 + 15.1489i −0.459691 + 0.796208i
$$363$$ 1.68466 0.0884216
$$364$$ 1.59612 1.24573i 0.0836593 0.0652941i
$$365$$ 0 0
$$366$$ −5.34233 + 9.25319i −0.279248 + 0.483672i
$$367$$ 15.4039 26.6803i 0.804076 1.39270i −0.112837 0.993614i $$-0.535994\pi$$
0.916913 0.399087i $$-0.130673\pi$$
$$368$$ −2.34233 4.05703i −0.122102 0.211487i
$$369$$ 5.12311 0.266698
$$370$$ 0 0
$$371$$ 3.43845 + 5.95557i 0.178515 + 0.309198i
$$372$$ 4.00000 0.207390
$$373$$ −11.7462 20.3450i −0.608196 1.05343i −0.991538 0.129819i $$-0.958560\pi$$
0.383342 0.923607i $$-0.374773\pi$$
$$374$$ −9.12311 + 15.8017i −0.471745 + 0.817086i
$$375$$ 0 0
$$376$$ 4.00000 0.206284
$$377$$ −20.2462 + 15.8017i −1.04273 + 0.813828i
$$378$$ 0.561553 0.0288832
$$379$$ −6.52699 + 11.3051i −0.335269 + 0.580703i −0.983536 0.180710i $$-0.942160\pi$$
0.648268 + 0.761413i $$0.275494\pi$$
$$380$$ 0 0
$$381$$ −0.596118 1.03251i −0.0305400 0.0528969i
$$382$$ −12.9309 −0.661601
$$383$$ 4.78078 + 8.28055i 0.244286 + 0.423116i 0.961931 0.273293i $$-0.0881130\pi$$
−0.717644 + 0.696410i $$0.754780\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ −1.50000 2.59808i −0.0763480 0.132239i
$$387$$ −2.28078 + 3.95042i −0.115938 + 0.200811i
$$388$$ −8.90388 + 15.4220i −0.452026 + 0.782932i
$$389$$ −13.3693 −0.677851 −0.338926 0.940813i $$-0.610064\pi$$
−0.338926 + 0.940813i $$0.610064\pi$$
$$390$$ 0 0
$$391$$ 24.0000 1.21373
$$392$$ 3.34233 5.78908i 0.168813 0.292393i
$$393$$ −4.56155 + 7.90084i −0.230100 + 0.398545i
$$394$$ 1.56155 + 2.70469i 0.0786699 + 0.136260i
$$395$$ 0 0
$$396$$ −1.78078 3.08440i −0.0894874 0.154997i
$$397$$ −5.40388 9.35980i −0.271213 0.469755i 0.697960 0.716137i $$-0.254091\pi$$
−0.969173 + 0.246382i $$0.920758\pi$$
$$398$$ −8.56155 −0.429152
$$399$$ 1.84233 + 3.19101i 0.0922318 + 0.159750i
$$400$$ 0 0
$$401$$ 18.6847 32.3628i 0.933067 1.61612i 0.155023 0.987911i $$-0.450455\pi$$
0.778045 0.628209i $$-0.216212\pi$$
$$402$$ −8.80776 −0.439291
$$403$$ −13.3693 5.40938i −0.665973 0.269460i
$$404$$ 10.2462 0.509768
$$405$$ 0 0
$$406$$ 2.00000 3.46410i 0.0992583 0.171920i
$$407$$ 6.34233 + 10.9852i 0.314378 + 0.544518i
$$408$$ 5.12311 0.253632
$$409$$ 0.123106 + 0.213225i 0.00608718 + 0.0105433i 0.869053 0.494719i $$-0.164729\pi$$
−0.862966 + 0.505262i $$0.831396\pi$$
$$410$$ 0 0
$$411$$ −16.4924 −0.813511
$$412$$ 4.28078 + 7.41452i 0.210899 + 0.365287i
$$413$$ −1.75379 + 3.03765i −0.0862983 + 0.149473i
$$414$$ −2.34233 + 4.05703i −0.115119 + 0.199392i
$$415$$ 0 0
$$416$$ 0.500000 + 3.57071i 0.0245145 + 0.175069i
$$417$$ 17.4384 0.853964
$$418$$ 11.6847 20.2384i 0.571515 0.989894i
$$419$$ −8.46543 + 14.6626i −0.413564 + 0.716313i −0.995276 0.0970811i $$-0.969049\pi$$
0.581713 + 0.813394i $$0.302383\pi$$
$$420$$ 0 0
$$421$$ 14.7538 0.719056 0.359528 0.933134i $$-0.382938\pi$$
0.359528 + 0.933134i $$0.382938\pi$$
$$422$$ 3.56155 + 6.16879i 0.173374 + 0.300292i
$$423$$ −2.00000 3.46410i −0.0972433 0.168430i
$$424$$ −12.2462 −0.594729
$$425$$ 0 0
$$426$$ −4.21922 + 7.30791i −0.204422 + 0.354069i
$$427$$ −3.00000 + 5.19615i −0.145180 + 0.251459i
$$428$$ −19.3693 −0.936251
$$429$$ 1.78078 + 12.7173i 0.0859767 + 0.613996i
$$430$$ 0 0
$$431$$ −15.3423 + 26.5737i −0.739014 + 1.28001i 0.213926 + 0.976850i $$0.431375\pi$$
−0.952940 + 0.303160i $$0.901958\pi$$
$$432$$ −0.500000 + 0.866025i −0.0240563 + 0.0416667i
$$433$$ 0.657671 + 1.13912i 0.0316056 + 0.0547426i 0.881396 0.472379i $$-0.156605\pi$$
−0.849790 + 0.527121i $$0.823271\pi$$
$$434$$ 2.24621 0.107822
$$435$$ 0 0
$$436$$ −8.90388 15.4220i −0.426419 0.738579i
$$437$$ −30.7386 −1.47043
$$438$$ −4.50000 7.79423i −0.215018 0.372423i
$$439$$ −10.9654 + 18.9927i −0.523352 + 0.906472i 0.476279 + 0.879294i $$0.341985\pi$$
−0.999631 + 0.0271774i $$0.991348\pi$$
$$440$$ 0 0
$$441$$ −6.68466 −0.318317
$$442$$ −17.1231 6.92820i −0.814463 0.329541i
$$443$$ 17.8078 0.846072 0.423036 0.906113i $$-0.360964\pi$$
0.423036 + 0.906113i $$0.360964\pi$$
$$444$$ 1.78078 3.08440i 0.0845119 0.146379i
$$445$$ 0 0
$$446$$ 2.28078 + 3.95042i 0.107998 + 0.187058i
$$447$$ 6.24621 0.295436
$$448$$ −0.280776 0.486319i −0.0132654 0.0229764i
$$449$$ −2.56155 4.43674i −0.120887 0.209383i 0.799231 0.601024i $$-0.205241\pi$$
−0.920118 + 0.391642i $$0.871907\pi$$
$$450$$ 0 0
$$451$$ −9.12311 15.8017i −0.429590 0.744072i
$$452$$ −2.00000 + 3.46410i −0.0940721 + 0.162938i
$$453$$ 2.15767 3.73720i 0.101376 0.175589i
$$454$$ 17.3153 0.812649
$$455$$ 0 0
$$456$$ −6.56155 −0.307273
$$457$$ −18.7462 + 32.4694i −0.876911 + 1.51885i −0.0221975 + 0.999754i $$0.507066\pi$$
−0.854713 + 0.519100i $$0.826267\pi$$
$$458$$ 11.7462 20.3450i 0.548864 0.950661i
$$459$$ −2.56155 4.43674i −0.119563 0.207089i
$$460$$ 0 0
$$461$$ −17.6847 30.6307i −0.823657 1.42662i −0.902942 0.429763i $$-0.858597\pi$$
0.0792850 0.996852i $$-0.474736\pi$$
$$462$$ −1.00000 1.73205i −0.0465242 0.0805823i
$$463$$ 7.19224 0.334252 0.167126 0.985936i $$-0.446551\pi$$
0.167126 + 0.985936i $$0.446551\pi$$
$$464$$ 3.56155 + 6.16879i 0.165341 + 0.286379i
$$465$$ 0 0
$$466$$ 0.315342 0.546188i 0.0146079 0.0253017i
$$467$$ −7.56155 −0.349907 −0.174953 0.984577i $$-0.555978\pi$$
−0.174953 + 0.984577i $$0.555978\pi$$
$$468$$ 2.84233 2.21837i 0.131387 0.102544i
$$469$$ −4.94602 −0.228386
$$470$$ 0 0
$$471$$ −0.376894 + 0.652800i −0.0173664 + 0.0300794i
$$472$$ −3.12311 5.40938i −0.143753 0.248987i
$$473$$ 16.2462 0.747002
$$474$$ −2.40388 4.16365i −0.110414 0.191243i
$$475$$ 0 0
$$476$$ 2.87689 0.131862
$$477$$ 6.12311 + 10.6055i 0.280358 + 0.485594i
$$478$$ 5.02699 8.70700i 0.229929 0.398249i
$$479$$ −14.8078 + 25.6478i −0.676584 + 1.17188i 0.299419 + 0.954122i $$0.403207\pi$$
−0.976003 + 0.217756i $$0.930126\pi$$
$$480$$ 0 0
$$481$$ −10.1231 + 7.90084i −0.461574 + 0.360247i
$$482$$ 11.4384 0.521007
$$483$$ −1.31534 + 2.27824i −0.0598501 + 0.103663i
$$484$$ −0.842329 + 1.45896i −0.0382877 + 0.0663162i
$$485$$ 0 0
$$486$$ 1.00000 0.0453609
$$487$$ −15.1577 26.2539i −0.686860 1.18968i −0.972849 0.231443i $$-0.925655\pi$$
0.285989 0.958233i $$-0.407678\pi$$
$$488$$ −5.34233 9.25319i −0.241836 0.418872i
$$489$$ 16.4924 0.745813
$$490$$ 0 0
$$491$$ 11.1501 19.3125i 0.503197 0.871562i −0.496797 0.867867i $$-0.665490\pi$$
0.999993 0.00369513i $$-0.00117620\pi$$
$$492$$ −2.56155 + 4.43674i −0.115484 + 0.200024i
$$493$$ −36.4924 −1.64354
$$494$$ 21.9309 + 8.87348i 0.986716 + 0.399237i
$$495$$ 0 0
$$496$$ −2.00000 + 3.46410i −0.0898027 + 0.155543i
$$497$$ −2.36932 + 4.10378i −0.106278 + 0.184080i
$$498$$ −1.21922 2.11176i −0.0546347 0.0946301i
$$499$$ −31.0540 −1.39017 −0.695083 0.718929i $$-0.744633\pi$$
−0.695083 + 0.718929i $$0.744633\pi$$
$$500$$ 0 0
$$501$$ −5.65767 9.79937i −0.252766 0.437804i
$$502$$ −4.93087 −0.220075
$$503$$ 18.3423 + 31.7698i 0.817844 + 1.41655i 0.907268 + 0.420554i $$0.138164\pi$$
−0.0894236 + 0.995994i $$0.528502\pi$$
$$504$$ −0.280776 + 0.486319i −0.0125068 + 0.0216624i
$$505$$ 0 0
$$506$$ 16.6847 0.741724
$$507$$ −12.5000 + 3.57071i −0.555144 + 0.158581i
$$508$$ 1.19224 0.0528969
$$509$$ −0.123106 + 0.213225i −0.00545656 + 0.00945104i −0.868741 0.495267i $$-0.835070\pi$$
0.863284 + 0.504718i $$0.168404\pi$$
$$510$$ 0 0
$$511$$ −2.52699 4.37687i −0.111787 0.193621i
$$512$$ 1.00000 0.0441942
$$513$$ 3.28078 + 5.68247i 0.144850 + 0.250887i
$$514$$ −13.8078 23.9157i −0.609034 1.05488i
$$515$$ 0 0
$$516$$ −2.28078 3.95042i −0.100406 0.173908i
$$517$$ −7.12311 + 12.3376i −0.313274 + 0.542606i
$$518$$ 1.00000 1.73205i 0.0439375 0.0761019i
$$519$$ −17.1231 −0.751621
$$520$$ 0 0
$$521$$ −14.7386 −0.645711 −0.322856 0.946448i $$-0.604643\pi$$
−0.322856 + 0.946448i $$0.604643\pi$$
$$522$$ 3.56155 6.16879i 0.155885 0.270001i
$$523$$ 1.96543 3.40423i 0.0859425 0.148857i −0.819850 0.572578i $$-0.805943\pi$$
0.905792 + 0.423722i $$0.139277\pi$$
$$524$$ −4.56155 7.90084i −0.199272 0.345150i
$$525$$ 0 0
$$526$$ −9.34233 16.1814i −0.407345 0.705542i
$$527$$ −10.2462 17.7470i −0.446332 0.773070i
$$528$$ 3.56155 0.154997
$$529$$ 0.526988 + 0.912769i 0.0229125 + 0.0396856i
$$530$$ 0 0
$$531$$ −3.12311 + 5.40938i −0.135531 + 0.234747i
$$532$$ −3.68466 −0.159750
$$533$$ 14.5616 11.3649i 0.630731 0.492270i
$$534$$ −6.24621 −0.270300
$$535$$ 0 0
$$536$$ 4.40388 7.62775i 0.190219 0.329469i
$$537$$ 1.65767 + 2.87117i 0.0715338 + 0.123900i
$$538$$ 21.3693 0.921297
$$539$$ 11.9039 + 20.6181i 0.512736 + 0.888086i
$$540$$ 0 0
$$541$$ −34.6847 −1.49121 −0.745605 0.666388i $$-0.767839\pi$$
−0.745605 + 0.666388i $$0.767839\pi$$
$$542$$ 9.96543 + 17.2606i 0.428052 + 0.741408i
$$543$$ −8.74621 + 15.1489i −0.375336 + 0.650101i
$$544$$ −2.56155 + 4.43674i −0.109826 + 0.190224i
$$545$$ 0 0
$$546$$ 1.59612 1.24573i 0.0683075 0.0533124i
$$547$$ −2.06913 −0.0884696 −0.0442348 0.999021i $$-0.514085\pi$$
−0.0442348 + 0.999021i $$0.514085\pi$$
$$548$$ 8.24621 14.2829i 0.352261 0.610133i
$$549$$ −5.34233 + 9.25319i −0.228005 + 0.394916i
$$550$$ 0 0
$$551$$ 46.7386 1.99113
$$552$$ −2.34233 4.05703i −0.0996962 0.172679i
$$553$$ −1.34991 2.33811i −0.0574039 0.0994264i
$$554$$ 5.00000 0.212430
$$555$$ 0 0
$$556$$ −8.71922 + 15.1021i −0.369777 + 0.640473i
$$557$$ −4.80776 + 8.32729i −0.203712 + 0.352839i −0.949721 0.313096i $$-0.898634\pi$$
0.746010 + 0.665935i $$0.231967\pi$$
$$558$$ 4.00000 0.169334
$$559$$ 2.28078 + 16.2880i 0.0964666 + 0.688909i
$$560$$ 0 0
$$561$$ −9.12311 + 15.8017i −0.385178 + 0.667148i
$$562$$ 9.12311 15.8017i 0.384835 0.666554i
$$563$$ −0.0961180 0.166481i −0.00405089 0.00701635i 0.863993 0.503504i $$-0.167956\pi$$
−0.868044 + 0.496488i $$0.834623\pi$$
$$564$$ 4.00000 0.168430
$$565$$ 0 0
$$566$$ 5.80776 + 10.0593i 0.244119 + 0.422826i
$$567$$ 0.561553 0.0235830
$$568$$ −4.21922 7.30791i −0.177035 0.306633i
$$569$$ 22.2462 38.5316i 0.932610 1.61533i 0.153768 0.988107i $$-0.450859\pi$$
0.778842 0.627220i $$-0.215807\pi$$
$$570$$ 0 0
$$571$$ −40.4233 −1.69166 −0.845831 0.533451i $$-0.820895\pi$$
−0.845831 + 0.533451i $$0.820895\pi$$
$$572$$ −11.9039 4.81645i −0.497726 0.201386i
$$573$$ −12.9309 −0.540195
$$574$$ −1.43845 + 2.49146i −0.0600396 + 0.103992i
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ 23.0000 0.957503 0.478751 0.877951i $$-0.341090\pi$$
0.478751 + 0.877951i $$0.341090\pi$$
$$578$$ −4.62311 8.00745i −0.192296 0.333066i
$$579$$ −1.50000 2.59808i −0.0623379 0.107972i
$$580$$ 0 0
$$581$$ −0.684658 1.18586i −0.0284044 0.0491979i
$$582$$ −8.90388 + 15.4220i −0.369078 + 0.639261i
$$583$$ 21.8078 37.7722i 0.903185 1.56436i
$$584$$ 9.00000 0.372423
$$585$$ 0 0
$$586$$ 3.75379 0.155068
$$587$$ −5.46543 + 9.46641i −0.225583 + 0.390721i −0.956494 0.291752i $$-0.905762\pi$$
0.730911 + 0.682472i $$0.239095\pi$$
$$588$$ 3.34233 5.78908i 0.137835 0.238738i
$$589$$ 13.1231 + 22.7299i 0.540728 + 0.936569i
$$590$$ 0 0
$$591$$ 1.56155 + 2.70469i 0.0642337 + 0.111256i
$$592$$ 1.78078 + 3.08440i 0.0731895 + 0.126768i
$$593$$ 26.9848 1.10813 0.554067 0.832472i $$-0.313075\pi$$
0.554067 + 0.832472i $$0.313075\pi$$
$$594$$ −1.78078 3.08440i −0.0730661 0.126554i
$$595$$ 0 0
$$596$$ −3.12311 + 5.40938i −0.127927 + 0.221577i
$$597$$ −8.56155 −0.350401
$$598$$ 2.34233 + 16.7276i 0.0957850 + 0.684041i
$$599$$ −30.6847 −1.25374 −0.626871 0.779123i $$-0.715665\pi$$
−0.626871 + 0.779123i $$0.715665\pi$$
$$600$$ 0 0
$$601$$ −7.40388 + 12.8239i −0.302011 + 0.523098i −0.976591 0.215103i $$-0.930991\pi$$
0.674581 + 0.738201i $$0.264324\pi$$
$$602$$ −1.28078 2.21837i −0.0522005 0.0904140i
$$603$$ −8.80776 −0.358680
$$604$$ 2.15767 + 3.73720i 0.0877944 + 0.152064i
$$605$$ 0 0
$$606$$ 10.2462 0.416224
$$607$$ 7.31534 + 12.6705i 0.296921 + 0.514281i 0.975430 0.220310i $$-0.0707070\pi$$
−0.678509 + 0.734592i $$0.737374\pi$$
$$608$$ 3.28078 5.68247i 0.133053 0.230455i
$$609$$ 2.00000 3.46410i 0.0810441 0.140372i
$$610$$ 0 0
$$611$$ −13.3693 5.40938i −0.540865 0.218840i
$$612$$ 5.12311 0.207089
$$613$$ −16.7732 + 29.0520i −0.677463 + 1.17340i 0.298279 + 0.954479i $$0.403587\pi$$
−0.975742 + 0.218922i $$0.929746\pi$$
$$614$$ −2.87689 + 4.98293i −0.116102 + 0.201095i
$$615$$ 0 0
$$616$$ 2.00000 0.0805823
$$617$$ −11.3153 19.5987i −0.455538 0.789016i 0.543180 0.839616i $$-0.317220\pi$$
−0.998719 + 0.0506001i $$0.983887\pi$$
$$618$$ 4.28078 + 7.41452i 0.172198 + 0.298256i
$$619$$ 41.3002 1.65999 0.829997 0.557767i $$-0.188342\pi$$
0.829997 + 0.557767i $$0.188342\pi$$
$$620$$ 0 0
$$621$$ −2.34233 + 4.05703i −0.0939944 + 0.162803i
$$622$$ 11.3423 19.6455i 0.454786 0.787712i
$$623$$ −3.50758 −0.140528
$$624$$ 0.500000 + 3.57071i 0.0200160 + 0.142943i
$$625$$ 0 0
$$626$$ −15.5000 + 26.8468i −0.619505 + 1.07301i
$$627$$ 11.6847 20.2384i 0.466640 0.808245i
$$628$$ −0.376894 0.652800i −0.0150397 0.0260496i
$$629$$ −18.2462 −0.727524
$$630$$ 0 0
$$631$$ −2.03457 3.52397i −0.0809948 0.140287i 0.822683 0.568501i $$-0.192476\pi$$
−0.903677 + 0.428214i $$0.859143\pi$$
$$632$$ 4.80776 0.191243
$$633$$ 3.56155 + 6.16879i 0.141559 + 0.245187i
$$634$$ 0.123106 0.213225i 0.00488915 0.00846825i
$$635$$ 0 0
$$636$$ −12.2462 −0.485594
$$637$$ −19.0000 + 14.8290i −0.752807 + 0.587548i
$$638$$ −25.3693 −1.00438
$$639$$ −4.21922 + 7.30791i −0.166910 + 0.289096i
$$640$$ 0 0
$$641$$ −10.8769 18.8393i −0.429611 0.744109i 0.567227 0.823561i $$-0.308016\pi$$
−0.996839 + 0.0794524i $$0.974683\pi$$
$$642$$ −19.3693 −0.764446
$$643$$ 22.7732 + 39.4443i 0.898087 + 1.55553i 0.829937 + 0.557858i $$0.188377\pi$$
0.0681507 + 0.997675i $$0.478290\pi$$
$$644$$ −1.31534 2.27824i −0.0518317 0.0897752i
$$645$$ 0 0
$$646$$ 16.8078 + 29.1119i 0.661293 + 1.14539i
$$647$$ 14.7116 25.4813i 0.578374 1.00177i −0.417291 0.908773i $$-0.637021\pi$$
0.995666 0.0930013i $$-0.0296461\pi$$
$$648$$ −0.500000 + 0.866025i −0.0196419 + 0.0340207i
$$649$$ 22.2462 0.873240
$$650$$ 0 0
$$651$$ 2.24621 0.0880360
$$652$$ −8.24621 + 14.2829i −0.322947 + 0.559360i
$$653$$ −1.80776 + 3.13114i −0.0707433 + 0.122531i −0.899227 0.437482i $$-0.855870\pi$$
0.828484 + 0.560013i $$0.189204\pi$$
$$654$$ −8.90388 15.4220i −0.348169 0.603047i
$$655$$ 0 0
$$656$$ −2.56155 4.43674i −0.100012 0.173226i
$$657$$ −4.50000 7.79423i −0.175562 0.304082i
$$658$$ 2.24621 0.0875664
$$659$$ −15.3423 26.5737i −0.597652 1.03516i −0.993167 0.116704i $$-0.962767\pi$$
0.395514 0.918460i $$-0.370566\pi$$
$$660$$ 0 0
$$661$$ −10.7732 + 18.6597i −0.419029 + 0.725779i −0.995842 0.0910968i $$-0.970963\pi$$
0.576813 + 0.816876i $$0.304296\pi$$
$$662$$ −4.31534 −0.167721
$$663$$ −17.1231 6.92820i −0.665006 0.269069i
$$664$$ 2.43845 0.0946301
$$665$$ 0 0
$$666$$ 1.78078 3.08440i 0.0690037 0.119518i
$$667$$ 16.6847 + 28.8987i 0.646033 + 1.11896i
$$668$$ 11.3153 0.437804
$$669$$ 2.28078 + 3.95042i 0.0881799 + 0.152732i
$$670$$ 0 0
$$671$$ 38.0540 1.46906
$$672$$ −0.280776 0.486319i −0.0108312 0.0187602i
$$673$$ −22.6231 + 39.1844i −0.872057 + 1.51045i −0.0121912 + 0.999926i $$0.503881\pi$$
−0.859865 + 0.510521i $$0.829453\pi$$
$$674$$ 14.5270 25.1615i 0.559559 0.969184i
$$675$$ 0 0
$$676$$ 3.15767 12.6107i 0.121449 0.485026i
$$677$$ −29.6155 −1.13822 −0.569109 0.822262i $$-0.692712\pi$$
−0.569109 + 0.822262i $$0.692712\pi$$
$$678$$ −2.00000 + 3.46410i −0.0768095 + 0.133038i
$$679$$ −5.00000 + 8.66025i −0.191882 + 0.332350i
$$680$$ 0 0
$$681$$ 17.3153 0.663525
$$682$$ −7.12311 12.3376i −0.272758 0.472430i
$$683$$ −9.78078 16.9408i −0.374251 0.648222i 0.615964 0.787775i $$-0.288767\pi$$
−0.990215 + 0.139553i $$0.955433\pi$$
$$684$$ −6.56155 −0.250887
$$685$$ 0 0
$$686$$ 3.84233 6.65511i 0.146701 0.254093i
$$687$$ 11.7462 20.3450i 0.448146 0.776211i
$$688$$ 4.56155 0.173908
$$689$$ 40.9309 + 16.5611i 1.55934 + 0.630927i
$$690$$ 0 0
$$691$$ 25.0885 43.4546i 0.954413 1.65309i 0.218707 0.975790i $$-0.429816\pi$$
0.735706 0.677301i $$-0.236851\pi$$
$$692$$ 8.56155 14.8290i 0.325461 0.563716i
$$693$$ −1.00000 1.73205i −0.0379869 0.0657952i
$$694$$ −4.19224 −0.159135
$$695$$ 0 0
$$696$$ 3.56155 + 6.16879i 0.135000 + 0.233827i
$$697$$ 26.2462 0.994146
$$698$$ 1.37689 + 2.38485i 0.0521162 + 0.0902679i
$$699$$ 0.315342 0.546188i 0.0119273 0.0206587i
$$700$$ 0 0
$$701$$ −9.12311 −0.344575 −0.172287 0.985047i $$-0.555116\pi$$
−0.172287 + 0.985047i $$0.555116\pi$$
$$702$$ 2.84233 2.21837i 0.107277 0.0837270i
$$703$$ 23.3693 0.881390
$$704$$ −1.78078 + 3.08440i −0.0671155 + 0.116248i
$$705$$ 0 0
$$706$$ 7.12311 + 12.3376i 0.268082 + 0.464331i
$$707$$ 5.75379 0.216393
$$708$$ −3.12311 5.40938i −0.117373 0.203297i
$$709$$ 22.6231 + 39.1844i 0.849629 + 1.47160i 0.881540 + 0.472109i $$0.156507\pi$$
−0.0319115 + 0.999491i $$0.510159\pi$$
$$710$$ 0 0
$$711$$ −2.40388 4.16365i −0.0901526 0.156149i
$$712$$ 3.12311 5.40938i 0.117043 0.202725i
$$713$$ −9.36932 + 16.2281i −0.350884 + 0.607748i
$$714$$ 2.87689 0.107665
$$715$$ 0 0
$$716$$ −3.31534 −0.123900
$$717$$ 5.02699 8.70700i 0.187736 0.325169i
$$718$$ 6.56155 11.3649i 0.244875 0.424136i
$$719$$ 10.7808 + 18.6729i 0.402055 + 0.696380i 0.993974 0.109618i $$-0.0349627\pi$$
−0.591919 + 0.805998i $$0.701629\pi$$
$$720$$ 0 0
$$721$$ 2.40388 + 4.16365i 0.0895252 + 0.155062i
$$722$$ −12.0270 20.8314i −0.447598 0.775263i
$$723$$ 11.4384 0.425400
$$724$$ −8.74621 15.1489i −0.325050 0.563004i
$$725$$ 0 0
$$726$$ −0.842329 + 1.45896i −0.0312618 + 0.0541470i
$$727$$ 35.7926 1.32747 0.663737 0.747966i $$-0.268969\pi$$
0.663737 + 0.747966i $$0.268969\pi$$
$$728$$ 0.280776 + 2.00514i 0.0104063 + 0.0743156i
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −11.6847 + 20.2384i −0.432173 + 0.748545i
$$732$$ −5.34233 9.25319i −0.197458 0.342008i
$$733$$ 17.9848 0.664285 0.332143 0.943229i $$-0.392228\pi$$
0.332143 + 0.943229i $$0.392228\pi$$
$$734$$ 15.4039 + 26.6803i 0.568568 + 0.984788i
$$735$$ 0 0
$$736$$ 4.68466 0.172679
$$737$$ 15.6847 + 27.1666i 0.577752 + 1.00070i
$$738$$ −2.56155 + 4.43674i −0.0942921 + 0.163319i
$$739$$ 2.43845 4.22351i 0.0896997 0.155364i −0.817684 0.575667i $$-0.804743\pi$$
0.907384 + 0.420302i $$0.138076\pi$$
$$740$$ 0 0
$$741$$ 21.9309 + 8.87348i 0.805651 + 0.325975i
$$742$$ −6.87689 −0.252459
$$743$$ −1.43845 + 2.49146i −0.0527715 + 0.0914029i −0.891204 0.453602i $$-0.850139\pi$$
0.838433 + 0.545005i $$0.183472\pi$$
$$744$$ −2.00000 + 3.46410i −0.0733236 + 0.127000i
$$745$$ 0 0
$$746$$ 23.4924 0.860119
$$747$$ −1.21922 2.11176i −0.0446091 0.0772652i
$$748$$ −9.12311 15.8017i −0.333574 0.577767i
$$749$$ −10.8769 −0.397433
$$750$$ 0 0
$$751$$ −16.8769 + 29.2316i −0.615847 + 1.06668i 0.374389 + 0.927272i $$0.377853\pi$$
−0.990235 + 0.139406i $$0.955481\pi$$
$$752$$ −2.00000 + 3.46410i −0.0729325 + 0.126323i
$$753$$ −4.93087 −0.179691
$$754$$ −3.56155 25.4346i −0.129704 0.926273i
$$755$$ 0 0
$$756$$ −0.280776 + 0.486319i −0.0102117 + 0.0176873i
$$757$$ 9.15767 15.8616i 0.332841 0.576498i −0.650227 0.759740i $$-0.725326\pi$$
0.983068 + 0.183243i $$0.0586594\pi$$
$$758$$ −6.52699 11.3051i −0.237071 0.410619i
$$759$$ 16.6847 0.605615
$$760$$ 0 0
$$761$$ −21.4924 37.2260i −0.779100 1.34944i −0.932461 0.361270i $$-0.882343\pi$$
0.153361 0.988170i $$-0.450990\pi$$
$$762$$ 1.19224 0.0431902
$$763$$ −5.00000 8.66025i −0.181012 0.313522i
$$764$$ 6.46543 11.1985i 0.233911 0.405146i
$$765$$ 0 0
$$766$$ −9.56155 −0.345473
$$767$$ 3.12311 + 22.3034i 0.112769 + 0.805330i
$$768$$ 1.00000 0.0360844
$$769$$ 10.8423 18.7795i 0.390984 0.677205i −0.601595 0.798801i $$-0.705468\pi$$
0.992580 + 0.121596i $$0.0388013\pi$$
$$770$$ 0 0
$$771$$ −13.8078 23.9157i −0.497274 0.861305i
$$772$$ 3.00000 0.107972
$$773$$ −5.80776 10.0593i −0.208891 0.361809i 0.742475 0.669874i $$-0.233652\pi$$
−0.951365 + 0.308065i $$0.900319\pi$$
$$774$$ −2.28078 3.95042i −0.0819808 0.141995i
$$775$$ 0 0
$$776$$ −8.90388 15.4220i −0.319631 0.553617i
$$777$$ 1.00000 1.73205i 0.0358748 0.0621370i
$$778$$ 6.68466 11.5782i 0.239657 0.415097i
$$779$$ −33.6155 −1.20440
$$780$$ 0 0
$$781$$ 30.0540 1.07542
$$782$$ −12.0000 + 20.7846i −0.429119 + 0.743256i
$$783$$ 3.56155 6.16879i 0.127280 0.220455i
$$784$$ 3.34233 + 5.78908i 0.119369 + 0.206753i