# Properties

 Label 476.2.i.a.137.1 Level $476$ Weight $2$ Character 476.137 Analytic conductor $3.801$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$476 = 2^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 476.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.80087913621$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 137.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 476.137 Dual form 476.2.i.a.205.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} -5.00000 q^{13} -4.00000 q^{15} +(0.500000 - 0.866025i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(2.00000 + 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.00000 q^{27} +8.00000 q^{29} +(1.50000 + 2.59808i) q^{33} +(-10.0000 - 3.46410i) q^{35} +(4.00000 + 6.92820i) q^{37} +(2.50000 - 4.33013i) q^{39} -8.00000 q^{41} +10.0000 q^{43} +(-4.00000 + 6.92820i) q^{45} +(1.00000 + 1.73205i) q^{47} +(1.00000 - 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{51} +(-1.50000 + 2.59808i) q^{53} +12.0000 q^{55} +6.00000 q^{57} +(-1.00000 + 1.73205i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(-10.0000 - 17.3205i) q^{65} +(-7.00000 + 12.1244i) q^{67} -4.00000 q^{69} +7.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(-5.50000 - 9.52628i) q^{75} +(1.50000 + 7.79423i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(10.0000 - 8.66025i) q^{91} +(12.0000 - 20.7846i) q^{95} +18.0000 q^{97} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10})$$ 2 * q - q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 $$2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} - 10 q^{13} - 8 q^{15} + q^{17} - 6 q^{19} - q^{21} + 4 q^{23} - 11 q^{25} - 10 q^{27} + 16 q^{29} + 3 q^{33} - 20 q^{35} + 8 q^{37} + 5 q^{39} - 16 q^{41} + 20 q^{43} - 8 q^{45} + 2 q^{47} + 2 q^{49} + q^{51} - 3 q^{53} + 24 q^{55} + 12 q^{57} - 2 q^{59} + 8 q^{61} - 10 q^{63} - 20 q^{65} - 14 q^{67} - 8 q^{69} + 14 q^{71} + 8 q^{73} - 11 q^{75} + 3 q^{77} - 15 q^{79} - q^{81} + 24 q^{83} + 8 q^{85} - 8 q^{87} - q^{89} + 20 q^{91} + 24 q^{95} + 36 q^{97} + 12 q^{99}+O(q^{100})$$ 2 * q - q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 + 3 * q^11 - 10 * q^13 - 8 * q^15 + q^17 - 6 * q^19 - q^21 + 4 * q^23 - 11 * q^25 - 10 * q^27 + 16 * q^29 + 3 * q^33 - 20 * q^35 + 8 * q^37 + 5 * q^39 - 16 * q^41 + 20 * q^43 - 8 * q^45 + 2 * q^47 + 2 * q^49 + q^51 - 3 * q^53 + 24 * q^55 + 12 * q^57 - 2 * q^59 + 8 * q^61 - 10 * q^63 - 20 * q^65 - 14 * q^67 - 8 * q^69 + 14 * q^71 + 8 * q^73 - 11 * q^75 + 3 * q^77 - 15 * q^79 - q^81 + 24 * q^83 + 8 * q^85 - 8 * q^87 - q^89 + 20 * q^91 + 24 * q^95 + 36 * q^97 + 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$$.

 $$n$$ $$239$$ $$309$$ $$409$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ 0 0
$$5$$ 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i $$0.185750\pi$$
0.0599153 + 0.998203i $$0.480917\pi$$
$$6$$ 0 0
$$7$$ −2.00000 + 1.73205i −0.755929 + 0.654654i
$$8$$ 0 0
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i $$-0.683949\pi$$
0.998526 + 0.0542666i $$0.0172821\pi$$
$$12$$ 0 0
$$13$$ −5.00000 −1.38675 −0.693375 0.720577i $$-0.743877\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ −4.00000 −1.03280
$$16$$ 0 0
$$17$$ 0.500000 0.866025i 0.121268 0.210042i
$$18$$ 0 0
$$19$$ −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i $$-0.925047\pi$$
0.284157 0.958778i $$-0.408286\pi$$
$$20$$ 0 0
$$21$$ −0.500000 2.59808i −0.109109 0.566947i
$$22$$ 0 0
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0 0
$$25$$ −5.50000 + 9.52628i −1.10000 + 1.90526i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ 8.00000 1.48556 0.742781 0.669534i $$-0.233506\pi$$
0.742781 + 0.669534i $$0.233506\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0 0
$$33$$ 1.50000 + 2.59808i 0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ −10.0000 3.46410i −1.69031 0.585540i
$$36$$ 0 0
$$37$$ 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i $$0.0617599\pi$$
−0.323640 + 0.946180i $$0.604907\pi$$
$$38$$ 0 0
$$39$$ 2.50000 4.33013i 0.400320 0.693375i
$$40$$ 0 0
$$41$$ −8.00000 −1.24939 −0.624695 0.780869i $$-0.714777\pi$$
−0.624695 + 0.780869i $$0.714777\pi$$
$$42$$ 0 0
$$43$$ 10.0000 1.52499 0.762493 0.646997i $$-0.223975\pi$$
0.762493 + 0.646997i $$0.223975\pi$$
$$44$$ 0 0
$$45$$ −4.00000 + 6.92820i −0.596285 + 1.03280i
$$46$$ 0 0
$$47$$ 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i $$-0.120070\pi$$
−0.783830 + 0.620975i $$0.786737\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 0 0
$$51$$ 0.500000 + 0.866025i 0.0700140 + 0.121268i
$$52$$ 0 0
$$53$$ −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i $$-0.899391\pi$$
0.744423 + 0.667708i $$0.232725\pi$$
$$54$$ 0 0
$$55$$ 12.0000 1.61808
$$56$$ 0 0
$$57$$ 6.00000 0.794719
$$58$$ 0 0
$$59$$ −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i $$-0.874892\pi$$
0.793560 + 0.608492i $$0.208225\pi$$
$$60$$ 0 0
$$61$$ 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i $$0.00448323\pi$$
−0.487753 + 0.872982i $$0.662183\pi$$
$$62$$ 0 0
$$63$$ −5.00000 1.73205i −0.629941 0.218218i
$$64$$ 0 0
$$65$$ −10.0000 17.3205i −1.24035 2.14834i
$$66$$ 0 0
$$67$$ −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i $$0.493224\pi$$
−0.876472 + 0.481452i $$0.840109\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 7.00000 0.830747 0.415374 0.909651i $$-0.363651\pi$$
0.415374 + 0.909651i $$0.363651\pi$$
$$72$$ 0 0
$$73$$ 4.00000 6.92820i 0.468165 0.810885i −0.531174 0.847263i $$-0.678249\pi$$
0.999338 + 0.0363782i $$0.0115821\pi$$
$$74$$ 0 0
$$75$$ −5.50000 9.52628i −0.635085 1.10000i
$$76$$ 0 0
$$77$$ 1.50000 + 7.79423i 0.170941 + 0.888235i
$$78$$ 0 0
$$79$$ −7.50000 12.9904i −0.843816 1.46153i −0.886646 0.462450i $$-0.846971\pi$$
0.0428296 0.999082i $$-0.486363\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 4.00000 0.433861
$$86$$ 0 0
$$87$$ −4.00000 + 6.92820i −0.428845 + 0.742781i
$$88$$ 0 0
$$89$$ −0.500000 0.866025i −0.0529999 0.0917985i 0.838308 0.545197i $$-0.183545\pi$$
−0.891308 + 0.453398i $$0.850212\pi$$
$$90$$ 0 0
$$91$$ 10.0000 8.66025i 1.04828 0.907841i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 12.0000 20.7846i 1.23117 2.13246i
$$96$$ 0 0
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ 0 0
$$99$$ 6.00000 0.603023
$$100$$ 0 0
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i $$-0.229808\pi$$
−0.947576 + 0.319531i $$0.896475\pi$$
$$104$$ 0 0
$$105$$ 8.00000 6.92820i 0.780720 0.676123i
$$106$$ 0 0
$$107$$ −0.500000 0.866025i −0.0483368 0.0837218i 0.840845 0.541276i $$-0.182059\pi$$
−0.889182 + 0.457555i $$0.848725\pi$$
$$108$$ 0 0
$$109$$ 4.00000 6.92820i 0.383131 0.663602i −0.608377 0.793648i $$-0.708179\pi$$
0.991508 + 0.130046i $$0.0415126\pi$$
$$110$$ 0 0
$$111$$ −8.00000 −0.759326
$$112$$ 0 0
$$113$$ −8.00000 −0.752577 −0.376288 0.926503i $$-0.622800\pi$$
−0.376288 + 0.926503i $$0.622800\pi$$
$$114$$ 0 0
$$115$$ −8.00000 + 13.8564i −0.746004 + 1.29212i
$$116$$ 0 0
$$117$$ −5.00000 8.66025i −0.462250 0.800641i
$$118$$ 0 0
$$119$$ 0.500000 + 2.59808i 0.0458349 + 0.238165i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 4.00000 6.92820i 0.360668 0.624695i
$$124$$ 0 0
$$125$$ −24.0000 −2.14663
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ −5.00000 + 8.66025i −0.440225 + 0.762493i
$$130$$ 0 0
$$131$$ 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i $$-0.110758\pi$$
−0.765331 + 0.643637i $$0.777425\pi$$
$$132$$ 0 0
$$133$$ 15.0000 + 5.19615i 1.30066 + 0.450564i
$$134$$ 0 0
$$135$$ −10.0000 17.3205i −0.860663 1.49071i
$$136$$ 0 0
$$137$$ 3.50000 6.06218i 0.299025 0.517927i −0.676888 0.736086i $$-0.736672\pi$$
0.975913 + 0.218159i $$0.0700052\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −0.0848189 −0.0424094 0.999100i $$-0.513503\pi$$
−0.0424094 + 0.999100i $$0.513503\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 0 0
$$143$$ −7.50000 + 12.9904i −0.627182 + 1.08631i
$$144$$ 0 0
$$145$$ 16.0000 + 27.7128i 1.32873 + 2.30142i
$$146$$ 0 0
$$147$$ 5.50000 + 4.33013i 0.453632 + 0.357143i
$$148$$ 0 0
$$149$$ 5.50000 + 9.52628i 0.450578 + 0.780423i 0.998422 0.0561570i $$-0.0178847\pi$$
−0.547844 + 0.836580i $$0.684551\pi$$
$$150$$ 0 0
$$151$$ −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i $$-0.966722\pi$$
0.587646 + 0.809118i $$0.300055\pi$$
$$152$$ 0 0
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.500000 + 0.866025i −0.0399043 + 0.0691164i −0.885288 0.465044i $$-0.846039\pi$$
0.845383 + 0.534160i $$0.179372\pi$$
$$158$$ 0 0
$$159$$ −1.50000 2.59808i −0.118958 0.206041i
$$160$$ 0 0
$$161$$ −10.0000 3.46410i −0.788110 0.273009i
$$162$$ 0 0
$$163$$ −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i $$-0.216737\pi$$
−0.933659 + 0.358162i $$0.883403\pi$$
$$164$$ 0 0
$$165$$ −6.00000 + 10.3923i −0.467099 + 0.809040i
$$166$$ 0 0
$$167$$ −19.0000 −1.47026 −0.735132 0.677924i $$-0.762880\pi$$
−0.735132 + 0.677924i $$0.762880\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ 6.00000 10.3923i 0.458831 0.794719i
$$172$$ 0 0
$$173$$ 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i $$-0.142443\pi$$
−0.825505 + 0.564396i $$0.809109\pi$$
$$174$$ 0 0
$$175$$ −5.50000 28.5788i −0.415761 2.16036i
$$176$$ 0 0
$$177$$ −1.00000 1.73205i −0.0751646 0.130189i
$$178$$ 0 0
$$179$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$180$$ 0 0
$$181$$ 18.0000 1.33793 0.668965 0.743294i $$-0.266738\pi$$
0.668965 + 0.743294i $$0.266738\pi$$
$$182$$ 0 0
$$183$$ −8.00000 −0.591377
$$184$$ 0 0
$$185$$ −16.0000 + 27.7128i −1.17634 + 2.03749i
$$186$$ 0 0
$$187$$ −1.50000 2.59808i −0.109691 0.189990i
$$188$$ 0 0
$$189$$ 10.0000 8.66025i 0.727393 0.629941i
$$190$$ 0 0
$$191$$ −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i $$-0.309616\pi$$
−0.997225 + 0.0744412i $$0.976283\pi$$
$$192$$ 0 0
$$193$$ 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i $$-0.716141\pi$$
0.987945 + 0.154805i $$0.0494748\pi$$
$$194$$ 0 0
$$195$$ 20.0000 1.43223
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i $$-0.753524\pi$$
0.963001 + 0.269498i $$0.0868577\pi$$
$$200$$ 0 0
$$201$$ −7.00000 12.1244i −0.493742 0.855186i
$$202$$ 0 0
$$203$$ −16.0000 + 13.8564i −1.12298 + 0.972529i
$$204$$ 0 0
$$205$$ −16.0000 27.7128i −1.11749 1.93555i
$$206$$ 0 0
$$207$$ −4.00000 + 6.92820i −0.278019 + 0.481543i
$$208$$ 0 0
$$209$$ −18.0000 −1.24509
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ −3.50000 + 6.06218i −0.239816 + 0.415374i
$$214$$ 0 0
$$215$$ 20.0000 + 34.6410i 1.36399 + 2.36250i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 4.00000 + 6.92820i 0.270295 + 0.468165i
$$220$$ 0 0
$$221$$ −2.50000 + 4.33013i −0.168168 + 0.291276i
$$222$$ 0 0
$$223$$ −6.00000 −0.401790 −0.200895 0.979613i $$-0.564385\pi$$
−0.200895 + 0.979613i $$0.564385\pi$$
$$224$$ 0 0
$$225$$ −22.0000 −1.46667
$$226$$ 0 0
$$227$$ −12.5000 + 21.6506i −0.829654 + 1.43700i 0.0686556 + 0.997640i $$0.478129\pi$$
−0.898310 + 0.439363i $$0.855204\pi$$
$$228$$ 0 0
$$229$$ 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i $$-0.0594799\pi$$
−0.652183 + 0.758062i $$0.726147\pi$$
$$230$$ 0 0
$$231$$ −7.50000 2.59808i −0.493464 0.170941i
$$232$$ 0 0
$$233$$ −14.0000 24.2487i −0.917170 1.58859i −0.803692 0.595045i $$-0.797134\pi$$
−0.113478 0.993540i $$-0.536199\pi$$
$$234$$ 0 0
$$235$$ −4.00000 + 6.92820i −0.260931 + 0.451946i
$$236$$ 0 0
$$237$$ 15.0000 0.974355
$$238$$ 0 0
$$239$$ 2.00000 0.129369 0.0646846 0.997906i $$-0.479396\pi$$
0.0646846 + 0.997906i $$0.479396\pi$$
$$240$$ 0 0
$$241$$ 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i $$-0.750381\pi$$
0.965615 + 0.259975i $$0.0837143\pi$$
$$242$$ 0 0
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ 0 0
$$245$$ 26.0000 10.3923i 1.66108 0.663940i
$$246$$ 0 0
$$247$$ 15.0000 + 25.9808i 0.954427 + 1.65312i
$$248$$ 0 0
$$249$$ −6.00000 + 10.3923i −0.380235 + 0.658586i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 12.0000 0.754434
$$254$$ 0 0
$$255$$ −2.00000 + 3.46410i −0.125245 + 0.216930i
$$256$$ 0 0
$$257$$ −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i $$-0.196494\pi$$
−0.909010 + 0.416775i $$0.863160\pi$$
$$258$$ 0 0
$$259$$ −20.0000 6.92820i −1.24274 0.430498i
$$260$$ 0 0
$$261$$ 8.00000 + 13.8564i 0.495188 + 0.857690i
$$262$$ 0 0
$$263$$ −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i $$-0.872689\pi$$
0.797752 + 0.602986i $$0.206023\pi$$
$$264$$ 0 0
$$265$$ −12.0000 −0.737154
$$266$$ 0 0
$$267$$ 1.00000 0.0611990
$$268$$ 0 0
$$269$$ 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i $$-0.648441\pi$$
0.998361 0.0572259i $$-0.0182255\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i $$0.0933238\pi$$
−0.228380 + 0.973572i $$0.573343\pi$$
$$272$$ 0 0
$$273$$ 2.50000 + 12.9904i 0.151307 + 0.786214i
$$274$$ 0 0
$$275$$ 16.5000 + 28.5788i 0.994987 + 1.72337i
$$276$$ 0 0
$$277$$ −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i $$-0.910591\pi$$
0.720473 + 0.693482i $$0.243925\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −19.0000 −1.13344 −0.566722 0.823909i $$-0.691789\pi$$
−0.566722 + 0.823909i $$0.691789\pi$$
$$282$$ 0 0
$$283$$ −7.50000 + 12.9904i −0.445829 + 0.772198i −0.998110 0.0614601i $$-0.980424\pi$$
0.552281 + 0.833658i $$0.313758\pi$$
$$284$$ 0 0
$$285$$ 12.0000 + 20.7846i 0.710819 + 1.23117i
$$286$$ 0 0
$$287$$ 16.0000 13.8564i 0.944450 0.817918i
$$288$$ 0 0
$$289$$ −0.500000 0.866025i −0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ −9.00000 + 15.5885i −0.527589 + 0.913812i
$$292$$ 0 0
$$293$$ −15.0000 −0.876309 −0.438155 0.898900i $$-0.644368\pi$$
−0.438155 + 0.898900i $$0.644368\pi$$
$$294$$ 0 0
$$295$$ −8.00000 −0.465778
$$296$$ 0 0
$$297$$ −7.50000 + 12.9904i −0.435194 + 0.753778i
$$298$$ 0 0
$$299$$ −10.0000 17.3205i −0.578315 1.00167i
$$300$$ 0 0
$$301$$ −20.0000 + 17.3205i −1.15278 + 0.998337i
$$302$$ 0 0
$$303$$ 3.00000 + 5.19615i 0.172345 + 0.298511i
$$304$$ 0 0
$$305$$ −16.0000 + 27.7128i −0.916157 + 1.58683i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ 4.00000 0.227552
$$310$$ 0 0
$$311$$ 6.50000 11.2583i 0.368581 0.638401i −0.620763 0.783998i $$-0.713177\pi$$
0.989344 + 0.145597i $$0.0465103\pi$$
$$312$$ 0 0
$$313$$ −15.0000 25.9808i −0.847850 1.46852i −0.883123 0.469142i $$-0.844563\pi$$
0.0352727 0.999378i $$-0.488770\pi$$
$$314$$ 0 0
$$315$$ −4.00000 20.7846i −0.225374 1.17108i
$$316$$ 0 0
$$317$$ 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i $$-0.148779\pi$$
−0.836576 + 0.547852i $$0.815446\pi$$
$$318$$ 0 0
$$319$$ 12.0000 20.7846i 0.671871 1.16371i
$$320$$ 0 0
$$321$$ 1.00000 0.0558146
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 0 0
$$325$$ 27.5000 47.6314i 1.52543 2.64211i
$$326$$ 0 0
$$327$$ 4.00000 + 6.92820i 0.221201 + 0.383131i
$$328$$ 0 0
$$329$$ −5.00000 1.73205i −0.275659 0.0954911i
$$330$$ 0 0
$$331$$ 3.00000 + 5.19615i 0.164895 + 0.285606i 0.936618 0.350352i $$-0.113938\pi$$
−0.771723 + 0.635959i $$0.780605\pi$$
$$332$$ 0 0
$$333$$ −8.00000 + 13.8564i −0.438397 + 0.759326i
$$334$$ 0 0
$$335$$ −56.0000 −3.05961
$$336$$ 0 0
$$337$$ 8.00000 0.435788 0.217894 0.975972i $$-0.430081\pi$$
0.217894 + 0.975972i $$0.430081\pi$$
$$338$$ 0 0
$$339$$ 4.00000 6.92820i 0.217250 0.376288i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ −8.00000 13.8564i −0.430706 0.746004i
$$346$$ 0 0
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ 0 0
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ 25.0000 1.33440
$$352$$ 0 0
$$353$$ 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i $$-0.644573\pi$$
0.997592 0.0693543i $$-0.0220939\pi$$
$$354$$ 0 0
$$355$$ 14.0000 + 24.2487i 0.743043 + 1.28699i
$$356$$ 0 0
$$357$$ −2.50000 0.866025i −0.132314 0.0458349i
$$358$$ 0 0
$$359$$ −11.0000 19.0526i −0.580558 1.00556i −0.995413 0.0956683i $$-0.969501\pi$$
0.414855 0.909887i $$-0.363832\pi$$
$$360$$ 0 0
$$361$$ −8.50000 + 14.7224i −0.447368 + 0.774865i
$$362$$ 0 0
$$363$$ −2.00000 −0.104973
$$364$$ 0 0
$$365$$ 32.0000 1.67496
$$366$$ 0 0
$$367$$ 4.50000 7.79423i 0.234898 0.406855i −0.724345 0.689438i $$-0.757858\pi$$
0.959243 + 0.282582i $$0.0911910\pi$$
$$368$$ 0 0
$$369$$ −8.00000 13.8564i −0.416463 0.721336i
$$370$$ 0 0
$$371$$ −1.50000 7.79423i −0.0778761 0.404656i
$$372$$ 0 0
$$373$$ −15.5000 26.8468i −0.802560 1.39007i −0.917926 0.396751i $$-0.870138\pi$$
0.115367 0.993323i $$-0.463196\pi$$
$$374$$ 0 0
$$375$$ 12.0000 20.7846i 0.619677 1.07331i
$$376$$ 0 0
$$377$$ −40.0000 −2.06010
$$378$$ 0 0
$$379$$ 1.00000 0.0513665 0.0256833 0.999670i $$-0.491824\pi$$
0.0256833 + 0.999670i $$0.491824\pi$$
$$380$$ 0 0
$$381$$ −4.00000 + 6.92820i −0.204926 + 0.354943i
$$382$$ 0 0
$$383$$ −1.00000 1.73205i −0.0510976 0.0885037i 0.839345 0.543599i $$-0.182939\pi$$
−0.890443 + 0.455095i $$0.849605\pi$$
$$384$$ 0 0
$$385$$ −24.0000 + 20.7846i −1.22315 + 1.05928i
$$386$$ 0 0
$$387$$ 10.0000 + 17.3205i 0.508329 + 0.880451i
$$388$$ 0 0
$$389$$ 13.5000 23.3827i 0.684477 1.18555i −0.289124 0.957292i $$-0.593364\pi$$
0.973601 0.228257i $$-0.0733028\pi$$
$$390$$ 0 0
$$391$$ 4.00000 0.202289
$$392$$ 0 0
$$393$$ −4.00000 −0.201773
$$394$$ 0 0
$$395$$ 30.0000 51.9615i 1.50946 2.61447i
$$396$$ 0 0
$$397$$ −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i $$-0.940407\pi$$
0.330075 0.943955i $$-0.392926\pi$$
$$398$$ 0 0
$$399$$ −12.0000 + 10.3923i −0.600751 + 0.520266i
$$400$$ 0 0
$$401$$ 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i $$-0.0182907\pi$$
−0.548911 + 0.835881i $$0.684957\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −4.00000 −0.198762
$$406$$ 0 0
$$407$$ 24.0000 1.18964
$$408$$ 0 0
$$409$$ −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i $$-0.921004\pi$$
0.697406 + 0.716677i $$0.254338\pi$$
$$410$$ 0 0
$$411$$ 3.50000 + 6.06218i 0.172642 + 0.299025i
$$412$$ 0 0
$$413$$ −1.00000 5.19615i −0.0492068 0.255686i
$$414$$ 0 0
$$415$$ 24.0000 + 41.5692i 1.17811 + 2.04055i
$$416$$ 0 0
$$417$$ 0.500000 0.866025i 0.0244851 0.0424094i
$$418$$ 0 0
$$419$$ 37.0000 1.80757 0.903784 0.427989i $$-0.140778\pi$$
0.903784 + 0.427989i $$0.140778\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ 0 0
$$423$$ −2.00000 + 3.46410i −0.0972433 + 0.168430i
$$424$$ 0 0
$$425$$ 5.50000 + 9.52628i 0.266789 + 0.462092i
$$426$$ 0 0
$$427$$ −20.0000 6.92820i −0.967868 0.335279i
$$428$$ 0 0
$$429$$ −7.50000 12.9904i −0.362103 0.627182i
$$430$$ 0 0
$$431$$ 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i $$-0.715679\pi$$
0.988169 + 0.153370i $$0.0490126\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 0 0
$$435$$ −32.0000 −1.53428
$$436$$ 0 0
$$437$$ 12.0000 20.7846i 0.574038 0.994263i
$$438$$ 0 0
$$439$$ 0.500000 + 0.866025i 0.0238637 + 0.0413331i 0.877711 0.479191i $$-0.159070\pi$$
−0.853847 + 0.520524i $$0.825737\pi$$
$$440$$ 0 0
$$441$$ 13.0000 5.19615i 0.619048 0.247436i
$$442$$ 0 0
$$443$$ −13.0000 22.5167i −0.617649 1.06980i −0.989914 0.141672i $$-0.954752\pi$$
0.372265 0.928126i $$-0.378581\pi$$
$$444$$ 0 0
$$445$$ 2.00000 3.46410i 0.0948091 0.164214i
$$446$$ 0 0
$$447$$ −11.0000 −0.520282
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ −12.0000 + 20.7846i −0.565058 + 0.978709i
$$452$$ 0 0
$$453$$ −5.00000 8.66025i −0.234920 0.406894i
$$454$$ 0 0
$$455$$ 50.0000 + 17.3205i 2.34404 + 0.811998i
$$456$$ 0 0
$$457$$ 13.0000 + 22.5167i 0.608114 + 1.05328i 0.991551 + 0.129718i $$0.0414071\pi$$
−0.383437 + 0.923567i $$0.625260\pi$$
$$458$$ 0 0
$$459$$ −2.50000 + 4.33013i −0.116690 + 0.202113i
$$460$$ 0 0
$$461$$ 15.0000 0.698620 0.349310 0.937007i $$-0.386416\pi$$
0.349310 + 0.937007i $$0.386416\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 14.0000 + 24.2487i 0.647843 + 1.12210i 0.983637 + 0.180161i $$0.0576619\pi$$
−0.335794 + 0.941935i $$0.609005\pi$$
$$468$$ 0 0
$$469$$ −7.00000 36.3731i −0.323230 1.67955i
$$470$$ 0 0
$$471$$ −0.500000 0.866025i −0.0230388 0.0399043i
$$472$$ 0 0
$$473$$ 15.0000 25.9808i 0.689701 1.19460i
$$474$$ 0 0
$$475$$ 66.0000 3.02829
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 0 0
$$479$$ −16.0000 + 27.7128i −0.731059 + 1.26623i 0.225372 + 0.974273i $$0.427640\pi$$
−0.956431 + 0.291958i $$0.905693\pi$$
$$480$$ 0 0
$$481$$ −20.0000 34.6410i −0.911922 1.57949i
$$482$$ 0 0
$$483$$ 8.00000 6.92820i 0.364013 0.315244i
$$484$$ 0 0
$$485$$ 36.0000 + 62.3538i 1.63468 + 2.83134i
$$486$$ 0 0
$$487$$ 2.50000 4.33013i 0.113286 0.196217i −0.803807 0.594890i $$-0.797196\pi$$
0.917093 + 0.398673i $$0.130529\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 0 0
$$493$$ 4.00000 6.92820i 0.180151 0.312031i
$$494$$ 0 0
$$495$$ 12.0000 + 20.7846i 0.539360 + 0.934199i
$$496$$ 0 0
$$497$$ −14.0000 + 12.1244i −0.627986 + 0.543852i
$$498$$ 0 0
$$499$$ −19.5000 33.7750i −0.872940 1.51198i −0.858941 0.512074i $$-0.828877\pi$$
−0.0139987 0.999902i $$-0.504456\pi$$
$$500$$ 0 0
$$501$$ 9.50000 16.4545i 0.424429 0.735132i
$$502$$ 0 0
$$503$$ 21.0000 0.936344 0.468172 0.883637i $$-0.344913\pi$$
0.468172 + 0.883637i $$0.344913\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ 0 0
$$507$$ −6.00000 + 10.3923i −0.266469 + 0.461538i
$$508$$ 0 0
$$509$$ −19.0000 32.9090i −0.842160 1.45866i −0.888065 0.459718i $$-0.847950\pi$$
0.0459045 0.998946i $$-0.485383\pi$$
$$510$$ 0 0
$$511$$ 4.00000 + 20.7846i 0.176950 + 0.919457i
$$512$$ 0 0
$$513$$ 15.0000 + 25.9808i 0.662266 + 1.14708i
$$514$$ 0 0
$$515$$ 8.00000 13.8564i 0.352522 0.610586i
$$516$$ 0 0
$$517$$ 6.00000 0.263880
$$518$$ 0 0
$$519$$ −2.00000 −0.0877903
$$520$$ 0 0
$$521$$ 12.0000 20.7846i 0.525730 0.910590i −0.473821 0.880621i $$-0.657126\pi$$
0.999551 0.0299693i $$-0.00954094\pi$$
$$522$$ 0 0
$$523$$ −3.00000 5.19615i −0.131181 0.227212i 0.792951 0.609285i $$-0.208544\pi$$
−0.924132 + 0.382073i $$0.875210\pi$$
$$524$$ 0 0
$$525$$ 27.5000 + 9.52628i 1.20020 + 0.415761i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 40.0000 1.73259
$$534$$ 0 0
$$535$$ 2.00000 3.46410i 0.0864675 0.149766i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −16.5000 12.9904i −0.710705 0.559535i
$$540$$ 0 0
$$541$$ −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i $$-0.263972\pi$$
−0.976352 + 0.216186i $$0.930638\pi$$
$$542$$ 0 0
$$543$$ −9.00000 + 15.5885i −0.386227 + 0.668965i
$$544$$ 0 0
$$545$$ 32.0000 1.37073
$$546$$ 0 0
$$547$$ −13.0000 −0.555840 −0.277920 0.960604i $$-0.589645\pi$$
−0.277920 + 0.960604i $$0.589645\pi$$
$$548$$ 0 0
$$549$$ −8.00000 + 13.8564i −0.341432 + 0.591377i
$$550$$ 0 0
$$551$$ −24.0000 41.5692i −1.02243 1.77091i
$$552$$ 0 0
$$553$$ 37.5000 + 12.9904i 1.59466 + 0.552407i
$$554$$ 0 0
$$555$$ −16.0000 27.7128i −0.679162 1.17634i
$$556$$ 0 0
$$557$$ −11.5000 + 19.9186i −0.487271 + 0.843978i −0.999893 0.0146368i $$-0.995341\pi$$
0.512622 + 0.858614i $$0.328674\pi$$
$$558$$ 0 0
$$559$$ −50.0000 −2.11477
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ 0 0
$$563$$ −15.0000 + 25.9808i −0.632175 + 1.09496i 0.354932 + 0.934892i $$0.384504\pi$$
−0.987106 + 0.160066i $$0.948829\pi$$
$$564$$ 0 0
$$565$$ −16.0000 27.7128i −0.673125 1.16589i
$$566$$ 0 0
$$567$$ −0.500000 2.59808i −0.0209980 0.109109i
$$568$$ 0 0
$$569$$ −16.5000 28.5788i −0.691716 1.19809i −0.971275 0.237959i $$-0.923522\pi$$
0.279559 0.960128i $$-0.409812\pi$$
$$570$$ 0 0
$$571$$ −18.0000 + 31.1769i −0.753277 + 1.30471i 0.192950 + 0.981209i $$0.438194\pi$$
−0.946227 + 0.323505i $$0.895139\pi$$
$$572$$ 0 0
$$573$$ 12.0000 0.501307
$$574$$ 0 0
$$575$$ −44.0000 −1.83493
$$576$$ 0 0
$$577$$ −6.50000 + 11.2583i −0.270599 + 0.468690i −0.969015 0.247001i $$-0.920555\pi$$
0.698417 + 0.715691i $$0.253888\pi$$
$$578$$ 0 0
$$579$$ 5.00000 + 8.66025i 0.207793 + 0.359908i
$$580$$ 0 0
$$581$$ −24.0000 + 20.7846i −0.995688 + 0.862291i
$$582$$ 0 0
$$583$$ 4.50000 + 7.79423i 0.186371 + 0.322804i
$$584$$ 0 0
$$585$$ 20.0000 34.6410i 0.826898 1.43223i
$$586$$ 0 0
$$587$$ −2.00000 −0.0825488 −0.0412744 0.999148i $$-0.513142\pi$$
−0.0412744 + 0.999148i $$0.513142\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −9.00000 + 15.5885i −0.370211 + 0.641223i
$$592$$ 0 0
$$593$$ −10.5000 18.1865i −0.431183 0.746831i 0.565792 0.824548i $$-0.308570\pi$$
−0.996976 + 0.0777165i $$0.975237\pi$$
$$594$$ 0 0
$$595$$ −8.00000 + 6.92820i −0.327968 + 0.284029i
$$596$$ 0 0
$$597$$ 3.50000 + 6.06218i 0.143245 + 0.248108i
$$598$$ 0 0
$$599$$ 17.0000 29.4449i 0.694601 1.20308i −0.275714 0.961240i $$-0.588914\pi$$
0.970315 0.241845i $$-0.0777525\pi$$
$$600$$ 0 0
$$601$$ −14.0000 −0.571072 −0.285536 0.958368i $$-0.592172\pi$$
−0.285536 + 0.958368i $$0.592172\pi$$
$$602$$ 0 0
$$603$$ −28.0000 −1.14025
$$604$$ 0 0
$$605$$ −4.00000 + 6.92820i −0.162623 + 0.281672i
$$606$$ 0 0
$$607$$ 11.5000 + 19.9186i 0.466771 + 0.808470i 0.999279 0.0379540i $$-0.0120840\pi$$
−0.532509 + 0.846424i $$0.678751\pi$$
$$608$$ 0 0
$$609$$ −4.00000 20.7846i −0.162088 0.842235i
$$610$$ 0 0
$$611$$ −5.00000 8.66025i −0.202278 0.350356i
$$612$$ 0 0
$$613$$ −8.50000 + 14.7224i −0.343312 + 0.594633i −0.985046 0.172294i $$-0.944882\pi$$
0.641734 + 0.766927i $$0.278215\pi$$
$$614$$ 0 0
$$615$$ 32.0000 1.29036
$$616$$ 0 0
$$617$$ −36.0000 −1.44931 −0.724653 0.689114i $$-0.758000\pi$$
−0.724653 + 0.689114i $$0.758000\pi$$
$$618$$ 0 0
$$619$$ 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i $$-0.722350\pi$$
0.984738 + 0.174042i $$0.0556830\pi$$
$$620$$ 0 0
$$621$$ −10.0000 17.3205i −0.401286 0.695048i
$$622$$ 0 0
$$623$$ 2.50000 + 0.866025i 0.100160 + 0.0346966i
$$624$$ 0 0
$$625$$ −20.5000 35.5070i −0.820000 1.42028i
$$626$$ 0 0
$$627$$ 9.00000 15.5885i 0.359425 0.622543i
$$628$$ 0 0
$$629$$ 8.00000 0.318981
$$630$$ 0 0
$$631$$ −30.0000 −1.19428 −0.597141 0.802137i $$-0.703697\pi$$
−0.597141 + 0.802137i $$0.703697\pi$$
$$632$$ 0 0
$$633$$ 2.00000 3.46410i 0.0794929 0.137686i
$$634$$ 0 0
$$635$$ 16.0000 + 27.7128i 0.634941 + 1.09975i
$$636$$ 0 0
$$637$$ −5.00000 + 34.6410i −0.198107 + 1.37253i
$$638$$ 0 0
$$639$$ 7.00000 + 12.1244i 0.276916 + 0.479632i
$$640$$ 0 0
$$641$$ −11.0000 + 19.0526i −0.434474 + 0.752531i −0.997253 0.0740768i $$-0.976399\pi$$
0.562779 + 0.826608i $$0.309732\pi$$
$$642$$ 0 0
$$643$$ −1.00000 −0.0394362 −0.0197181 0.999806i $$-0.506277\pi$$
−0.0197181 + 0.999806i $$0.506277\pi$$
$$644$$ 0 0
$$645$$ −40.0000 −1.57500
$$646$$ 0 0
$$647$$ −14.0000 + 24.2487i −0.550397 + 0.953315i 0.447849 + 0.894109i $$0.352190\pi$$
−0.998246 + 0.0592060i $$0.981143\pi$$
$$648$$ 0 0
$$649$$ 3.00000 + 5.19615i 0.117760 + 0.203967i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 5.00000 + 8.66025i 0.195665 + 0.338902i 0.947118 0.320884i $$-0.103980\pi$$
−0.751453 + 0.659786i $$0.770647\pi$$
$$654$$ 0 0
$$655$$ −8.00000 + 13.8564i −0.312586 + 0.541415i
$$656$$ 0 0
$$657$$ 16.0000 0.624219
$$658$$ 0 0
$$659$$ −30.0000 −1.16863 −0.584317 0.811525i $$-0.698638\pi$$
−0.584317 + 0.811525i $$0.698638\pi$$
$$660$$ 0 0
$$661$$ −9.00000 + 15.5885i −0.350059 + 0.606321i −0.986260 0.165203i $$-0.947172\pi$$
0.636200 + 0.771524i $$0.280505\pi$$
$$662$$ 0 0
$$663$$ −2.50000 4.33013i −0.0970920 0.168168i
$$664$$ 0 0
$$665$$ 12.0000 + 62.3538i 0.465340 + 2.41798i
$$666$$ 0 0
$$667$$ 16.0000 + 27.7128i 0.619522 + 1.07304i
$$668$$ 0 0
$$669$$ 3.00000 5.19615i 0.115987 0.200895i
$$670$$ 0 0
$$671$$ 24.0000 0.926510
$$672$$ 0 0
$$673$$ 28.0000 1.07932 0.539660 0.841883i $$-0.318553\pi$$
0.539660 + 0.841883i $$0.318553\pi$$
$$674$$ 0 0
$$675$$ 27.5000 47.6314i 1.05848 1.83333i
$$676$$ 0 0
$$677$$ 4.00000 + 6.92820i 0.153732 + 0.266272i 0.932597 0.360920i $$-0.117537\pi$$
−0.778864 + 0.627192i $$0.784204\pi$$
$$678$$ 0 0
$$679$$ −36.0000 + 31.1769i −1.38155 + 1.19646i
$$680$$ 0 0
$$681$$ −12.5000 21.6506i −0.479001 0.829654i
$$682$$ 0 0
$$683$$ 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i $$-0.701728\pi$$
0.993940 + 0.109926i $$0.0350613\pi$$
$$684$$ 0 0
$$685$$ 28.0000 1.06983
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ 0 0
$$689$$ 7.50000 12.9904i 0.285727 0.494894i
$$690$$ 0 0
$$691$$ −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i $$-0.215292\pi$$
−0.932024 + 0.362397i $$0.881959\pi$$
$$692$$ 0 0
$$693$$ −12.0000 + 10.3923i −0.455842 + 0.394771i
$$694$$ 0 0
$$695$$ −2.00000 3.46410i −0.0758643 0.131401i
$$696$$ 0 0
$$697$$ −4.00000 + 6.92820i −0.151511 + 0.262424i
$$698$$ 0 0
$$699$$ 28.0000 1.05906
$$700$$ 0 0
$$701$$ 31.0000 1.17085 0.585427 0.810725i $$-0.300927\pi$$
0.585427 + 0.810725i $$0.300927\pi$$
$$702$$ 0 0
$$703$$ 24.0000 41.5692i 0.905177 1.56781i
$$704$$ 0 0
$$705$$ −4.00000 6.92820i −0.150649 0.260931i
$$706$$ 0 0
$$707$$ 3.00000 + 15.5885i 0.112827 + 0.586264i
$$708$$ 0 0
$$709$$ 25.0000 + 43.3013i 0.938895 + 1.62621i 0.767537 + 0.641004i $$0.221482\pi$$
0.171358 + 0.985209i $$0.445185\pi$$
$$710$$ 0 0
$$711$$ 15.0000 25.9808i 0.562544 0.974355i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −60.0000 −2.24387
$$716$$ 0 0
$$717$$ −1.00000 + 1.73205i −0.0373457 + 0.0646846i
$$718$$ 0 0
$$719$$ 17.5000 + 30.3109i 0.652640 + 1.13041i 0.982480 + 0.186369i $$0.0596719\pi$$
−0.329840 + 0.944037i $$0.606995\pi$$
$$720$$ 0 0
$$721$$ 10.0000 + 3.46410i 0.372419 + 0.129010i
$$722$$ 0 0
$$723$$ 4.00000 + 6.92820i 0.148762 + 0.257663i
$$724$$ 0 0
$$725$$ −44.0000 + 76.2102i −1.63412 + 2.83038i
$$726$$ 0 0
$$727$$ 18.0000 0.667583 0.333792 0.942647i $$-0.391672\pi$$
0.333792 + 0.942647i $$0.391672\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 5.00000 8.66025i 0.184932 0.320311i
$$732$$ 0 0
$$733$$ −1.50000 2.59808i −0.0554038 0.0959621i 0.836993 0.547213i $$-0.184311\pi$$
−0.892397 + 0.451251i $$0.850978\pi$$
$$734$$ 0 0
$$735$$ −4.00000 + 27.7128i −0.147542 + 1.02220i
$$736$$ 0 0
$$737$$ 21.0000 + 36.3731i 0.773545 + 1.33982i
$$738$$ 0 0
$$739$$ −15.0000 + 25.9808i −0.551784 + 0.955718i 0.446362 + 0.894852i $$0.352719\pi$$
−0.998146 + 0.0608653i $$0.980614\pi$$
$$740$$ 0 0
$$741$$ −30.0000 −1.10208
$$742$$ 0 0
$$743$$ 1.00000 0.0366864 0.0183432 0.999832i $$-0.494161\pi$$
0.0183432 + 0.999832i $$0.494161\pi$$
$$744$$ 0 0
$$745$$ −22.0000 + 38.1051i −0.806018 + 1.39606i
$$746$$ 0 0
$$747$$ 12.0000 + 20.7846i 0.439057 + 0.760469i
$$748$$ 0 0
$$749$$ 2.50000 + 0.866025i 0.0913480 + 0.0316439i
$$750$$ 0 0
$$751$$ −1.50000 2.59808i −0.0547358 0.0948051i 0.837359 0.546653i $$-0.184098\pi$$
−0.892095 + 0.451848i $$0.850765\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −40.0000 −1.45575
$$756$$ 0 0
$$757$$ 9.00000 0.327111 0.163555 0.986534i $$-0.447704\pi$$
0.163555 + 0.986534i $$0.447704\pi$$
$$758$$ 0 0
$$759$$ −6.00000 + 10.3923i −0.217786 + 0.377217i
$$760$$ 0 0
$$761$$ −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i $$-0.863060\pi$$
0.0932544 0.995642i $$-0.470273\pi$$
$$762$$ 0 0
$$763$$ 4.00000 + 20.7846i 0.144810 + 0.752453i
$$764$$ 0 0
$$765$$ 4.00000 + 6.92820i 0.144620 + 0.250490i
$$766$$ 0 0
$$767$$ 5.00000 8.66025i 0.180540 0.312704i
$$768$$ 0 0
$$769$$ 1.00000 0.0360609 0.0180305 0.999837i $$-0.494260\pi$$
0.0180305 + 0.999837i $$0.494260\pi$$
$$770$$ 0 0
$$771$$ 3.00000 0.108042
$$772$$ 0 0
$$773$$ −4.50000 + 7.79423i −0.161854 + 0.280339i −0.935534 0.353238i $$-0.885081\pi$$
0.773680 + 0.633577i $$0.218414\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 16.0000 13.8564i 0.573997 0.497096i
$$778$$ 0 0
$$779$$ 24.0000 + 41.5692i 0.859889 + 1.48937i
$$780$$ 0 0
$$781$$ 10.5000 18.1865i 0.375720 0.650765i
$$782$$ 0 0
$$783$$ −40.0000 −1.42948
$$784$$ 0 0
$$785$$ −4.00000 −0.142766
$$786$$ 0 0
$$787$$ −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i $$-0.856046\pi$$
0.828176 + 0.560469i $$0.189379\pi$$
$$788$$ 0 0
$$789$$ −2.00000 3.46410i −0.0712019 0.123325i
$$790$$ 0 0
$$791$$ 16.0000 13.8564i 0.568895 0.492677i
$$792$$ 0 0
$$793$$ −20.0000 34.6410i −0.710221 1.23014i
$$794$$ 0 0