# Properties

 Label 144.3.o.a.79.2 Level $144$ Weight $3$ Character 144.79 Analytic conductor $3.924$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 144.o (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.92371580679$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.856615824.2 Defining polynomial: $$x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{2}\cdot 3^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 79.2 Root $$-0.385731i$$ of defining polynomial Character $$\chi$$ $$=$$ 144.79 Dual form 144.3.o.a.31.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.28651 - 2.71015i) q^{3} +(-0.454613 - 0.787412i) q^{5} +(-6.10709 - 3.52593i) q^{7} +(-5.68980 + 6.97325i) q^{9} +O(q^{10})$$ $$q+(-1.28651 - 2.71015i) q^{3} +(-0.454613 - 0.787412i) q^{5} +(-6.10709 - 3.52593i) q^{7} +(-5.68980 + 6.97325i) q^{9} +(-6.96661 - 4.02218i) q^{11} +(3.35952 + 5.81886i) q^{13} +(-1.54914 + 2.24508i) q^{15} -26.3462 q^{17} -20.5603i q^{19} +(-1.69897 + 21.0873i) q^{21} +(-21.8305 + 12.6038i) q^{23} +(12.0867 - 20.9347i) q^{25} +(26.2185 + 6.44905i) q^{27} +(15.1693 - 26.2741i) q^{29} +(-0.120040 + 0.0693050i) q^{31} +(-1.93809 + 24.0551i) q^{33} +6.41173i q^{35} +69.7588 q^{37} +(11.4479 - 16.5908i) q^{39} +(-29.3794 - 50.8866i) q^{41} +(2.45853 + 1.41943i) q^{43} +(8.07748 + 1.31009i) q^{45} +(70.7583 + 40.8523i) q^{47} +(0.364383 + 0.631130i) q^{49} +(33.8946 + 71.4022i) q^{51} -30.0259 q^{53} +7.31413i q^{55} +(-55.7213 + 26.4509i) q^{57} +(-77.1442 + 44.5392i) q^{59} +(24.0688 - 41.6885i) q^{61} +(59.3353 - 22.5244i) q^{63} +(3.05456 - 5.29066i) q^{65} +(44.0829 - 25.4513i) q^{67} +(62.2432 + 42.9488i) q^{69} -68.4355i q^{71} -22.1474 q^{73} +(-72.2857 - 5.82397i) q^{75} +(28.3638 + 49.1276i) q^{77} +(-34.4343 - 19.8807i) q^{79} +(-16.2524 - 79.3527i) q^{81} +(-23.0801 - 13.3253i) q^{83} +(11.9773 + 20.7453i) q^{85} +(-90.7221 - 7.30936i) q^{87} -25.7926 q^{89} -47.3818i q^{91} +(0.342259 + 0.236164i) q^{93} +(-16.1894 + 9.34695i) q^{95} +(-52.3697 + 90.7070i) q^{97} +(67.6863 - 25.6946i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + O(q^{10})$$ $$8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + 18q^{11} + 5q^{13} - 21q^{15} + 6q^{17} - 33q^{21} - 81q^{23} - 23q^{25} + 108q^{27} + 69q^{29} + 45q^{31} + 72q^{33} - 20q^{37} - 141q^{39} + 54q^{41} - 117q^{45} + 207q^{47} + 41q^{49} - 141q^{51} - 252q^{53} - 273q^{57} - 306q^{59} + 7q^{61} + 441q^{63} + 93q^{65} + 12q^{67} + 189q^{69} + 74q^{73} - 387q^{75} + 207q^{77} + 33q^{79} + 117q^{81} + 549q^{83} - 30q^{85} - 87q^{87} - 168q^{89} - 27q^{93} - 684q^{95} - 10q^{97} + 585q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$$.

 $$n$$ $$37$$ $$65$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$

## 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
$$3$$ −1.28651 2.71015i −0.428836 0.903382i
$$4$$ 0 0
$$5$$ −0.454613 0.787412i −0.0909226 0.157482i 0.816977 0.576670i $$-0.195648\pi$$
−0.907900 + 0.419188i $$0.862315\pi$$
$$6$$ 0 0
$$7$$ −6.10709 3.52593i −0.872442 0.503704i −0.00428285 0.999991i $$-0.501363\pi$$
−0.868159 + 0.496286i $$0.834697\pi$$
$$8$$ 0 0
$$9$$ −5.68980 + 6.97325i −0.632200 + 0.774806i
$$10$$ 0 0
$$11$$ −6.96661 4.02218i −0.633329 0.365652i 0.148711 0.988881i $$-0.452487\pi$$
−0.782040 + 0.623228i $$0.785821\pi$$
$$12$$ 0 0
$$13$$ 3.35952 + 5.81886i 0.258425 + 0.447605i 0.965820 0.259213i $$-0.0834632\pi$$
−0.707395 + 0.706818i $$0.750130\pi$$
$$14$$ 0 0
$$15$$ −1.54914 + 2.24508i −0.103276 + 0.149672i
$$16$$ 0 0
$$17$$ −26.3462 −1.54978 −0.774889 0.632097i $$-0.782194\pi$$
−0.774889 + 0.632097i $$0.782194\pi$$
$$18$$ 0 0
$$19$$ 20.5603i 1.08212i −0.840984 0.541059i $$-0.818023\pi$$
0.840984 0.541059i $$-0.181977\pi$$
$$20$$ 0 0
$$21$$ −1.69897 + 21.0873i −0.0809035 + 1.00416i
$$22$$ 0 0
$$23$$ −21.8305 + 12.6038i −0.949150 + 0.547992i −0.892817 0.450420i $$-0.851274\pi$$
−0.0563333 + 0.998412i $$0.517941\pi$$
$$24$$ 0 0
$$25$$ 12.0867 20.9347i 0.483466 0.837388i
$$26$$ 0 0
$$27$$ 26.2185 + 6.44905i 0.971056 + 0.238854i
$$28$$ 0 0
$$29$$ 15.1693 26.2741i 0.523081 0.906002i −0.476558 0.879143i $$-0.658116\pi$$
0.999639 0.0268597i $$-0.00855072\pi$$
$$30$$ 0 0
$$31$$ −0.120040 + 0.0693050i −0.00387225 + 0.00223565i −0.501935 0.864905i $$-0.667378\pi$$
0.498063 + 0.867141i $$0.334045\pi$$
$$32$$ 0 0
$$33$$ −1.93809 + 24.0551i −0.0587300 + 0.728943i
$$34$$ 0 0
$$35$$ 6.41173i 0.183192i
$$36$$ 0 0
$$37$$ 69.7588 1.88537 0.942687 0.333679i $$-0.108290\pi$$
0.942687 + 0.333679i $$0.108290\pi$$
$$38$$ 0 0
$$39$$ 11.4479 16.5908i 0.293537 0.425405i
$$40$$ 0 0
$$41$$ −29.3794 50.8866i −0.716571 1.24114i −0.962351 0.271811i $$-0.912377\pi$$
0.245780 0.969326i $$-0.420956\pi$$
$$42$$ 0 0
$$43$$ 2.45853 + 1.41943i 0.0571751 + 0.0330100i 0.528315 0.849048i $$-0.322824\pi$$
−0.471140 + 0.882058i $$0.656157\pi$$
$$44$$ 0 0
$$45$$ 8.07748 + 1.31009i 0.179500 + 0.0291131i
$$46$$ 0 0
$$47$$ 70.7583 + 40.8523i 1.50550 + 0.869198i 0.999980 + 0.00638063i $$0.00203103\pi$$
0.505516 + 0.862817i $$0.331302\pi$$
$$48$$ 0 0
$$49$$ 0.364383 + 0.631130i 0.00743639 + 0.0128802i
$$50$$ 0 0
$$51$$ 33.8946 + 71.4022i 0.664600 + 1.40004i
$$52$$ 0 0
$$53$$ −30.0259 −0.566526 −0.283263 0.959042i $$-0.591417\pi$$
−0.283263 + 0.959042i $$0.591417\pi$$
$$54$$ 0 0
$$55$$ 7.31413i 0.132984i
$$56$$ 0 0
$$57$$ −55.7213 + 26.4509i −0.977567 + 0.464051i
$$58$$ 0 0
$$59$$ −77.1442 + 44.5392i −1.30753 + 0.754902i −0.981683 0.190520i $$-0.938983\pi$$
−0.325846 + 0.945423i $$0.605649\pi$$
$$60$$ 0 0
$$61$$ 24.0688 41.6885i 0.394571 0.683417i −0.598475 0.801141i $$-0.704226\pi$$
0.993046 + 0.117724i $$0.0375598\pi$$
$$62$$ 0 0
$$63$$ 59.3353 22.5244i 0.941830 0.357531i
$$64$$ 0 0
$$65$$ 3.05456 5.29066i 0.0469933 0.0813948i
$$66$$ 0 0
$$67$$ 44.0829 25.4513i 0.657953 0.379870i −0.133543 0.991043i $$-0.542636\pi$$
0.791497 + 0.611173i $$0.209302\pi$$
$$68$$ 0 0
$$69$$ 62.2432 + 42.9488i 0.902076 + 0.622447i
$$70$$ 0 0
$$71$$ 68.4355i 0.963881i −0.876204 0.481940i $$-0.839932\pi$$
0.876204 0.481940i $$-0.160068\pi$$
$$72$$ 0 0
$$73$$ −22.1474 −0.303389 −0.151695 0.988427i $$-0.548473\pi$$
−0.151695 + 0.988427i $$0.548473\pi$$
$$74$$ 0 0
$$75$$ −72.2857 5.82397i −0.963809 0.0776529i
$$76$$ 0 0
$$77$$ 28.3638 + 49.1276i 0.368362 + 0.638021i
$$78$$ 0 0
$$79$$ −34.4343 19.8807i −0.435877 0.251654i 0.265970 0.963981i $$-0.414308\pi$$
−0.701847 + 0.712327i $$0.747641\pi$$
$$80$$ 0 0
$$81$$ −16.2524 79.3527i −0.200647 0.979664i
$$82$$ 0 0
$$83$$ −23.0801 13.3253i −0.278073 0.160546i 0.354478 0.935065i $$-0.384659\pi$$
−0.632551 + 0.774519i $$0.717992\pi$$
$$84$$ 0 0
$$85$$ 11.9773 + 20.7453i 0.140910 + 0.244063i
$$86$$ 0 0
$$87$$ −90.7221 7.30936i −1.04278 0.0840157i
$$88$$ 0 0
$$89$$ −25.7926 −0.289804 −0.144902 0.989446i $$-0.546287\pi$$
−0.144902 + 0.989446i $$0.546287\pi$$
$$90$$ 0 0
$$91$$ 47.3818i 0.520679i
$$92$$ 0 0
$$93$$ 0.342259 + 0.236164i 0.00368020 + 0.00253940i
$$94$$ 0 0
$$95$$ −16.1894 + 9.34695i −0.170415 + 0.0983890i
$$96$$ 0 0
$$97$$ −52.3697 + 90.7070i −0.539894 + 0.935123i 0.459016 + 0.888428i $$0.348202\pi$$
−0.998909 + 0.0466950i $$0.985131\pi$$
$$98$$ 0 0
$$99$$ 67.6863 25.6946i 0.683700 0.259541i
$$100$$ 0 0
$$101$$ 20.4790 35.4707i 0.202763 0.351195i −0.746655 0.665212i $$-0.768341\pi$$
0.949418 + 0.314016i $$0.101675\pi$$
$$102$$ 0 0
$$103$$ −125.278 + 72.3293i −1.21629 + 0.702227i −0.964123 0.265456i $$-0.914477\pi$$
−0.252169 + 0.967683i $$0.581144\pi$$
$$104$$ 0 0
$$105$$ 17.3767 8.24874i 0.165493 0.0785595i
$$106$$ 0 0
$$107$$ 177.858i 1.66222i −0.556105 0.831112i $$-0.687705\pi$$
0.556105 0.831112i $$-0.312295\pi$$
$$108$$ 0 0
$$109$$ −142.616 −1.30840 −0.654200 0.756322i $$-0.726994\pi$$
−0.654200 + 0.756322i $$0.726994\pi$$
$$110$$ 0 0
$$111$$ −89.7452 189.057i −0.808516 1.70321i
$$112$$ 0 0
$$113$$ 100.147 + 173.459i 0.886254 + 1.53504i 0.844270 + 0.535918i $$0.180034\pi$$
0.0419835 + 0.999118i $$0.486632\pi$$
$$114$$ 0 0
$$115$$ 19.8488 + 11.4597i 0.172598 + 0.0996497i
$$116$$ 0 0
$$117$$ −59.6914 9.68136i −0.510183 0.0827467i
$$118$$ 0 0
$$119$$ 160.899 + 92.8950i 1.35209 + 0.780630i
$$120$$ 0 0
$$121$$ −28.1442 48.7472i −0.232597 0.402869i
$$122$$ 0 0
$$123$$ −100.113 + 145.089i −0.813930 + 1.17958i
$$124$$ 0 0
$$125$$ −44.7096 −0.357677
$$126$$ 0 0
$$127$$ 181.723i 1.43089i 0.698670 + 0.715445i $$0.253776\pi$$
−0.698670 + 0.715445i $$0.746224\pi$$
$$128$$ 0 0
$$129$$ 0.683954 8.48908i 0.00530197 0.0658068i
$$130$$ 0 0
$$131$$ −52.9361 + 30.5627i −0.404092 + 0.233303i −0.688248 0.725475i $$-0.741620\pi$$
0.284156 + 0.958778i $$0.408287\pi$$
$$132$$ 0 0
$$133$$ −72.4940 + 125.563i −0.545068 + 0.944085i
$$134$$ 0 0
$$135$$ −6.84120 23.5766i −0.0506756 0.174641i
$$136$$ 0 0
$$137$$ 18.1131 31.3729i 0.132213 0.228999i −0.792317 0.610110i $$-0.791125\pi$$
0.924529 + 0.381111i $$0.124458\pi$$
$$138$$ 0 0
$$139$$ 154.652 89.2885i 1.11261 0.642363i 0.173103 0.984904i $$-0.444621\pi$$
0.939503 + 0.342541i $$0.111287\pi$$
$$140$$ 0 0
$$141$$ 19.6847 244.322i 0.139608 1.73278i
$$142$$ 0 0
$$143$$ 54.0504i 0.377975i
$$144$$ 0 0
$$145$$ −27.5847 −0.190239
$$146$$ 0 0
$$147$$ 1.24167 1.79949i 0.00844676 0.0122414i
$$148$$ 0 0
$$149$$ 120.043 + 207.921i 0.805660 + 1.39544i 0.915845 + 0.401533i $$0.131522\pi$$
−0.110185 + 0.993911i $$0.535144\pi$$
$$150$$ 0 0
$$151$$ 98.1393 + 56.6607i 0.649929 + 0.375237i 0.788429 0.615126i $$-0.210895\pi$$
−0.138500 + 0.990362i $$0.544228\pi$$
$$152$$ 0 0
$$153$$ 149.905 183.719i 0.979769 1.20078i
$$154$$ 0 0
$$155$$ 0.109143 + 0.0630139i 0.000704150 + 0.000406541i
$$156$$ 0 0
$$157$$ −60.3604 104.547i −0.384461 0.665907i 0.607233 0.794524i $$-0.292280\pi$$
−0.991694 + 0.128617i $$0.958946\pi$$
$$158$$ 0 0
$$159$$ 38.6285 + 81.3746i 0.242947 + 0.511790i
$$160$$ 0 0
$$161$$ 177.761 1.10410
$$162$$ 0 0
$$163$$ 20.3498i 0.124845i −0.998050 0.0624226i $$-0.980117\pi$$
0.998050 0.0624226i $$-0.0198827\pi$$
$$164$$ 0 0
$$165$$ 19.8224 9.40969i 0.120136 0.0570284i
$$166$$ 0 0
$$167$$ 151.530 87.4858i 0.907365 0.523867i 0.0277823 0.999614i $$-0.491155\pi$$
0.879582 + 0.475747i $$0.157822\pi$$
$$168$$ 0 0
$$169$$ 61.9272 107.261i 0.366433 0.634681i
$$170$$ 0 0
$$171$$ 143.372 + 116.984i 0.838431 + 0.684115i
$$172$$ 0 0
$$173$$ 55.9175 96.8520i 0.323223 0.559838i −0.657928 0.753080i $$-0.728567\pi$$
0.981151 + 0.193243i $$0.0619004\pi$$
$$174$$ 0 0
$$175$$ −147.629 + 85.2334i −0.843592 + 0.487048i
$$176$$ 0 0
$$177$$ 219.955 + 151.772i 1.24268 + 0.857470i
$$178$$ 0 0
$$179$$ 18.6939i 0.104435i −0.998636 0.0522176i $$-0.983371\pi$$
0.998636 0.0522176i $$-0.0166289\pi$$
$$180$$ 0 0
$$181$$ −98.0536 −0.541733 −0.270866 0.962617i $$-0.587310\pi$$
−0.270866 + 0.962617i $$0.587310\pi$$
$$182$$ 0 0
$$183$$ −143.947 11.5976i −0.786594 0.0633748i
$$184$$ 0 0
$$185$$ −31.7132 54.9290i −0.171423 0.296913i
$$186$$ 0 0
$$187$$ 183.544 + 105.969i 0.981519 + 0.566680i
$$188$$ 0 0
$$189$$ −137.380 131.830i −0.726878 0.697511i
$$190$$ 0 0
$$191$$ 240.713 + 138.976i 1.26028 + 0.727621i 0.973128 0.230265i $$-0.0739592\pi$$
0.287149 + 0.957886i $$0.407293\pi$$
$$192$$ 0 0
$$193$$ 81.1285 + 140.519i 0.420355 + 0.728076i 0.995974 0.0896419i $$-0.0285722\pi$$
−0.575619 + 0.817718i $$0.695239\pi$$
$$194$$ 0 0
$$195$$ −18.2682 1.47184i −0.0936830 0.00754792i
$$196$$ 0 0
$$197$$ −106.182 −0.538993 −0.269496 0.963001i $$-0.586857\pi$$
−0.269496 + 0.963001i $$0.586857\pi$$
$$198$$ 0 0
$$199$$ 63.3880i 0.318532i 0.987236 + 0.159266i $$0.0509128\pi$$
−0.987236 + 0.159266i $$0.949087\pi$$
$$200$$ 0 0
$$201$$ −125.690 86.7278i −0.625321 0.431482i
$$202$$ 0 0
$$203$$ −185.281 + 106.972i −0.912715 + 0.526956i
$$204$$ 0 0
$$205$$ −26.7125 + 46.2674i −0.130305 + 0.225695i
$$206$$ 0 0
$$207$$ 36.3213 223.942i 0.175465 1.08185i
$$208$$ 0 0
$$209$$ −82.6970 + 143.235i −0.395679 + 0.685337i
$$210$$ 0 0
$$211$$ −4.98019 + 2.87531i −0.0236028 + 0.0136271i −0.511755 0.859131i $$-0.671004\pi$$
0.488152 + 0.872759i $$0.337671\pi$$
$$212$$ 0 0
$$213$$ −185.470 + 88.0428i −0.870753 + 0.413347i
$$214$$ 0 0
$$215$$ 2.58117i 0.0120054i
$$216$$ 0 0
$$217$$ 0.977459 0.00450442
$$218$$ 0 0
$$219$$ 28.4928 + 60.0228i 0.130104 + 0.274076i
$$220$$ 0 0
$$221$$ −88.5107 153.305i −0.400501 0.693688i
$$222$$ 0 0
$$223$$ −179.786 103.799i −0.806215 0.465469i 0.0394246 0.999223i $$-0.487448\pi$$
−0.845640 + 0.533754i $$0.820781\pi$$
$$224$$ 0 0
$$225$$ 77.2123 + 203.397i 0.343166 + 0.903989i
$$226$$ 0 0
$$227$$ −78.8889 45.5465i −0.347528 0.200646i 0.316068 0.948737i $$-0.397637\pi$$
−0.663596 + 0.748091i $$0.730971\pi$$
$$228$$ 0 0
$$229$$ 2.04945 + 3.54974i 0.00894954 + 0.0155011i 0.870465 0.492229i $$-0.163818\pi$$
−0.861516 + 0.507731i $$0.830485\pi$$
$$230$$ 0 0
$$231$$ 96.6528 140.073i 0.418410 0.606378i
$$232$$ 0 0
$$233$$ 171.761 0.737170 0.368585 0.929594i $$-0.379842\pi$$
0.368585 + 0.929594i $$0.379842\pi$$
$$234$$ 0 0
$$235$$ 74.2879i 0.316119i
$$236$$ 0 0
$$237$$ −9.57951 + 118.899i −0.0404199 + 0.501682i
$$238$$ 0 0
$$239$$ −78.9068 + 45.5569i −0.330154 + 0.190614i −0.655909 0.754840i $$-0.727715\pi$$
0.325755 + 0.945454i $$0.394381\pi$$
$$240$$ 0 0
$$241$$ 37.2352 64.4933i 0.154503 0.267607i −0.778375 0.627800i $$-0.783956\pi$$
0.932878 + 0.360193i $$0.117289\pi$$
$$242$$ 0 0
$$243$$ −194.149 + 146.134i −0.798966 + 0.601376i
$$244$$ 0 0
$$245$$ 0.331306 0.573840i 0.00135227 0.00234220i
$$246$$ 0 0
$$247$$ 119.637 69.0726i 0.484362 0.279646i
$$248$$ 0 0
$$249$$ −6.42081 + 79.6935i −0.0257864 + 0.320054i
$$250$$ 0 0
$$251$$ 216.868i 0.864014i −0.901870 0.432007i $$-0.857806\pi$$
0.901870 0.432007i $$-0.142194\pi$$
$$252$$ 0 0
$$253$$ 202.779 0.801499
$$254$$ 0 0
$$255$$ 40.8140 59.1494i 0.160055 0.231958i
$$256$$ 0 0
$$257$$ −143.577 248.682i −0.558665 0.967636i −0.997608 0.0691212i $$-0.977980\pi$$
0.438943 0.898515i $$-0.355353\pi$$
$$258$$ 0 0
$$259$$ −426.023 245.965i −1.64488 0.949671i
$$260$$ 0 0
$$261$$ 96.9052 + 255.274i 0.371284 + 0.978060i
$$262$$ 0 0
$$263$$ −361.740 208.851i −1.37544 0.794108i −0.383830 0.923404i $$-0.625395\pi$$
−0.991606 + 0.129295i $$0.958728\pi$$
$$264$$ 0 0
$$265$$ 13.6502 + 23.6428i 0.0515100 + 0.0892180i
$$266$$ 0 0
$$267$$ 33.1823 + 69.9016i 0.124278 + 0.261804i
$$268$$ 0 0
$$269$$ −489.868 −1.82107 −0.910535 0.413433i $$-0.864330\pi$$
−0.910535 + 0.413433i $$0.864330\pi$$
$$270$$ 0 0
$$271$$ 325.133i 1.19975i −0.800093 0.599876i $$-0.795216\pi$$
0.800093 0.599876i $$-0.204784\pi$$
$$272$$ 0 0
$$273$$ −128.412 + 60.9570i −0.470372 + 0.223286i
$$274$$ 0 0
$$275$$ −168.406 + 97.2293i −0.612386 + 0.353561i
$$276$$ 0 0
$$277$$ 86.0882 149.109i 0.310788 0.538300i −0.667745 0.744390i $$-0.732740\pi$$
0.978533 + 0.206089i $$0.0660738\pi$$
$$278$$ 0 0
$$279$$ 0.199721 1.23140i 0.000715846 0.00441362i
$$280$$ 0 0
$$281$$ −60.1019 + 104.100i −0.213886 + 0.370461i −0.952927 0.303199i $$-0.901945\pi$$
0.739042 + 0.673660i $$0.235279\pi$$
$$282$$ 0 0
$$283$$ 95.8910 55.3627i 0.338837 0.195628i −0.320920 0.947106i $$-0.603992\pi$$
0.659758 + 0.751478i $$0.270659\pi$$
$$284$$ 0 0
$$285$$ 46.1594 + 31.8507i 0.161963 + 0.111757i
$$286$$ 0 0
$$287$$ 414.359i 1.44376i
$$288$$ 0 0
$$289$$ 405.124 1.40181
$$290$$ 0 0
$$291$$ 313.203 + 25.2344i 1.07630 + 0.0867161i
$$292$$ 0 0
$$293$$ 42.3365 + 73.3289i 0.144493 + 0.250269i 0.929184 0.369618i $$-0.120512\pi$$
−0.784691 + 0.619888i $$0.787178\pi$$
$$294$$ 0 0
$$295$$ 70.1415 + 40.4962i 0.237768 + 0.137275i
$$296$$ 0 0
$$297$$ −156.715 150.383i −0.527660 0.506342i
$$298$$ 0 0
$$299$$ −146.680 84.6856i −0.490568 0.283229i
$$300$$ 0 0
$$301$$ −10.0096 17.3372i −0.0332546 0.0575987i
$$302$$ 0 0
$$303$$ −122.477 9.86784i −0.404215 0.0325671i
$$304$$ 0 0
$$305$$ −43.7680 −0.143502
$$306$$ 0 0
$$307$$ 220.477i 0.718167i −0.933306 0.359083i $$-0.883089\pi$$
0.933306 0.359083i $$-0.116911\pi$$
$$308$$ 0 0
$$309$$ 357.194 + 246.470i 1.15597 + 0.797637i
$$310$$ 0 0
$$311$$ 268.968 155.289i 0.864849 0.499321i −0.000784168 1.00000i $$-0.500250\pi$$
0.865633 + 0.500679i $$0.166916\pi$$
$$312$$ 0 0
$$313$$ −65.5787 + 113.586i −0.209516 + 0.362893i −0.951562 0.307456i $$-0.900522\pi$$
0.742046 + 0.670349i $$0.233856\pi$$
$$314$$ 0 0
$$315$$ −44.7106 36.4815i −0.141938 0.115814i
$$316$$ 0 0
$$317$$ 169.980 294.414i 0.536214 0.928750i −0.462889 0.886416i $$-0.653187\pi$$
0.999104 0.0423342i $$-0.0134794\pi$$
$$318$$ 0 0
$$319$$ −211.358 + 122.028i −0.662564 + 0.382532i
$$320$$ 0 0
$$321$$ −482.022 + 228.816i −1.50162 + 0.712822i
$$322$$ 0 0
$$323$$ 541.685i 1.67704i
$$324$$ 0 0
$$325$$ 162.422 0.499759
$$326$$ 0 0
$$327$$ 183.476 + 386.509i 0.561089 + 1.18199i
$$328$$ 0 0
$$329$$ −288.085 498.978i −0.875638 1.51665i
$$330$$ 0 0
$$331$$ 394.447 + 227.734i 1.19168 + 0.688018i 0.958688 0.284460i $$-0.0918143\pi$$
0.232994 + 0.972478i $$0.425148\pi$$
$$332$$ 0 0
$$333$$ −396.913 + 486.446i −1.19193 + 1.46080i
$$334$$ 0 0
$$335$$ −40.0813 23.1409i −0.119646 0.0690774i
$$336$$ 0 0
$$337$$ −21.9543 38.0259i −0.0651462 0.112837i 0.831613 0.555356i $$-0.187418\pi$$
−0.896759 + 0.442520i $$0.854085\pi$$
$$338$$ 0 0
$$339$$ 341.260 494.569i 1.00667 1.45890i
$$340$$ 0 0
$$341$$ 1.11503 0.00326988
$$342$$ 0 0
$$343$$ 340.402i 0.992426i
$$344$$ 0 0
$$345$$ 5.52187 68.5362i 0.0160054 0.198656i
$$346$$ 0 0
$$347$$ 340.283 196.462i 0.980642 0.566174i 0.0781781 0.996939i $$-0.475090\pi$$
0.902464 + 0.430766i $$0.141756\pi$$
$$348$$ 0 0
$$349$$ 271.979 471.082i 0.779310 1.34981i −0.153029 0.988222i $$-0.548903\pi$$
0.932340 0.361584i $$-0.117764\pi$$
$$350$$ 0 0
$$351$$ 50.5555 + 174.228i 0.144033 + 0.496375i
$$352$$ 0 0
$$353$$ −63.7961 + 110.498i −0.180725 + 0.313026i −0.942128 0.335254i $$-0.891178\pi$$
0.761402 + 0.648280i $$0.224511\pi$$
$$354$$ 0 0
$$355$$ −53.8870 + 31.1117i −0.151794 + 0.0876385i
$$356$$ 0 0
$$357$$ 44.7615 555.570i 0.125382 1.55622i
$$358$$ 0 0
$$359$$ 285.077i 0.794085i 0.917800 + 0.397043i $$0.129963\pi$$
−0.917800 + 0.397043i $$0.870037\pi$$
$$360$$ 0 0
$$361$$ −61.7239 −0.170980
$$362$$ 0 0
$$363$$ −95.9043 + 138.988i −0.264199 + 0.382888i
$$364$$ 0 0
$$365$$ 10.0685 + 17.4391i 0.0275849 + 0.0477785i
$$366$$ 0 0
$$367$$ −280.084 161.706i −0.763171 0.440617i 0.0672623 0.997735i $$-0.478574\pi$$
−0.830433 + 0.557119i $$0.811907\pi$$
$$368$$ 0 0
$$369$$ 522.008 + 84.6646i 1.41466 + 0.229443i
$$370$$ 0 0
$$371$$ 183.371 + 105.869i 0.494261 + 0.285362i
$$372$$ 0 0
$$373$$ 257.740 + 446.419i 0.690993 + 1.19683i 0.971513 + 0.236987i $$0.0761597\pi$$
−0.280520 + 0.959848i $$0.590507\pi$$
$$374$$ 0 0
$$375$$ 57.5193 + 121.170i 0.153385 + 0.323119i
$$376$$ 0 0
$$377$$ 203.847 0.540708
$$378$$ 0 0
$$379$$ 21.2535i 0.0560779i 0.999607 + 0.0280389i $$0.00892624\pi$$
−0.999607 + 0.0280389i $$0.991074\pi$$
$$380$$ 0 0
$$381$$ 492.496 233.788i 1.29264 0.613617i
$$382$$ 0 0
$$383$$ −93.4125 + 53.9317i −0.243897 + 0.140814i −0.616966 0.786989i $$-0.711639\pi$$
0.373070 + 0.927803i $$0.378305\pi$$
$$384$$ 0 0
$$385$$ 25.7891 44.6681i 0.0669847 0.116021i
$$386$$ 0 0
$$387$$ −23.8866 + 9.06765i −0.0617224 + 0.0234306i
$$388$$ 0 0
$$389$$ 75.1474 130.159i 0.193181 0.334599i −0.753122 0.657881i $$-0.771453\pi$$
0.946303 + 0.323282i $$0.104786\pi$$
$$390$$ 0 0
$$391$$ 575.150 332.063i 1.47097 0.849266i
$$392$$ 0 0
$$393$$ 150.932 + 104.145i 0.384051 + 0.265001i
$$394$$ 0 0
$$395$$ 36.1520i 0.0915241i
$$396$$ 0 0
$$397$$ 137.203 0.345600 0.172800 0.984957i $$-0.444719\pi$$
0.172800 + 0.984957i $$0.444719\pi$$
$$398$$ 0 0
$$399$$ 433.559 + 34.9313i 1.08661 + 0.0875472i
$$400$$ 0 0
$$401$$ −133.366 230.996i −0.332583 0.576050i 0.650435 0.759562i $$-0.274587\pi$$
−0.983017 + 0.183512i $$0.941253\pi$$
$$402$$ 0 0
$$403$$ −0.806553 0.465664i −0.00200137 0.00115549i
$$404$$ 0 0
$$405$$ −55.0948 + 48.8721i −0.136037 + 0.120672i
$$406$$ 0 0
$$407$$ −485.983 280.582i −1.19406 0.689391i
$$408$$ 0 0
$$409$$ −341.404 591.329i −0.834729 1.44579i −0.894251 0.447565i $$-0.852291\pi$$
0.0595226 0.998227i $$-0.481042\pi$$
$$410$$ 0 0
$$411$$ −108.328 8.72784i −0.263571 0.0212356i
$$412$$ 0 0
$$413$$ 628.169 1.52099
$$414$$ 0 0
$$415$$ 24.2314i 0.0583889i
$$416$$ 0 0
$$417$$ −440.946 304.260i −1.05742 0.729640i
$$418$$ 0 0
$$419$$ 449.030 259.248i 1.07167 0.618730i 0.143034 0.989718i $$-0.454314\pi$$
0.928638 + 0.370988i $$0.120981\pi$$
$$420$$ 0 0
$$421$$ −170.758 + 295.761i −0.405601 + 0.702521i −0.994391 0.105765i $$-0.966271\pi$$
0.588790 + 0.808286i $$0.299604\pi$$
$$422$$ 0 0
$$423$$ −687.474 + 260.974i −1.62523 + 0.616959i
$$424$$ 0 0
$$425$$ −318.438 + 551.550i −0.749265 + 1.29777i
$$426$$ 0 0
$$427$$ −293.981 + 169.730i −0.688481 + 0.397495i
$$428$$ 0 0
$$429$$ −146.484 + 69.5362i −0.341456 + 0.162089i
$$430$$ 0 0
$$431$$ 166.603i 0.386550i −0.981145 0.193275i $$-0.938089\pi$$
0.981145 0.193275i $$-0.0619110\pi$$
$$432$$ 0 0
$$433$$ −677.766 −1.56528 −0.782640 0.622475i $$-0.786127\pi$$
−0.782640 + 0.622475i $$0.786127\pi$$
$$434$$ 0 0
$$435$$ 35.4879 + 74.7586i 0.0815815 + 0.171859i
$$436$$ 0 0
$$437$$ 259.138 + 448.840i 0.592992 + 1.02709i
$$438$$ 0 0
$$439$$ 427.032 + 246.547i 0.972738 + 0.561610i 0.900070 0.435746i $$-0.143515\pi$$
0.0726678 + 0.997356i $$0.476849\pi$$
$$440$$ 0 0
$$441$$ −6.47429 1.05007i −0.0146809 0.00238111i
$$442$$ 0 0
$$443$$ −284.084 164.016i −0.641273 0.370239i 0.143832 0.989602i $$-0.454058\pi$$
−0.785105 + 0.619363i $$0.787391\pi$$
$$444$$ 0 0
$$445$$ 11.7256 + 20.3094i 0.0263497 + 0.0456391i
$$446$$ 0 0
$$447$$ 409.060 592.827i 0.915124 1.32624i
$$448$$ 0 0
$$449$$ 19.0862 0.0425082 0.0212541 0.999774i $$-0.493234\pi$$
0.0212541 + 0.999774i $$0.493234\pi$$
$$450$$ 0 0
$$451$$ 472.677i 1.04806i
$$452$$ 0 0
$$453$$ 27.3020 338.866i 0.0602694 0.748049i
$$454$$ 0 0
$$455$$ −37.3090 + 21.5404i −0.0819978 + 0.0473415i
$$456$$ 0 0
$$457$$ −137.806 + 238.686i −0.301544 + 0.522289i −0.976486 0.215581i $$-0.930835\pi$$
0.674942 + 0.737871i $$0.264169\pi$$
$$458$$ 0 0
$$459$$ −690.759 169.908i −1.50492 0.370170i
$$460$$ 0 0
$$461$$ −199.467 + 345.486i −0.432683 + 0.749428i −0.997103 0.0760589i $$-0.975766\pi$$
0.564421 + 0.825487i $$0.309100\pi$$
$$462$$ 0 0
$$463$$ 15.7881 9.11524i 0.0340995 0.0196873i −0.482853 0.875701i $$-0.660400\pi$$
0.516953 + 0.856014i $$0.327066\pi$$
$$464$$ 0 0
$$465$$ 0.0303633 0.376862i 6.52974e−5 0.000810456i
$$466$$ 0 0
$$467$$ 499.275i 1.06911i 0.845133 + 0.534555i $$0.179521\pi$$
−0.845133 + 0.534555i $$0.820479\pi$$
$$468$$ 0 0
$$469$$ −358.958 −0.765368
$$470$$ 0 0
$$471$$ −205.685 + 298.087i −0.436698 + 0.632880i
$$472$$ 0 0
$$473$$ −11.4184 19.7773i −0.0241404 0.0418124i
$$474$$ 0 0
$$475$$ −430.423 248.505i −0.906153 0.523168i
$$476$$ 0 0
$$477$$ 170.841 209.378i 0.358158 0.438948i
$$478$$ 0 0
$$479$$ 52.4473 + 30.2805i 0.109493 + 0.0632160i 0.553747 0.832685i $$-0.313198\pi$$
−0.444253 + 0.895901i $$0.646531\pi$$
$$480$$ 0 0
$$481$$ 234.356 + 405.917i 0.487227 + 0.843902i
$$482$$ 0 0
$$483$$ −228.691 481.758i −0.473479 0.997428i
$$484$$ 0 0
$$485$$ 95.2317 0.196354
$$486$$ 0 0
$$487$$ 852.354i 1.75021i −0.483931 0.875106i $$-0.660791\pi$$
0.483931 0.875106i $$-0.339209\pi$$
$$488$$ 0 0
$$489$$ −55.1509 + 26.1801i −0.112783 + 0.0535381i
$$490$$ 0 0
$$491$$ 585.457 338.014i 1.19238 0.688419i 0.233532 0.972349i $$-0.424972\pi$$
0.958845 + 0.283930i $$0.0916382\pi$$
$$492$$ 0 0
$$493$$ −399.655 + 692.223i −0.810659 + 1.40410i
$$494$$ 0 0
$$495$$ −51.0033 41.6159i −0.103037 0.0840726i
$$496$$ 0 0
$$497$$ −241.299 + 417.942i −0.485511 + 0.840930i
$$498$$ 0 0
$$499$$ −736.084 + 424.978i −1.47512 + 0.851660i −0.999607 0.0280487i $$-0.991071\pi$$
−0.475512 + 0.879709i $$0.657737\pi$$
$$500$$ 0 0
$$501$$ −432.044 298.117i −0.862363 0.595044i
$$502$$ 0 0
$$503$$ 945.179i 1.87908i −0.342433 0.939542i $$-0.611251\pi$$
0.342433 0.939542i $$-0.388749\pi$$
$$504$$ 0 0
$$505$$ −37.2401 −0.0737428
$$506$$ 0 0
$$507$$ −370.363 29.8397i −0.730499 0.0588554i
$$508$$ 0 0
$$509$$ 125.931 + 218.119i 0.247409 + 0.428524i 0.962806 0.270194i $$-0.0870877\pi$$
−0.715397 + 0.698718i $$0.753754\pi$$
$$510$$ 0 0
$$511$$ 135.256 + 78.0903i 0.264689 + 0.152819i
$$512$$ 0 0
$$513$$ 132.594 539.059i 0.258468 1.05080i
$$514$$ 0 0
$$515$$ 113.906 + 65.7637i 0.221177 + 0.127696i
$$516$$ 0 0
$$517$$ −328.630 569.205i −0.635649 1.10098i
$$518$$ 0 0
$$519$$ −334.421 26.9439i −0.644357 0.0519150i
$$520$$ 0 0
$$521$$ 856.423 1.64381 0.821903 0.569628i $$-0.192913\pi$$
0.821903 + 0.569628i $$0.192913\pi$$
$$522$$ 0 0
$$523$$ 741.634i 1.41804i 0.705189 + 0.709019i $$0.250862\pi$$
−0.705189 + 0.709019i $$0.749138\pi$$
$$524$$ 0 0
$$525$$ 420.920 + 290.442i 0.801753 + 0.553223i
$$526$$ 0 0
$$527$$ 3.16260 1.82593i 0.00600113 0.00346475i
$$528$$ 0 0
$$529$$ 53.2125 92.1667i 0.100591 0.174228i
$$530$$ 0 0
$$531$$ 128.352 791.365i 0.241717 1.49033i
$$532$$ 0 0
$$533$$ 197.402 341.910i 0.370359 0.641481i
$$534$$ 0 0
$$535$$ −140.048 + 80.8565i −0.261771 + 0.151134i
$$536$$ 0 0
$$537$$ −50.6632 + 24.0498i −0.0943449 + 0.0447856i
$$538$$ 0 0
$$539$$ 5.86245i 0.0108765i
$$540$$ 0 0
$$541$$ −434.157 −0.802509 −0.401254 0.915967i $$-0.631426\pi$$
−0.401254 + 0.915967i $$0.631426\pi$$
$$542$$ 0 0
$$543$$ 126.147 + 265.740i 0.232314 + 0.489392i
$$544$$ 0 0
$$545$$ 64.8349 + 112.297i 0.118963 + 0.206050i
$$546$$ 0 0
$$547$$ 235.269 + 135.832i 0.430107 + 0.248323i 0.699392 0.714738i $$-0.253454\pi$$
−0.269285 + 0.963061i $$0.586787\pi$$
$$548$$ 0 0
$$549$$ 153.757 + 405.037i 0.280068 + 0.737772i
$$550$$ 0 0
$$551$$ −540.201 311.885i −0.980402 0.566035i
$$552$$ 0 0
$$553$$ 140.196 + 242.826i 0.253518 + 0.439107i
$$554$$ 0 0
$$555$$ −108.066 + 156.614i −0.194714 + 0.282188i
$$556$$ 0 0
$$557$$ 41.7759 0.0750016 0.0375008 0.999297i $$-0.488060\pi$$
0.0375008 + 0.999297i $$0.488060\pi$$
$$558$$ 0 0
$$559$$ 19.0744i 0.0341224i
$$560$$ 0 0
$$561$$ 51.0614 633.761i 0.0910185 1.12970i
$$562$$ 0 0
$$563$$ 388.403 224.245i 0.689882 0.398303i −0.113686 0.993517i $$-0.536266\pi$$
0.803568 + 0.595213i $$0.202932\pi$$
$$564$$ 0 0
$$565$$ 91.0559 157.713i 0.161161 0.279139i
$$566$$ 0 0
$$567$$ −180.537 + 541.919i −0.318408 + 0.955766i
$$568$$ 0 0
$$569$$ −180.208 + 312.130i −0.316710 + 0.548559i −0.979800 0.199982i $$-0.935912\pi$$
0.663089 + 0.748540i $$0.269245\pi$$
$$570$$ 0 0
$$571$$ 665.784 384.391i 1.16600 0.673189i 0.213263 0.976995i $$-0.431591\pi$$
0.952734 + 0.303806i $$0.0982574\pi$$
$$572$$ 0 0
$$573$$ 66.9656 831.161i 0.116868 1.45054i
$$574$$ 0 0
$$575$$ 609.352i 1.05974i
$$576$$ 0 0
$$577$$ −413.359 −0.716394 −0.358197 0.933646i $$-0.616608\pi$$
−0.358197 + 0.933646i $$0.616608\pi$$
$$578$$ 0 0
$$579$$ 276.454 400.649i 0.477468 0.691966i
$$580$$ 0 0
$$581$$ 93.9682 + 162.758i 0.161735 + 0.280134i
$$582$$ 0 0
$$583$$ 209.179 + 120.769i 0.358797 + 0.207152i
$$584$$ 0 0
$$585$$ 19.5132 + 51.4030i 0.0333560 + 0.0878684i
$$586$$ 0 0
$$587$$ 1.41240 + 0.815451i 0.00240614 + 0.00138918i 0.501203 0.865330i $$-0.332891\pi$$
−0.498796 + 0.866719i $$0.666224\pi$$
$$588$$ 0 0
$$589$$ 1.42493 + 2.46805i 0.00241923 + 0.00419024i
$$590$$ 0 0
$$591$$ 136.603 + 287.768i 0.231139 + 0.486916i
$$592$$ 0 0
$$593$$ 652.407 1.10018 0.550091 0.835105i $$-0.314593\pi$$
0.550091 + 0.835105i $$0.314593\pi$$
$$594$$ 0 0
$$595$$ 168.925i 0.283908i
$$596$$ 0 0
$$597$$ 171.791 81.5491i 0.287757 0.136598i
$$598$$ 0 0
$$599$$ −148.315 + 85.6298i −0.247605 + 0.142955i −0.618667 0.785653i $$-0.712327\pi$$
0.371062 + 0.928608i $$0.378994\pi$$
$$600$$ 0 0
$$601$$ −65.9875 + 114.294i −0.109796 + 0.190173i −0.915688 0.401891i $$-0.868353\pi$$
0.805891 + 0.592063i $$0.201686\pi$$
$$602$$ 0 0
$$603$$ −73.3446 + 452.213i −0.121633 + 0.749939i
$$604$$ 0 0
$$605$$ −25.5894 + 44.3222i −0.0422966 + 0.0732598i
$$606$$ 0 0
$$607$$ 514.763 297.199i 0.848045 0.489619i −0.0119458 0.999929i $$-0.503803\pi$$
0.859991 + 0.510310i $$0.170469\pi$$
$$608$$ 0 0
$$609$$ 528.276 + 364.519i 0.867448 + 0.598553i
$$610$$ 0 0
$$611$$ 548.977i 0.898489i
$$612$$ 0 0
$$613$$ 367.632 0.599727 0.299863 0.953982i $$-0.403059\pi$$
0.299863 + 0.953982i $$0.403059\pi$$
$$614$$ 0 0
$$615$$ 159.757 + 12.8714i 0.259768 + 0.0209292i
$$616$$ 0 0
$$617$$ 21.0806 + 36.5126i 0.0341662 + 0.0591776i 0.882603 0.470119i $$-0.155789\pi$$
−0.848437 + 0.529297i $$0.822456\pi$$
$$618$$ 0 0
$$619$$ 214.298 + 123.725i 0.346200 + 0.199879i 0.663010 0.748610i $$-0.269279\pi$$
−0.316810 + 0.948489i $$0.602612\pi$$
$$620$$ 0 0
$$621$$ −653.644 + 189.668i −1.05257 + 0.305423i
$$622$$ 0 0
$$623$$ 157.518 + 90.9428i 0.252837 + 0.145976i
$$624$$ 0 0
$$625$$ −281.841 488.163i −0.450945 0.781060i
$$626$$ 0 0
$$627$$ 494.579 + 39.8476i 0.788802 + 0.0635528i
$$628$$ 0 0
$$629$$ −1837.88 −2.92191
$$630$$ 0 0
$$631$$ 725.556i 1.14985i 0.818206 + 0.574926i $$0.194969\pi$$
−0.818206 + 0.574926i $$0.805031\pi$$
$$632$$ 0 0
$$633$$ 14.1996 + 9.79793i 0.0224322 + 0.0154786i
$$634$$ 0 0
$$635$$ 143.091 82.6136i 0.225340 0.130100i
$$636$$ 0 0
$$637$$ −2.44831 + 4.24059i −0.00384349 + 0.00665713i
$$638$$ 0 0
$$639$$ 477.218 + 389.384i 0.746820 + 0.609365i
$$640$$ 0 0
$$641$$ 458.006 793.290i 0.714518 1.23758i −0.248626 0.968599i $$-0.579979\pi$$
0.963145 0.268983i $$-0.0866875\pi$$
$$642$$ 0 0
$$643$$ −686.803 + 396.526i −1.06812 + 0.616681i −0.927668 0.373406i $$-0.878190\pi$$
−0.140455 + 0.990087i $$0.544857\pi$$
$$644$$ 0 0
$$645$$ −6.99534 + 3.32069i −0.0108455 + 0.00514836i
$$646$$ 0 0
$$647$$ 78.3837i 0.121150i −0.998164 0.0605748i $$-0.980707\pi$$
0.998164 0.0605748i $$-0.0192934\pi$$
$$648$$ 0 0
$$649$$ 716.579 1.10413
$$650$$ 0 0
$$651$$ −1.25751 2.64906i −0.00193166 0.00406921i
$$652$$ 0 0
$$653$$ 131.250 + 227.332i 0.200996 + 0.348135i 0.948850 0.315728i $$-0.102249\pi$$
−0.747854 + 0.663864i $$0.768915\pi$$
$$654$$ 0 0
$$655$$ 48.1308 + 27.7883i 0.0734822 + 0.0424250i
$$656$$ 0 0
$$657$$ 126.014 154.439i 0.191803 0.235068i
$$658$$ 0 0
$$659$$ 1116.03 + 644.339i 1.69352 + 0.977753i 0.951638 + 0.307221i $$0.0993990\pi$$
0.741880 + 0.670533i $$0.233934\pi$$
$$660$$ 0 0
$$661$$ −184.429 319.441i −0.279016 0.483270i 0.692125 0.721778i $$-0.256675\pi$$
−0.971140 + 0.238508i $$0.923342\pi$$
$$662$$ 0 0
$$663$$ −301.610 + 437.105i −0.454917 + 0.659284i
$$664$$ 0 0
$$665$$ 131.827 0.198236
$$666$$ 0 0
$$667$$ 764.766i 1.14658i
$$668$$ 0 0
$$669$$ −50.0159 + 620.785i −0.0747622 + 0.927930i
$$670$$ 0 0
$$671$$ −335.357 + 193.618i −0.499787 + 0.288552i
$$672$$ 0 0
$$673$$ 127.862 221.463i 0.189988 0.329069i −0.755258 0.655428i $$-0.772488\pi$$
0.945246 + 0.326359i $$0.105822\pi$$
$$674$$ 0 0
$$675$$ 451.903 470.929i 0.669486 0.697673i
$$676$$ 0 0
$$677$$ 566.571 981.330i 0.836885 1.44953i −0.0556014 0.998453i $$-0.517708\pi$$
0.892486 0.451074i $$-0.148959\pi$$
$$678$$ 0 0
$$679$$ 639.653 369.304i 0.942052 0.543894i
$$680$$ 0 0
$$681$$ −21.9466 + 272.397i −0.0322271 + 0.399995i
$$682$$ 0 0
$$683$$ 941.046i 1.37781i −0.724850 0.688907i $$-0.758091\pi$$
0.724850 0.688907i $$-0.241909\pi$$
$$684$$ 0 0
$$685$$ −32.9379 −0.0480845
$$686$$ 0 0
$$687$$ 6.98370 10.1211i 0.0101655 0.0147323i
$$688$$ 0 0
$$689$$ −100.873 174.717i −0.146404 0.253580i
$$690$$ 0 0
$$691$$ −1163.81 671.923i −1.68423 0.972393i −0.958792 0.284109i $$-0.908302\pi$$
−0.725441 0.688284i $$-0.758364\pi$$
$$692$$ 0 0
$$693$$ −503.964 81.7380i −0.727220 0.117948i
$$694$$ 0 0
$$695$$ −140.614 81.1834i −0.202322 0.116811i
$$696$$ 0 0
$$697$$ 774.036 + 1340.67i 1.11053 + 1.92349i
$$698$$ 0 0
$$699$$ −220.971 465.497i −0.316125 0.665946i
$$700$$ 0 0
$$701$$ −28.1783 −0.0401973 −0.0200986 0.999798i $$-0.506398\pi$$
−0.0200986 + 0.999798i $$0.506398\pi$$
$$702$$ 0 0
$$703$$ 1434.26i 2.04020i
$$704$$ 0 0
$$705$$ −201.331 + 95.5720i −0.285576 + 0.135563i
$$706$$ 0 0
$$707$$ −250.135 + 144.415i −0.353797 + 0.204265i
$$708$$ 0 0
$$709$$ 624.660 1081.94i 0.881043 1.52601i 0.0308605 0.999524i $$-0.490175\pi$$
0.850183 0.526488i $$-0.176491\pi$$
$$710$$ 0 0
$$711$$ 334.557 127.002i 0.470544 0.178625i
$$712$$ 0 0
$$713$$ 1.74702 3.02592i 0.00245023 0.00424393i
$$714$$ 0 0
$$715$$ −42.5599 + 24.5720i −0.0595244 + 0.0343664i
$$716$$ 0 0
$$717$$ 224.980 + 155.240i 0.313780 + 0.216513i
$$718$$ 0 0
$$719$$ 738.132i 1.02661i 0.858206 + 0.513305i $$0.171579\pi$$
−0.858206 + 0.513305i $$0.828421\pi$$
$$720$$ 0 0
$$721$$ 1020.11 1.41486
$$722$$ 0 0
$$723$$ −222.690 17.9418i −0.308008 0.0248158i
$$724$$ 0 0
$$725$$ −366.693 635.131i −0.505784 0.876043i
$$726$$ 0 0
$$727$$ 326.676 + 188.606i 0.449348 + 0.259431i 0.707555 0.706659i $$-0.249798\pi$$
−0.258207 + 0.966090i $$0.583132\pi$$
$$728$$ 0 0
$$729$$ 645.820 + 338.169i 0.885898 + 0.463880i
$$730$$ 0 0
$$731$$ −64.7729 37.3967i −0.0886087 0.0511582i
$$732$$ 0 0
$$733$$ 280.849 + 486.445i 0.383150 + 0.663635i 0.991511 0.130025i $$-0.0415059\pi$$
−0.608361 + 0.793661i $$0.708173\pi$$
$$734$$ 0 0
$$735$$ −1.98142 0.159640i −0.00269581 0.000217198i
$$736$$ 0 0
$$737$$ −409.478 −0.555601
$$738$$ 0 0
$$739$$ 912.732i 1.23509i −0.786535 0.617545i $$-0.788127\pi$$
0.786535 0.617545i $$-0.211873\pi$$
$$740$$ 0 0
$$741$$ −341.111 235.372i −0.460339 0.317641i
$$742$$ 0 0
$$743$$ −913.005 + 527.123i −1.22881 + 0.709453i −0.966781 0.255608i $$-0.917725\pi$$
−0.262028 + 0.965060i $$0.584391\pi$$
$$744$$ 0 0
$$745$$ 109.146 189.047i 0.146505 0.253755i
$$746$$ 0 0
$$747$$ 224.242 85.1250i 0.300190 0.113956i
$$748$$ 0 0
$$749$$ −627.115 + 1086.20i −0.837270 + 1.45019i
$$750$$ 0 0
$$751$$ −916.482 + 529.131i −1.22035 + 0.704569i −0.964992 0.262278i $$-0.915526\pi$$
−0.255357 + 0.966847i $$0.582193\pi$$
$$752$$ 0 0
$$753$$ −587.743 + 279.002i −0.780535 + 0.370520i
$$754$$ 0 0
$$755$$ 103.035i 0.136470i
$$756$$ 0 0
$$757$$ −359.804 −0.475302 −0.237651 0.971351i $$-0.576377\pi$$
−0.237651 + 0.971351i $$0.576377\pi$$
$$758$$ 0 0
$$759$$ −260.877 549.561i −0.343711 0.724060i
$$760$$ 0 0
$$761$$ −311.474 539.489i −0.409296 0.708921i 0.585515 0.810661i $$-0.300892\pi$$
−0.994811 + 0.101740i $$0.967559\pi$$
$$762$$ 0 0
$$763$$ 870.966 + 502.853i 1.14150 + 0.659047i
$$764$$ 0 0
$$765$$ −212.811 34.5159i −0.278184 0.0451188i
$$766$$ 0 0
$$767$$ −518.336 299.261i −0.675796 0.390171i
$$768$$ 0 0
$$769$$ −534.453 925.699i −0.694997 1.20377i −0.970182 0.242379i $$-0.922072\pi$$
0.275185 0.961391i $$-0.411261\pi$$
$$770$$ 0 0
$$771$$ −489.253 + 709.046i −0.634570 + 0.919645i
$$772$$ 0 0
$$773$$ −512.261 −0.662692 −0.331346 0.943509i $$-0.607503\pi$$
−0.331346 + 0.943509i $$0.607503\pi$$
$$774$$ 0 0
$$775$$ 3.35066i 0.00432344i
$$776$$ 0 0
$$777$$ −118.518 + 1471.02i −0.152533 + 1.89321i
$$778$$ 0 0
$$779$$ −1046.24 + 604.048i −1.34306 + 0.775415i
$$780$$ 0 0
$$781$$ −275.260 + 476.764i −0.352445 + 0.610453i
$$782$$ 0 0
$$783$$ 567.160 591.039i 0.724343 0.754839i
$$784$$ 0 0
$$785$$ −54.8813 + 95.0571i −0.0699124 + 0.121092i
$$786$$ 0 0
$$787$$ 153.809 88.8019i 0.195438 0.112836i −0.399088 0.916913i $$-0.630673\pi$$
0.594526 + 0.804077i $$0.297340\pi$$
$$788$$ 0 0
$$789$$ −100.635 + 1249.06i −0.127547 + 1.58309i
$$790$$ 0 0
$$791$$ 1412.44i 1.78564i
$$792$$ 0 0
$$793$$ 323.439 0.407868
$$794$$ 0 0