# Properties

 Label 144.4.k.a.37.3 Level $144$ Weight $4$ Character 144.37 Analytic conductor $8.496$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$8.49627504083$$ Analytic rank: $$0$$ Dimension: $$10$$ Relative dimension: $$5$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ Defining polynomial: $$x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$2^{10}$$ Twist minimal: no (minimal twist has level 16) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 37.3 Root $$-1.62580 - 1.16481i$$ of defining polynomial Character $$\chi$$ $$=$$ 144.37 Dual form 144.4.k.a.109.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.460984 + 2.79061i) q^{2} +(-7.57499 - 2.57285i) q^{4} +(-8.22587 - 8.22587i) q^{5} +2.67171i q^{7} +(10.6718 - 19.9528i) q^{8} +O(q^{10})$$ $$q+(-0.460984 + 2.79061i) q^{2} +(-7.57499 - 2.57285i) q^{4} +(-8.22587 - 8.22587i) q^{5} +2.67171i q^{7} +(10.6718 - 19.9528i) q^{8} +(26.7472 - 19.1632i) q^{10} +(45.2213 + 45.2213i) q^{11} +(35.3968 - 35.3968i) q^{13} +(-7.45568 - 1.23161i) q^{14} +(50.7609 + 38.9786i) q^{16} +72.4991 q^{17} +(19.4427 - 19.4427i) q^{19} +(41.1470 + 83.4748i) q^{20} +(-147.041 + 105.349i) q^{22} -139.462i q^{23} +10.3299i q^{25} +(82.4612 + 115.096i) q^{26} +(6.87389 - 20.2381i) q^{28} +(-66.0434 + 66.0434i) q^{29} +188.682 q^{31} +(-132.174 + 123.685i) q^{32} +(-33.4209 + 202.317i) q^{34} +(21.9771 - 21.9771i) q^{35} +(-84.0653 - 84.0653i) q^{37} +(45.2941 + 63.2196i) q^{38} +(-251.914 + 76.3445i) q^{40} +104.629i q^{41} +(-31.4857 - 31.4857i) q^{43} +(-226.203 - 458.898i) q^{44} +(389.183 + 64.2896i) q^{46} +488.151 q^{47} +335.862 q^{49} +(-28.8266 - 4.76190i) q^{50} +(-359.201 + 177.060i) q^{52} +(-149.560 - 149.560i) q^{53} -743.968i q^{55} +(53.3080 + 28.5118i) q^{56} +(-153.856 - 214.746i) q^{58} +(-284.698 - 284.698i) q^{59} +(-228.069 + 228.069i) q^{61} +(-86.9792 + 526.537i) q^{62} +(-284.227 - 425.863i) q^{64} -582.338 q^{65} +(139.151 - 139.151i) q^{67} +(-549.180 - 186.529i) q^{68} +(51.1984 + 71.4606i) q^{70} -453.655i q^{71} +259.747i q^{73} +(273.346 - 195.841i) q^{74} +(-197.301 + 97.2550i) q^{76} +(-120.818 + 120.818i) q^{77} +323.190 q^{79} +(-96.9197 - 738.185i) q^{80} +(-291.979 - 48.2323i) q^{82} +(563.897 - 563.897i) q^{83} +(-596.368 - 596.368i) q^{85} +(102.379 - 73.3499i) q^{86} +(1384.88 - 419.700i) q^{88} +866.853i q^{89} +(94.5697 + 94.5697i) q^{91} +(-358.814 + 1056.42i) q^{92} +(-225.030 + 1362.24i) q^{94} -319.866 q^{95} -936.077 q^{97} +(-154.827 + 937.259i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q + 2q^{2} + 8q^{4} + 2q^{5} + 44q^{8} + O(q^{10})$$ $$10q + 2q^{2} + 8q^{4} + 2q^{5} + 44q^{8} - 68q^{10} - 18q^{11} - 2q^{13} - 188q^{14} + 280q^{16} + 4q^{17} - 26q^{19} + 196q^{20} - 588q^{22} + 264q^{26} + 280q^{28} + 202q^{29} + 368q^{31} - 968q^{32} + 436q^{34} - 476q^{35} - 10q^{37} + 1232q^{38} - 1336q^{40} - 838q^{43} - 868q^{44} + 1132q^{46} + 944q^{47} + 94q^{49} - 726q^{50} - 236q^{52} + 378q^{53} + 488q^{56} + 8q^{58} - 1706q^{59} + 910q^{61} + 80q^{62} + 512q^{64} + 492q^{65} + 1942q^{67} + 880q^{68} + 160q^{70} + 452q^{74} - 1228q^{76} + 268q^{77} - 4416q^{79} + 2648q^{80} - 704q^{82} + 2562q^{83} - 12q^{85} - 3764q^{86} + 1528q^{88} + 3332q^{91} - 632q^{92} - 3248q^{94} - 6900q^{95} - 4q^{97} - 314q^{98} + O(q^{100})$$

## Character values

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

 $$n$$ $$37$$ $$65$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.460984 + 2.79061i −0.162982 + 0.986629i
$$3$$ 0 0
$$4$$ −7.57499 2.57285i −0.946874 0.321606i
$$5$$ −8.22587 8.22587i −0.735744 0.735744i 0.236007 0.971751i $$-0.424161\pi$$
−0.971751 + 0.236007i $$0.924161\pi$$
$$6$$ 0 0
$$7$$ 2.67171i 0.144259i 0.997395 + 0.0721293i $$0.0229794\pi$$
−0.997395 + 0.0721293i $$0.977021\pi$$
$$8$$ 10.6718 19.9528i 0.471630 0.881797i
$$9$$ 0 0
$$10$$ 26.7472 19.1632i 0.845820 0.605993i
$$11$$ 45.2213 + 45.2213i 1.23952 + 1.23952i 0.960197 + 0.279323i $$0.0901099\pi$$
0.279323 + 0.960197i $$0.409890\pi$$
$$12$$ 0 0
$$13$$ 35.3968 35.3968i 0.755176 0.755176i −0.220264 0.975440i $$-0.570692\pi$$
0.975440 + 0.220264i $$0.0706918\pi$$
$$14$$ −7.45568 1.23161i −0.142330 0.0235116i
$$15$$ 0 0
$$16$$ 50.7609 + 38.9786i 0.793139 + 0.609041i
$$17$$ 72.4991 1.03433 0.517165 0.855886i $$-0.326987\pi$$
0.517165 + 0.855886i $$0.326987\pi$$
$$18$$ 0 0
$$19$$ 19.4427 19.4427i 0.234761 0.234761i −0.579916 0.814676i $$-0.696915\pi$$
0.814676 + 0.579916i $$0.196915\pi$$
$$20$$ 41.1470 + 83.4748i 0.460037 + 0.933277i
$$21$$ 0 0
$$22$$ −147.041 + 105.349i −1.42497 + 1.02093i
$$23$$ 139.462i 1.26434i −0.774830 0.632170i $$-0.782165\pi$$
0.774830 0.632170i $$-0.217835\pi$$
$$24$$ 0 0
$$25$$ 10.3299i 0.0826390i
$$26$$ 82.4612 + 115.096i 0.621999 + 0.868159i
$$27$$ 0 0
$$28$$ 6.87389 20.2381i 0.0463944 0.136595i
$$29$$ −66.0434 + 66.0434i −0.422895 + 0.422895i −0.886199 0.463304i $$-0.846664\pi$$
0.463304 + 0.886199i $$0.346664\pi$$
$$30$$ 0 0
$$31$$ 188.682 1.09317 0.546584 0.837404i $$-0.315928\pi$$
0.546584 + 0.837404i $$0.315928\pi$$
$$32$$ −132.174 + 123.685i −0.730165 + 0.683271i
$$33$$ 0 0
$$34$$ −33.4209 + 202.317i −0.168577 + 1.02050i
$$35$$ 21.9771 21.9771i 0.106137 0.106137i
$$36$$ 0 0
$$37$$ −84.0653 84.0653i −0.373520 0.373520i 0.495237 0.868758i $$-0.335081\pi$$
−0.868758 + 0.495237i $$0.835081\pi$$
$$38$$ 45.2941 + 63.2196i 0.193360 + 0.269884i
$$39$$ 0 0
$$40$$ −251.914 + 76.3445i −0.995776 + 0.301778i
$$41$$ 104.629i 0.398545i 0.979944 + 0.199272i $$0.0638578\pi$$
−0.979944 + 0.199272i $$0.936142\pi$$
$$42$$ 0 0
$$43$$ −31.4857 31.4857i −0.111663 0.111663i 0.649067 0.760731i $$-0.275159\pi$$
−0.760731 + 0.649067i $$0.775159\pi$$
$$44$$ −226.203 458.898i −0.775032 1.57231i
$$45$$ 0 0
$$46$$ 389.183 + 64.2896i 1.24743 + 0.206065i
$$47$$ 488.151 1.51498 0.757491 0.652846i $$-0.226425\pi$$
0.757491 + 0.652846i $$0.226425\pi$$
$$48$$ 0 0
$$49$$ 335.862 0.979189
$$50$$ −28.8266 4.76190i −0.0815341 0.0134687i
$$51$$ 0 0
$$52$$ −359.201 + 177.060i −0.957926 + 0.472187i
$$53$$ −149.560 149.560i −0.387617 0.387617i 0.486220 0.873837i $$-0.338376\pi$$
−0.873837 + 0.486220i $$0.838376\pi$$
$$54$$ 0 0
$$55$$ 743.968i 1.82394i
$$56$$ 53.3080 + 28.5118i 0.127207 + 0.0680366i
$$57$$ 0 0
$$58$$ −153.856 214.746i −0.348316 0.486165i
$$59$$ −284.698 284.698i −0.628212 0.628212i 0.319406 0.947618i $$-0.396517\pi$$
−0.947618 + 0.319406i $$0.896517\pi$$
$$60$$ 0 0
$$61$$ −228.069 + 228.069i −0.478709 + 0.478709i −0.904719 0.426010i $$-0.859919\pi$$
0.426010 + 0.904719i $$0.359919\pi$$
$$62$$ −86.9792 + 526.537i −0.178167 + 1.07855i
$$63$$ 0 0
$$64$$ −284.227 425.863i −0.555131 0.831763i
$$65$$ −582.338 −1.11123
$$66$$ 0 0
$$67$$ 139.151 139.151i 0.253730 0.253730i −0.568768 0.822498i $$-0.692580\pi$$
0.822498 + 0.568768i $$0.192580\pi$$
$$68$$ −549.180 186.529i −0.979380 0.332647i
$$69$$ 0 0
$$70$$ 51.1984 + 71.4606i 0.0874197 + 0.122017i
$$71$$ 453.655i 0.758294i −0.925336 0.379147i $$-0.876217\pi$$
0.925336 0.379147i $$-0.123783\pi$$
$$72$$ 0 0
$$73$$ 259.747i 0.416454i 0.978081 + 0.208227i $$0.0667692\pi$$
−0.978081 + 0.208227i $$0.933231\pi$$
$$74$$ 273.346 195.841i 0.429403 0.307649i
$$75$$ 0 0
$$76$$ −197.301 + 97.2550i −0.297789 + 0.146788i
$$77$$ −120.818 + 120.818i −0.178811 + 0.178811i
$$78$$ 0 0
$$79$$ 323.190 0.460275 0.230138 0.973158i $$-0.426082\pi$$
0.230138 + 0.973158i $$0.426082\pi$$
$$80$$ −96.9197 738.185i −0.135449 1.03165i
$$81$$ 0 0
$$82$$ −291.979 48.2323i −0.393216 0.0649557i
$$83$$ 563.897 563.897i 0.745732 0.745732i −0.227943 0.973674i $$-0.573200\pi$$
0.973674 + 0.227943i $$0.0732000\pi$$
$$84$$ 0 0
$$85$$ −596.368 596.368i −0.761002 0.761002i
$$86$$ 102.379 73.3499i 0.128369 0.0919711i
$$87$$ 0 0
$$88$$ 1384.88 419.700i 1.67760 0.508411i
$$89$$ 866.853i 1.03243i 0.856459 + 0.516215i $$0.172659\pi$$
−0.856459 + 0.516215i $$0.827341\pi$$
$$90$$ 0 0
$$91$$ 94.5697 + 94.5697i 0.108941 + 0.108941i
$$92$$ −358.814 + 1056.42i −0.406619 + 1.19717i
$$93$$ 0 0
$$94$$ −225.030 + 1362.24i −0.246915 + 1.49472i
$$95$$ −319.866 −0.345448
$$96$$ 0 0
$$97$$ −936.077 −0.979837 −0.489919 0.871768i $$-0.662974\pi$$
−0.489919 + 0.871768i $$0.662974\pi$$
$$98$$ −154.827 + 937.259i −0.159591 + 0.966097i
$$99$$ 0 0
$$100$$ 26.5772 78.2487i 0.0265772 0.0782487i
$$101$$ 1.58844 + 1.58844i 0.00156491 + 0.00156491i 0.707889 0.706324i $$-0.249648\pi$$
−0.706324 + 0.707889i $$0.749648\pi$$
$$102$$ 0 0
$$103$$ 1388.28i 1.32807i 0.747700 + 0.664036i $$0.231158\pi$$
−0.747700 + 0.664036i $$0.768842\pi$$
$$104$$ −328.518 1084.01i −0.309749 1.02208i
$$105$$ 0 0
$$106$$ 486.310 348.420i 0.445609 0.319260i
$$107$$ 821.526 + 821.526i 0.742243 + 0.742243i 0.973009 0.230767i $$-0.0741234\pi$$
−0.230767 + 0.973009i $$0.574123\pi$$
$$108$$ 0 0
$$109$$ 532.797 532.797i 0.468190 0.468190i −0.433138 0.901328i $$-0.642594\pi$$
0.901328 + 0.433138i $$0.142594\pi$$
$$110$$ 2076.12 + 342.957i 1.79955 + 0.297270i
$$111$$ 0 0
$$112$$ −104.139 + 135.618i −0.0878593 + 0.114417i
$$113$$ 67.2680 0.0560003 0.0280002 0.999608i $$-0.491086\pi$$
0.0280002 + 0.999608i $$0.491086\pi$$
$$114$$ 0 0
$$115$$ −1147.19 + 1147.19i −0.930230 + 0.930230i
$$116$$ 670.198 330.359i 0.536434 0.264423i
$$117$$ 0 0
$$118$$ 925.722 663.240i 0.722200 0.517425i
$$119$$ 193.696i 0.149211i
$$120$$ 0 0
$$121$$ 2758.92i 2.07282i
$$122$$ −531.315 741.587i −0.394287 0.550329i
$$123$$ 0 0
$$124$$ −1429.26 485.449i −1.03509 0.351570i
$$125$$ −943.262 + 943.262i −0.674943 + 0.674943i
$$126$$ 0 0
$$127$$ 1903.59 1.33005 0.665026 0.746820i $$-0.268421\pi$$
0.665026 + 0.746820i $$0.268421\pi$$
$$128$$ 1319.44 596.851i 0.911118 0.412146i
$$129$$ 0 0
$$130$$ 268.448 1625.08i 0.181111 1.09638i
$$131$$ −918.430 + 918.430i −0.612546 + 0.612546i −0.943609 0.331062i $$-0.892593\pi$$
0.331062 + 0.943609i $$0.392593\pi$$
$$132$$ 0 0
$$133$$ 51.9451 + 51.9451i 0.0338662 + 0.0338662i
$$134$$ 324.169 + 452.461i 0.208984 + 0.291691i
$$135$$ 0 0
$$136$$ 773.693 1446.56i 0.487821 0.912069i
$$137$$ 477.234i 0.297612i 0.988866 + 0.148806i $$0.0475430\pi$$
−0.988866 + 0.148806i $$0.952457\pi$$
$$138$$ 0 0
$$139$$ −1513.89 1513.89i −0.923788 0.923788i 0.0735064 0.997295i $$-0.476581\pi$$
−0.997295 + 0.0735064i $$0.976581\pi$$
$$140$$ −223.020 + 109.933i −0.134633 + 0.0663642i
$$141$$ 0 0
$$142$$ 1265.97 + 209.127i 0.748155 + 0.123589i
$$143$$ 3201.37 1.87211
$$144$$ 0 0
$$145$$ 1086.53 0.622285
$$146$$ −724.853 119.739i −0.410885 0.0678746i
$$147$$ 0 0
$$148$$ 420.507 + 853.081i 0.233550 + 0.473803i
$$149$$ −375.353 375.353i −0.206377 0.206377i 0.596349 0.802725i $$-0.296618\pi$$
−0.802725 + 0.596349i $$0.796618\pi$$
$$150$$ 0 0
$$151$$ 2997.52i 1.61546i −0.589553 0.807730i $$-0.700696\pi$$
0.589553 0.807730i $$-0.299304\pi$$
$$152$$ −180.448 595.423i −0.0962912 0.317731i
$$153$$ 0 0
$$154$$ −281.460 392.850i −0.147277 0.205564i
$$155$$ −1552.07 1552.07i −0.804293 0.804293i
$$156$$ 0 0
$$157$$ −1509.01 + 1509.01i −0.767082 + 0.767082i −0.977592 0.210510i $$-0.932488\pi$$
0.210510 + 0.977592i $$0.432488\pi$$
$$158$$ −148.985 + 901.897i −0.0750167 + 0.454121i
$$159$$ 0 0
$$160$$ 2104.66 + 69.8265i 1.03993 + 0.0345017i
$$161$$ 372.601 0.182392
$$162$$ 0 0
$$163$$ −1425.19 + 1425.19i −0.684844 + 0.684844i −0.961088 0.276244i $$-0.910910\pi$$
0.276244 + 0.961088i $$0.410910\pi$$
$$164$$ 269.195 792.565i 0.128174 0.377371i
$$165$$ 0 0
$$166$$ 1313.67 + 1833.56i 0.614219 + 0.857301i
$$167$$ 792.415i 0.367179i −0.983003 0.183590i $$-0.941228\pi$$
0.983003 0.183590i $$-0.0587717\pi$$
$$168$$ 0 0
$$169$$ 308.861i 0.140583i
$$170$$ 1939.15 1389.31i 0.874857 0.626797i
$$171$$ 0 0
$$172$$ 157.496 + 319.512i 0.0698195 + 0.141643i
$$173$$ 773.594 773.594i 0.339972 0.339972i −0.516384 0.856357i $$-0.672722\pi$$
0.856357 + 0.516384i $$0.172722\pi$$
$$174$$ 0 0
$$175$$ −27.5984 −0.0119214
$$176$$ 532.810 + 4058.13i 0.228194 + 1.73803i
$$177$$ 0 0
$$178$$ −2419.05 399.605i −1.01862 0.168268i
$$179$$ −426.050 + 426.050i −0.177902 + 0.177902i −0.790441 0.612539i $$-0.790148\pi$$
0.612539 + 0.790441i $$0.290148\pi$$
$$180$$ 0 0
$$181$$ −2618.06 2618.06i −1.07513 1.07513i −0.996938 0.0781951i $$-0.975084\pi$$
−0.0781951 0.996938i $$-0.524916\pi$$
$$182$$ −307.502 + 220.312i −0.125239 + 0.0897286i
$$183$$ 0 0
$$184$$ −2782.65 1488.30i −1.11489 0.596300i
$$185$$ 1383.02i 0.549631i
$$186$$ 0 0
$$187$$ 3278.50 + 3278.50i 1.28207 + 1.28207i
$$188$$ −3697.74 1255.94i −1.43450 0.487227i
$$189$$ 0 0
$$190$$ 147.453 892.620i 0.0563019 0.340829i
$$191$$ −3216.39 −1.21848 −0.609240 0.792986i $$-0.708525\pi$$
−0.609240 + 0.792986i $$0.708525\pi$$
$$192$$ 0 0
$$193$$ 2852.57 1.06390 0.531950 0.846776i $$-0.321459\pi$$
0.531950 + 0.846776i $$0.321459\pi$$
$$194$$ 431.516 2612.22i 0.159696 0.966736i
$$195$$ 0 0
$$196$$ −2544.15 864.122i −0.927169 0.314913i
$$197$$ −1609.02 1609.02i −0.581918 0.581918i 0.353512 0.935430i $$-0.384987\pi$$
−0.935430 + 0.353512i $$0.884987\pi$$
$$198$$ 0 0
$$199$$ 747.136i 0.266146i −0.991106 0.133073i $$-0.957516\pi$$
0.991106 0.133073i $$-0.0424845\pi$$
$$200$$ 206.110 + 110.238i 0.0728708 + 0.0389750i
$$201$$ 0 0
$$202$$ −5.16496 + 3.70047i −0.00179904 + 0.00128893i
$$203$$ −176.449 176.449i −0.0610062 0.0610062i
$$204$$ 0 0
$$205$$ 860.666 860.666i 0.293227 0.293227i
$$206$$ −3874.15 639.975i −1.31032 0.216452i
$$207$$ 0 0
$$208$$ 3176.49 417.055i 1.05889 0.139027i
$$209$$ 1758.44 0.581981
$$210$$ 0 0
$$211$$ −2227.13 + 2227.13i −0.726645 + 0.726645i −0.969950 0.243305i $$-0.921769\pi$$
0.243305 + 0.969950i $$0.421769\pi$$
$$212$$ 748.122 + 1517.72i 0.242364 + 0.491684i
$$213$$ 0 0
$$214$$ −2671.27 + 1913.85i −0.853290 + 0.611346i
$$215$$ 517.995i 0.164311i
$$216$$ 0 0
$$217$$ 504.102i 0.157699i
$$218$$ 1241.22 + 1732.44i 0.385623 + 0.538237i
$$219$$ 0 0
$$220$$ −1914.12 + 5635.55i −0.586590 + 1.72704i
$$221$$ 2566.23 2566.23i 0.781102 0.781102i
$$222$$ 0 0
$$223$$ −358.053 −0.107520 −0.0537601 0.998554i $$-0.517121\pi$$
−0.0537601 + 0.998554i $$0.517121\pi$$
$$224$$ −330.451 353.130i −0.0985677 0.105332i
$$225$$ 0 0
$$226$$ −31.0094 + 187.719i −0.00912706 + 0.0552516i
$$227$$ −3455.40 + 3455.40i −1.01032 + 1.01032i −0.0103741 + 0.999946i $$0.503302\pi$$
−0.999946 + 0.0103741i $$0.996698\pi$$
$$228$$ 0 0
$$229$$ −1430.03 1430.03i −0.412659 0.412659i 0.470005 0.882664i $$-0.344252\pi$$
−0.882664 + 0.470005i $$0.844252\pi$$
$$230$$ −2672.53 3730.21i −0.766181 1.06940i
$$231$$ 0 0
$$232$$ 612.951 + 2022.55i 0.173458 + 0.572357i
$$233$$ 926.479i 0.260496i −0.991481 0.130248i $$-0.958423\pi$$
0.991481 0.130248i $$-0.0415774\pi$$
$$234$$ 0 0
$$235$$ −4015.47 4015.47i −1.11464 1.11464i
$$236$$ 1424.10 + 2889.07i 0.392801 + 0.796875i
$$237$$ 0 0
$$238$$ −540.530 89.2908i −0.147216 0.0243187i
$$239$$ 792.472 0.214480 0.107240 0.994233i $$-0.465799\pi$$
0.107240 + 0.994233i $$0.465799\pi$$
$$240$$ 0 0
$$241$$ 1449.01 0.387299 0.193650 0.981071i $$-0.437967\pi$$
0.193650 + 0.981071i $$0.437967\pi$$
$$242$$ −7699.07 1271.82i −2.04510 0.337833i
$$243$$ 0 0
$$244$$ 2314.41 1140.83i 0.607233 0.299321i
$$245$$ −2762.76 2762.76i −0.720433 0.720433i
$$246$$ 0 0
$$247$$ 1376.42i 0.354572i
$$248$$ 2013.57 3764.73i 0.515571 0.963953i
$$249$$ 0 0
$$250$$ −2197.45 3067.10i −0.555915 0.775922i
$$251$$ 3580.04 + 3580.04i 0.900280 + 0.900280i 0.995460 0.0951802i $$-0.0303427\pi$$
−0.0951802 + 0.995460i $$0.530343\pi$$
$$252$$ 0 0
$$253$$ 6306.64 6306.64i 1.56717 1.56717i
$$254$$ −877.525 + 5312.18i −0.216775 + 1.31227i
$$255$$ 0 0
$$256$$ 1057.34 + 3957.18i 0.258139 + 0.966108i
$$257$$ 4708.87 1.14292 0.571461 0.820629i $$-0.306377\pi$$
0.571461 + 0.820629i $$0.306377\pi$$
$$258$$ 0 0
$$259$$ 224.598 224.598i 0.0538835 0.0538835i
$$260$$ 4411.21 + 1498.27i 1.05220 + 0.357379i
$$261$$ 0 0
$$262$$ −2139.60 2986.36i −0.504522 0.704190i
$$263$$ 2967.82i 0.695830i −0.937526 0.347915i $$-0.886890\pi$$
0.937526 0.347915i $$-0.113110\pi$$
$$264$$ 0 0
$$265$$ 2460.53i 0.570374i
$$266$$ −168.904 + 121.013i −0.0389330 + 0.0278938i
$$267$$ 0 0
$$268$$ −1412.08 + 696.050i −0.321852 + 0.158649i
$$269$$ 663.633 663.633i 0.150418 0.150418i −0.627887 0.778305i $$-0.716080\pi$$
0.778305 + 0.627887i $$0.216080\pi$$
$$270$$ 0 0
$$271$$ 8058.74 1.80640 0.903199 0.429223i $$-0.141212\pi$$
0.903199 + 0.429223i $$0.141212\pi$$
$$272$$ 3680.12 + 2825.91i 0.820368 + 0.629949i
$$273$$ 0 0
$$274$$ −1331.77 219.997i −0.293633 0.0485055i
$$275$$ −467.130 + 467.130i −0.102433 + 0.102433i
$$276$$ 0 0
$$277$$ 482.477 + 482.477i 0.104654 + 0.104654i 0.757495 0.652841i $$-0.226423\pi$$
−0.652841 + 0.757495i $$0.726423\pi$$
$$278$$ 4922.56 3526.80i 1.06200 0.760875i
$$279$$ 0 0
$$280$$ −203.970 673.039i −0.0435341 0.143649i
$$281$$ 5899.10i 1.25235i −0.779682 0.626175i $$-0.784619\pi$$
0.779682 0.626175i $$-0.215381\pi$$
$$282$$ 0 0
$$283$$ −679.897 679.897i −0.142812 0.142812i 0.632086 0.774898i $$-0.282199\pi$$
−0.774898 + 0.632086i $$0.782199\pi$$
$$284$$ −1167.18 + 3436.43i −0.243872 + 0.718009i
$$285$$ 0 0
$$286$$ −1475.78 + 8933.77i −0.305121 + 1.84708i
$$287$$ −279.538 −0.0574935
$$288$$ 0 0
$$289$$ 343.118 0.0698388
$$290$$ −500.872 + 3032.08i −0.101421 + 0.613965i
$$291$$ 0 0
$$292$$ 668.290 1967.58i 0.133934 0.394329i
$$293$$ 3552.87 + 3552.87i 0.708398 + 0.708398i 0.966198 0.257800i $$-0.0829976\pi$$
−0.257800 + 0.966198i $$0.582998\pi$$
$$294$$ 0 0
$$295$$ 4683.78i 0.924407i
$$296$$ −2574.46 + 780.213i −0.505532 + 0.153206i
$$297$$ 0 0
$$298$$ 1220.49 874.432i 0.237253 0.169981i
$$299$$ −4936.50 4936.50i −0.954799 0.954799i
$$300$$ 0 0
$$301$$ 84.1205 84.1205i 0.0161084 0.0161084i
$$302$$ 8364.89 + 1381.81i 1.59386 + 0.263291i
$$303$$ 0 0
$$304$$ 1744.78 229.079i 0.329177 0.0432191i
$$305$$ 3752.13 0.704415
$$306$$ 0 0
$$307$$ 2735.56 2735.56i 0.508556 0.508556i −0.405527 0.914083i $$-0.632912\pi$$
0.914083 + 0.405527i $$0.132912\pi$$
$$308$$ 1226.04 604.348i 0.226819 0.111805i
$$309$$ 0 0
$$310$$ 5046.70 3615.74i 0.924624 0.662453i
$$311$$ 5796.70i 1.05692i 0.848960 + 0.528458i $$0.177229\pi$$
−0.848960 + 0.528458i $$0.822771\pi$$
$$312$$ 0 0
$$313$$ 8362.62i 1.51017i −0.655627 0.755085i $$-0.727596\pi$$
0.655627 0.755085i $$-0.272404\pi$$
$$314$$ −3515.42 4906.67i −0.631804 0.881846i
$$315$$ 0 0
$$316$$ −2448.16 831.519i −0.435822 0.148027i
$$317$$ 344.406 344.406i 0.0610214 0.0610214i −0.675938 0.736959i $$-0.736261\pi$$
0.736959 + 0.675938i $$0.236261\pi$$
$$318$$ 0 0
$$319$$ −5973.13 −1.04837
$$320$$ −1165.07 + 5841.11i −0.203530 + 1.02040i
$$321$$ 0 0
$$322$$ −171.763 + 1039.78i −0.0297266 + 0.179953i
$$323$$ 1409.58 1409.58i 0.242820 0.242820i
$$324$$ 0 0
$$325$$ 365.644 + 365.644i 0.0624071 + 0.0624071i
$$326$$ −3320.16 4634.14i −0.564069 0.787304i
$$327$$ 0 0
$$328$$ 2087.64 + 1116.58i 0.351435 + 0.187965i
$$329$$ 1304.20i 0.218549i
$$330$$ 0 0
$$331$$ 2687.86 + 2687.86i 0.446339 + 0.446339i 0.894135 0.447797i $$-0.147791\pi$$
−0.447797 + 0.894135i $$0.647791\pi$$
$$332$$ −5722.33 + 2820.69i −0.945945 + 0.466282i
$$333$$ 0 0
$$334$$ 2211.32 + 365.290i 0.362270 + 0.0598437i
$$335$$ −2289.27 −0.373361
$$336$$ 0 0
$$337$$ −1795.31 −0.290199 −0.145099 0.989417i $$-0.546350\pi$$
−0.145099 + 0.989417i $$0.546350\pi$$
$$338$$ 861.910 + 142.380i 0.138703 + 0.0229125i
$$339$$ 0 0
$$340$$ 2983.12 + 6051.85i 0.475830 + 0.965316i
$$341$$ 8532.42 + 8532.42i 1.35500 + 1.35500i
$$342$$ 0 0
$$343$$ 1813.72i 0.285515i
$$344$$ −964.235 + 292.220i −0.151128 + 0.0458007i
$$345$$ 0 0
$$346$$ 1802.18 + 2515.41i 0.280017 + 0.390836i
$$347$$ 1967.33 + 1967.33i 0.304357 + 0.304357i 0.842716 0.538359i $$-0.180955\pi$$
−0.538359 + 0.842716i $$0.680955\pi$$
$$348$$ 0 0
$$349$$ −7363.37 + 7363.37i −1.12938 + 1.12938i −0.139097 + 0.990279i $$0.544420\pi$$
−0.990279 + 0.139097i $$0.955580\pi$$
$$350$$ 12.7224 77.0163i 0.00194297 0.0117620i
$$351$$ 0 0
$$352$$ −11570.3 383.867i −1.75198 0.0581255i
$$353$$ −10644.3 −1.60493 −0.802466 0.596698i $$-0.796479\pi$$
−0.802466 + 0.596698i $$0.796479\pi$$
$$354$$ 0 0
$$355$$ −3731.70 + 3731.70i −0.557911 + 0.557911i
$$356$$ 2230.28 6566.40i 0.332036 0.977580i
$$357$$ 0 0
$$358$$ −992.537 1385.34i −0.146529 0.204518i
$$359$$ 7459.42i 1.09664i 0.836269 + 0.548319i $$0.184732\pi$$
−0.836269 + 0.548319i $$0.815268\pi$$
$$360$$ 0 0
$$361$$ 6102.96i 0.889775i
$$362$$ 8512.87 6099.10i 1.23599 0.885530i
$$363$$ 0 0
$$364$$ −473.051 959.678i −0.0681170 0.138189i
$$365$$ 2136.65 2136.65i 0.306403 0.306403i
$$366$$ 0 0
$$367$$ −6251.35 −0.889149 −0.444574 0.895742i $$-0.646645\pi$$
−0.444574 + 0.895742i $$0.646645\pi$$
$$368$$ 5436.03 7079.21i 0.770034 1.00280i
$$369$$ 0 0
$$370$$ −3859.47 637.550i −0.542282 0.0895801i
$$371$$ 399.582 399.582i 0.0559171 0.0559171i
$$372$$ 0 0
$$373$$ 8911.86 + 8911.86i 1.23710 + 1.23710i 0.961180 + 0.275921i $$0.0889827\pi$$
0.275921 + 0.961180i $$0.411017\pi$$
$$374$$ −10660.3 + 7637.67i −1.47389 + 1.05598i
$$375$$ 0 0
$$376$$ 5209.43 9739.97i 0.714510 1.33591i
$$377$$ 4675.45i 0.638721i
$$378$$ 0 0
$$379$$ 1184.03 + 1184.03i 0.160473 + 0.160473i 0.782776 0.622303i $$-0.213803\pi$$
−0.622303 + 0.782776i $$0.713803\pi$$
$$380$$ 2422.98 + 822.966i 0.327095 + 0.111098i
$$381$$ 0 0
$$382$$ 1482.70 8975.67i 0.198591 1.20219i
$$383$$ 2880.38 0.384283 0.192142 0.981367i $$-0.438457\pi$$
0.192142 + 0.981367i $$0.438457\pi$$
$$384$$ 0 0
$$385$$ 1987.66 0.263119
$$386$$ −1314.99 + 7960.42i −0.173397 + 1.04968i
$$387$$ 0 0
$$388$$ 7090.77 + 2408.38i 0.927782 + 0.315122i
$$389$$ −9244.24 9244.24i −1.20489 1.20489i −0.972662 0.232226i $$-0.925399\pi$$
−0.232226 0.972662i $$-0.574601\pi$$
$$390$$ 0 0
$$391$$ 10110.9i 1.30774i
$$392$$ 3584.24 6701.38i 0.461815 0.863446i
$$393$$ 0 0
$$394$$ 5231.87 3748.41i 0.668979 0.479295i
$$395$$ −2658.52 2658.52i −0.338645 0.338645i
$$396$$ 0 0
$$397$$ −4257.80 + 4257.80i −0.538270 + 0.538270i −0.923020 0.384751i $$-0.874287\pi$$
0.384751 + 0.923020i $$0.374287\pi$$
$$398$$ 2084.96 + 344.417i 0.262587 + 0.0433771i
$$399$$ 0 0
$$400$$ −402.644 + 524.354i −0.0503305 + 0.0655442i
$$401$$ −12722.6 −1.58437 −0.792187 0.610278i $$-0.791058\pi$$
−0.792187 + 0.610278i $$0.791058\pi$$
$$402$$ 0 0
$$403$$ 6678.72 6678.72i 0.825535 0.825535i
$$404$$ −7.94560 16.1192i −0.000978486 0.00198505i
$$405$$ 0 0
$$406$$ 573.739 411.059i 0.0701335 0.0502476i
$$407$$ 7603.08i 0.925972i
$$408$$ 0 0
$$409$$ 232.991i 0.0281678i −0.999901 0.0140839i $$-0.995517\pi$$
0.999901 0.0140839i $$-0.00448320\pi$$
$$410$$ 2005.03 + 2798.53i 0.241515 + 0.337097i
$$411$$ 0 0
$$412$$ 3571.84 10516.2i 0.427116 1.25752i
$$413$$ 760.629 760.629i 0.0906250 0.0906250i
$$414$$ 0 0
$$415$$ −9277.08 −1.09734
$$416$$ −300.471 + 9056.59i −0.0354129 + 1.06739i
$$417$$ 0 0
$$418$$ −810.614 + 4907.13i −0.0948527 + 0.574200i
$$419$$ 6125.69 6125.69i 0.714223 0.714223i −0.253193 0.967416i $$-0.581481\pi$$
0.967416 + 0.253193i $$0.0814807\pi$$
$$420$$ 0 0
$$421$$ −8308.44 8308.44i −0.961825 0.961825i 0.0374725 0.999298i $$-0.488069\pi$$
−0.999298 + 0.0374725i $$0.988069\pi$$
$$422$$ −5188.38 7241.73i −0.598499 0.835360i
$$423$$ 0 0
$$424$$ −4580.22 + 1388.07i −0.524611 + 0.158988i
$$425$$ 748.907i 0.0854760i
$$426$$ 0 0
$$427$$ −609.333 609.333i −0.0690579 0.0690579i
$$428$$ −4109.39 8336.72i −0.464100 0.941520i
$$429$$ 0 0
$$430$$ −1445.52 238.787i −0.162114 0.0267798i
$$431$$ −8737.57 −0.976506 −0.488253 0.872702i $$-0.662366\pi$$
−0.488253 + 0.872702i $$0.662366\pi$$
$$432$$ 0 0
$$433$$ −11627.5 −1.29049 −0.645247 0.763974i $$-0.723245\pi$$
−0.645247 + 0.763974i $$0.723245\pi$$
$$434$$ −1406.75 232.383i −0.155590 0.0257021i
$$435$$ 0 0
$$436$$ −5406.74 + 2665.13i −0.593890 + 0.292744i
$$437$$ −2711.51 2711.51i −0.296817 0.296817i
$$438$$ 0 0
$$439$$ 17631.8i 1.91690i 0.285261 + 0.958450i $$0.407920\pi$$
−0.285261 + 0.958450i $$0.592080\pi$$
$$440$$ −14844.2 7939.45i −1.60834 0.860224i
$$441$$ 0 0
$$442$$ 5978.36 + 8344.34i 0.643352 + 0.897963i
$$443$$ 4549.81 + 4549.81i 0.487964 + 0.487964i 0.907663 0.419699i $$-0.137864\pi$$
−0.419699 + 0.907663i $$0.637864\pi$$
$$444$$ 0 0
$$445$$ 7130.62 7130.62i 0.759604 0.759604i
$$446$$ 165.057 999.186i 0.0175239 0.106083i
$$447$$ 0 0
$$448$$ 1137.78 759.371i 0.119989 0.0800824i
$$449$$ 12926.5 1.35867 0.679334 0.733830i $$-0.262269\pi$$
0.679334 + 0.733830i $$0.262269\pi$$
$$450$$ 0 0
$$451$$ −4731.46 + 4731.46i −0.494004 + 0.494004i
$$452$$ −509.554 173.070i −0.0530252 0.0180101i
$$453$$ 0 0
$$454$$ −8049.78 11235.5i −0.832147 1.16148i
$$455$$ 1555.84i 0.160305i
$$456$$ 0 0
$$457$$ 9320.32i 0.954018i −0.878898 0.477009i $$-0.841721\pi$$
0.878898 0.477009i $$-0.158279\pi$$
$$458$$ 4649.87 3331.43i 0.474398 0.339886i
$$459$$ 0 0
$$460$$ 11641.5 5738.43i 1.17998 0.581643i
$$461$$ −12885.0 + 12885.0i −1.30177 + 1.30177i −0.374566 + 0.927200i $$0.622208\pi$$
−0.927200 + 0.374566i $$0.877792\pi$$
$$462$$ 0 0
$$463$$ 7038.37 0.706482 0.353241 0.935532i $$-0.385080\pi$$
0.353241 + 0.935532i $$0.385080\pi$$
$$464$$ −5926.71 + 778.144i −0.592975 + 0.0778543i
$$465$$ 0 0
$$466$$ 2585.44 + 427.091i 0.257013 + 0.0424563i
$$467$$ −6001.76 + 6001.76i −0.594707 + 0.594707i −0.938899 0.344192i $$-0.888153\pi$$
0.344192 + 0.938899i $$0.388153\pi$$
$$468$$ 0 0
$$469$$ 371.769 + 371.769i 0.0366028 + 0.0366028i
$$470$$ 13056.7 9354.53i 1.28140 0.918069i
$$471$$ 0 0
$$472$$ −8718.75 + 2642.29i −0.850239 + 0.257672i
$$473$$ 2847.65i 0.276818i
$$474$$ 0 0
$$475$$ 200.840 + 200.840i 0.0194004 + 0.0194004i
$$476$$ 498.351 1467.25i 0.0479872 0.141284i
$$477$$ 0 0
$$478$$ −365.317 + 2211.48i −0.0349565 + 0.211612i
$$479$$ 587.317 0.0560234 0.0280117 0.999608i $$-0.491082\pi$$
0.0280117 + 0.999608i $$0.491082\pi$$
$$480$$ 0 0
$$481$$ −5951.28 −0.564148
$$482$$ −667.971 + 4043.63i −0.0631229 + 0.382121i
$$483$$ 0 0
$$484$$ 7098.29 20898.8i 0.666631 1.96270i
$$485$$ 7700.05 + 7700.05i 0.720910 + 0.720910i
$$486$$ 0 0
$$487$$ 8366.45i 0.778481i 0.921136 + 0.389240i $$0.127262\pi$$
−0.921136 + 0.389240i $$0.872738\pi$$
$$488$$ 2116.71 + 6984.51i 0.196351 + 0.647897i
$$489$$ 0 0
$$490$$ 8983.36 6436.19i 0.828218 0.593382i
$$491$$ −1529.30 1529.30i −0.140563 0.140563i 0.633324 0.773887i $$-0.281690\pi$$
−0.773887 + 0.633324i $$0.781690\pi$$
$$492$$ 0 0
$$493$$ −4788.09 + 4788.09i −0.437413 + 0.437413i
$$494$$ 3841.04 + 634.505i 0.349831 + 0.0577889i
$$495$$ 0 0
$$496$$ 9577.65 + 7354.55i 0.867035 + 0.665784i
$$497$$ 1212.03 0.109390
$$498$$ 0 0
$$499$$ 11364.5 11364.5i 1.01952 1.01952i 0.0197191 0.999806i $$-0.493723\pi$$
0.999806 0.0197191i $$-0.00627718\pi$$
$$500$$ 9572.06 4718.33i 0.856151 0.422020i
$$501$$ 0 0
$$502$$ −11640.8 + 8340.15i −1.03497 + 0.741513i
$$503$$ 12570.2i 1.11427i −0.830421 0.557137i $$-0.811900\pi$$
0.830421 0.557137i $$-0.188100\pi$$
$$504$$ 0 0
$$505$$ 26.1326i 0.00230274i
$$506$$ 14692.1 + 20506.6i 1.29080 + 1.80164i
$$507$$ 0 0
$$508$$ −14419.7 4897.66i −1.25939 0.427753i
$$509$$ −11880.4 + 11880.4i −1.03456 + 1.03456i −0.0351750 + 0.999381i $$0.511199\pi$$
−0.999381 + 0.0351750i $$0.988801\pi$$
$$510$$ 0 0
$$511$$ −693.968 −0.0600770
$$512$$ −11530.3 + 1126.42i −0.995262 + 0.0972291i
$$513$$ 0 0
$$514$$ −2170.71 + 13140.6i −0.186276 + 1.12764i
$$515$$ 11419.8 11419.8i 0.977122 0.977122i
$$516$$ 0 0
$$517$$ 22074.8 + 22074.8i 1.87785 + 1.87785i
$$518$$ 523.229 + 730.300i 0.0443810 + 0.0619451i
$$519$$ 0 0
$$520$$ −6214.57 + 11619.3i −0.524090 + 0.979882i
$$521$$ 6612.98i 0.556085i −0.960569 0.278042i $$-0.910314\pi$$
0.960569 0.278042i $$-0.0896856\pi$$
$$522$$ 0 0
$$523$$ 5129.30 + 5129.30i 0.428850 + 0.428850i 0.888236 0.459387i $$-0.151931\pi$$
−0.459387 + 0.888236i $$0.651931\pi$$
$$524$$ 9320.07 4594.11i 0.777003 0.383005i
$$525$$ 0 0
$$526$$ 8282.01 + 1368.11i 0.686526 + 0.113408i
$$527$$ 13679.3 1.13070
$$528$$ 0 0
$$529$$ −7282.60 −0.598553
$$530$$ −6866.38 1134.26i −0.562748 0.0929609i
$$531$$ 0 0
$$532$$ −259.837 527.130i −0.0211755 0.0429586i
$$533$$ 3703.53 + 3703.53i 0.300972 + 0.300972i
$$534$$ 0 0
$$535$$ 13515.5i 1.09220i
$$536$$ −1291.46 4261.42i −0.104072 0.343406i
$$537$$ 0 0
$$538$$ 1546.02 + 2157.86i 0.123891 + 0.172922i
$$539$$ 15188.1 + 15188.1i 1.21372 + 1.21372i
$$540$$ 0 0
$$541$$ −10968.5 + 10968.5i −0.871672 + 0.871672i −0.992655 0.120983i $$-0.961395\pi$$
0.120983 + 0.992655i $$0.461395\pi$$
$$542$$ −3714.95 + 22488.8i −0.294411 + 1.78224i
$$543$$ 0 0
$$544$$ −9582.49 + 8967.07i −0.755231 + 0.706728i
$$545$$ −8765.44 −0.688936
$$546$$ 0 0
$$547$$ 13088.8 13088.8i 1.02311 1.02311i 0.0233784 0.999727i $$-0.492558\pi$$
0.999727 0.0233784i $$-0.00744226\pi$$
$$548$$ 1227.85 3615.04i 0.0957138 0.281801i
$$549$$ 0 0
$$550$$ −1088.24 1518.92i −0.0843684 0.117758i
$$551$$ 2568.12i 0.198558i
$$552$$ 0 0
$$553$$ 863.469i 0.0663986i
$$554$$ −1568.82 + 1123.99i −0.120312 + 0.0861981i
$$555$$ 0 0
$$556$$ 7572.70 + 15362.7i 0.577615 + 1.17181i
$$557$$ −5049.87 + 5049.87i −0.384147 + 0.384147i −0.872594 0.488447i $$-0.837564\pi$$
0.488447 + 0.872594i $$0.337564\pi$$
$$558$$ 0 0
$$559$$ −2228.98 −0.168651
$$560$$ 1972.21 258.941i 0.148824 0.0195397i
$$561$$ 0 0
$$562$$ 16462.1 + 2719.39i 1.23561 + 0.204111i
$$563$$ 3249.06 3249.06i 0.243217 0.243217i −0.574962 0.818180i $$-0.694983\pi$$
0.818180 + 0.574962i $$0.194983\pi$$
$$564$$ 0 0
$$565$$ −553.338 553.338i −0.0412019 0.0412019i
$$566$$ 2210.75 1583.90i 0.164178 0.117626i
$$567$$ 0 0
$$568$$ −9051.67 4841.29i −0.668661 0.357634i
$$569$$ 2806.05i 0.206741i 0.994643 + 0.103371i $$0.0329628\pi$$
−0.994643 + 0.103371i $$0.967037\pi$$
$$570$$ 0 0
$$571$$ −12038.8 12038.8i −0.882324 0.882324i 0.111446 0.993770i $$-0.464452\pi$$
−0.993770 + 0.111446i $$0.964452\pi$$
$$572$$ −24250.3 8236.64i −1.77265 0.602083i
$$573$$ 0 0
$$574$$ 128.863 780.082i 0.00937042 0.0567247i
$$575$$ 1440.62 0.104484
$$576$$ 0 0
$$577$$ 7206.84 0.519973 0.259987 0.965612i $$-0.416282\pi$$
0.259987 + 0.965612i $$0.416282\pi$$
$$578$$ −158.172 + 957.508i −0.0113825 + 0.0689050i
$$579$$ 0 0
$$580$$ −8230.45 2795.48i −0.589226 0.200131i
$$581$$ 1506.57 + 1506.57i 0.107578 + 0.107578i
$$582$$ 0 0
$$583$$ 13526.6i 0.960918i
$$584$$ 5182.68 + 2771.96i 0.367227 + 0.196412i
$$585$$ 0 0
$$586$$ −11552.5 + 8276.84i −0.814382 + 0.583470i
$$587$$ −10377.0 10377.0i −0.729647 0.729647i 0.240903 0.970549i $$-0.422557\pi$$
−0.970549 + 0.240903i $$0.922557\pi$$
$$588$$ 0 0
$$589$$ 3668.48 3668.48i 0.256633 0.256633i
$$590$$ −13070.6 2159.14i −0.912047 0.150662i
$$591$$ 0 0
$$592$$ −990.483 7543.98i −0.0687645 0.523743i
$$593$$ 4758.60 0.329531 0.164766 0.986333i $$-0.447313\pi$$
0.164766 + 0.986333i $$0.447313\pi$$
$$594$$ 0 0
$$595$$ 1593.32 1593.32i 0.109781 0.109781i
$$596$$ 1877.57 + 3809.02i 0.129041 + 0.261785i
$$597$$ 0 0
$$598$$ 16051.5 11500.2i 1.09765 0.786417i
$$599$$ 14256.4i 0.972455i 0.873832 + 0.486227i $$0.161627\pi$$
−0.873832 + 0.486227i $$0.838373\pi$$
$$600$$ 0 0
$$601$$ 10385.2i 0.704862i −0.935838 0.352431i $$-0.885355\pi$$
0.935838 0.352431i $$-0.114645\pi$$
$$602$$ 195.969 + 273.526i 0.0132676 + 0.0185184i
$$603$$ 0 0
$$604$$ −7712.16 + 22706.2i −0.519542 + 1.52964i
$$605$$ 22694.5 22694.5i 1.52506 1.52506i
$$606$$ 0 0
$$607$$ −16243.6 −1.08618 −0.543088 0.839676i $$-0.682745\pi$$
−0.543088 + 0.839676i $$0.682745\pi$$
$$608$$ −165.042 + 4974.59i −0.0110088 + 0.331819i
$$609$$ 0 0
$$610$$ −1729.67 + 10470.7i −0.114807 + 0.694996i
$$611$$ 17279.0 17279.0i 1.14408 1.14408i
$$612$$ 0 0
$$613$$ −500.502 500.502i −0.0329773 0.0329773i 0.690426 0.723403i $$-0.257423\pi$$
−0.723403 + 0.690426i $$0.757423\pi$$
$$614$$ 6372.83 + 8894.92i 0.418870 + 0.584642i
$$615$$ 0 0
$$616$$ 1121.31 + 3699.99i 0.0733426 + 0.242008i
$$617$$ 11575.9i 0.755316i 0.925945 + 0.377658i $$0.123271\pi$$
−0.925945 + 0.377658i $$0.876729\pi$$
$$618$$ 0 0
$$619$$ 18356.1 + 18356.1i 1.19191 + 1.19191i 0.976530 + 0.215380i $$0.0690992\pi$$
0.215380 + 0.976530i $$0.430901\pi$$
$$620$$ 7763.68 + 15750.2i 0.502898 + 1.02023i
$$621$$ 0 0
$$622$$ −16176.3 2672.18i −1.04278 0.172258i
$$623$$ −2315.98 −0.148937
$$624$$ 0 0
$$625$$ 16809.5 1.07581
$$626$$ 23336.8 + 3855.03i 1.48998 + 0.246131i
$$627$$ 0 0
$$628$$ 15313.2 7548.26i 0.973027 0.479631i
$$629$$ −6094.66 6094.66i −0.386343 0.386343i
$$630$$ 0 0
$$631$$ 10224.8i 0.645079i 0.946556 + 0.322539i $$0.104537\pi$$
−0.946556 + 0.322539i $$0.895463\pi$$
$$632$$ 3449.01 6448.54i 0.217079 0.405869i
$$633$$ 0 0
$$634$$ 802.338 + 1119.87i 0.0502601 + 0.0701509i
$$635$$ −15658.7 15658.7i −0.978578 0.978578i
$$636$$ 0 0
$$637$$ 11888.4 11888.4i 0.739461 0.739461i
$$638$$ 2753.52 16668.7i 0.170866 1.03436i
$$639$$ 0 0
$$640$$ −15763.2 5943.92i −0.973584 0.367116i
$$641$$ −19804.4 −1.22032 −0.610162 0.792277i $$-0.708896\pi$$
−0.610162 + 0.792277i $$0.708896\pi$$
$$642$$ 0 0
$$643$$ 15680.7 15680.7i 0.961723 0.961723i −0.0375712 0.999294i $$-0.511962\pi$$
0.999294 + 0.0375712i $$0.0119621\pi$$
$$644$$ −2822.45 958.646i −0.172702 0.0586583i
$$645$$ 0 0
$$646$$ 3283.78 + 4583.37i 0.199998 + 0.279149i
$$647$$ 9232.26i 0.560985i −0.959856 0.280493i $$-0.909502\pi$$
0.959856 0.280493i $$-0.0904978\pi$$
$$648$$ 0 0
$$649$$ 25748.8i 1.55736i
$$650$$ −1188.93 + 851.814i −0.0717438 + 0.0514014i
$$651$$ 0 0
$$652$$ 14462.6 7129.00i 0.868710 0.428210i
$$653$$ 19697.9 19697.9i 1.18046 1.18046i 0.200833 0.979626i $$-0.435635\pi$$
0.979626 0.200833i $$-0.0643648\pi$$
$$654$$ 0 0
$$655$$ 15109.8 0.901355
$$656$$ −4078.30 + 5311.07i −0.242730 + 0.316101i
$$657$$ 0 0
$$658$$ −3639.50 601.213i −0.215627 0.0356196i
$$659$$ −3888.06 + 3888.06i −0.229829 + 0.229829i −0.812621 0.582792i $$-0.801960\pi$$
0.582792 + 0.812621i $$0.301960\pi$$
$$660$$ 0 0
$$661$$ −8110.20 8110.20i −0.477232 0.477232i 0.427013 0.904245i $$-0.359566\pi$$
−0.904245 + 0.427013i $$0.859566\pi$$
$$662$$ −8739.82 + 6261.70i −0.513116 + 0.367625i
$$663$$ 0 0
$$664$$ −5233.54 17269.1i −0.305875 1.00929i
$$665$$ 854.587i 0.0498338i
$$666$$ 0 0
$$667$$ 9210.54 + 9210.54i 0.534683 + 0.534683i
$$668$$ −2038.76 + 6002.54i −0.118087 + 0.347672i
$$669$$ 0 0
$$670$$ 1055.31 6388.45i 0.0608513 0.368369i
$$671$$ −20627.1 −1.18674
$$672$$ 0 0
$$673$$ −28428.2 −1.62827 −0.814135 0.580676i $$-0.802788\pi$$
−0.814135 + 0.580676i $$0.802788\pi$$
$$674$$ 827.610 5010.02i 0.0472972 0.286318i
$$675$$ 0 0
$$676$$ −794.652 + 2339.62i −0.0452124 + 0.133114i
$$677$$ 16967.4 + 16967.4i 0.963235 + 0.963235i 0.999348 0.0361128i $$-0.0114975\pi$$
−0.0361128 + 0.999348i $$0.511498\pi$$
$$678$$ 0 0
$$679$$ 2500.92i 0.141350i
$$680$$ −18263.5 + 5534.91i −1.02996 + 0.312138i
$$681$$ 0 0
$$682$$ −27744.0 + 19877.3i −1.55773 + 1.11605i
$$683$$ 9550.16 + 9550.16i 0.535032 + 0.535032i 0.922066 0.387034i $$-0.126500\pi$$
−0.387034 + 0.922066i $$0.626500\pi$$
$$684$$ 0 0
$$685$$ 3925.66 3925.66i 0.218966 0.218966i
$$686$$ −5061.38 836.095i −0.281697 0.0465339i
$$687$$ 0 0
$$688$$ −370.974 2825.51i −0.0205570 0.156572i
$$689$$ −10587.9 −0.585439
$$690$$ 0 0
$$691$$ −20859.7 + 20859.7i −1.14839 + 1.14839i −0.161527 + 0.986868i $$0.551642\pi$$
−0.986868 + 0.161527i $$0.948358\pi$$
$$692$$ −7850.30 + 3869.62i −0.431248 + 0.212574i
$$693$$ 0 0
$$694$$ −6396.96 + 4583.14i −0.349892 + 0.250683i
$$695$$ 24906.1i 1.35934i
$$696$$ 0 0
$$697$$ 7585.52i 0.412227i
$$698$$ −17153.9 23942.7i −0.930207 1.29834i
$$699$$ 0 0
$$700$$ 209.058 + 71.0065i 0.0112880 + 0.00383399i
$$701$$ −23495.4 + 23495.4i −1.26592 + 1.26592i −0.317740 + 0.948178i $$0.602924\pi$$
−0.948178 + 0.317740i $$0.897076\pi$$
$$702$$ 0 0
$$703$$ −3268.91 −0.175376
$$704$$ 6404.93 32111.1i 0.342890 1.71908i
$$705$$ 0 0
$$706$$ 4906.86 29704.2i 0.261575 1.58347i
$$707$$ −4.24384 + 4.24384i −0.000225751 + 0.000225751i
$$708$$ 0 0
$$709$$ 4559.45 + 4559.45i 0.241515 + 0.241515i 0.817477 0.575962i $$-0.195372\pi$$
−0.575962 + 0.817477i $$0.695372\pi$$
$$710$$ −8693.47 12134.0i −0.459521 0.641380i
$$711$$ 0 0
$$712$$ 17296.1 + 9250.84i 0.910393 + 0.486924i
$$713$$ 26313.9i 1.38214i
$$714$$ 0 0
$$715$$ −26334.1 26334.1i −1.37740 1.37740i
$$716$$ 4323.49 2131.16i 0.225665 0.111236i
$$717$$ 0 0
$$718$$ −20816.3 3438.67i −1.08198 0.178733i
$$719$$ 6494.67 0.336871 0.168436 0.985713i $$-0.446128\pi$$
0.168436 + 0.985713i $$0.446128\pi$$
$$720$$ 0 0
$$721$$ −3709.08 −0.191586
$$722$$ −17031.0 2813.37i −0.877878 0.145018i
$$723$$ 0 0
$$724$$ 13095.9 + 26567.7i 0.672246 + 1.36378i
$$725$$ −682.221 682.221i −0.0349476 0.0349476i
$$726$$ 0 0
$$727$$ 24866.4i 1.26856i 0.773103 + 0.634280i $$0.218704\pi$$
−0.773103 + 0.634280i $$0.781296\pi$$
$$728$$ 2896.15 877.704i 0.147443 0.0446839i
$$729$$ 0 0
$$730$$ 4977.59 + 6947.50i 0.252368 + 0.352245i
$$731$$ −2282.68 2282.68i −0.115497 0.115497i
$$732$$ 0 0
$$733$$ −14914.3 + 14914.3i −0.751533 + 0.751533i −0.974765 0.223232i $$-0.928339\pi$$
0.223232 + 0.974765i $$0.428339\pi$$
$$734$$ 2881.77 17445.1i 0.144916 0.877260i
$$735$$ 0 0
$$736$$ 17249.4 + 18433.2i 0.863886 + 0.923176i
$$737$$ 12585.1 0.629008
$$738$$ 0 0
$$739$$ 8451.86 8451.86i 0.420713 0.420713i −0.464737 0.885449i $$-0.653851\pi$$
0.885449 + 0.464737i $$0.153851\pi$$
$$740$$ 3558.30 10476.4i 0.176765 0.520431i
$$741$$ 0 0
$$742$$ 930.875 + 1299.28i 0.0460559 + 0.0642829i
$$743$$ 5622.43i 0.277614i −0.990319 0.138807i $$-0.955673\pi$$
0.990319 0.138807i $$-0.0443267\pi$$
$$744$$ 0 0
$$745$$ 6175.21i 0.303681i
$$746$$ −28977.7 + 20761.3i −1.42219 + 1.01893i
$$747$$ 0 0
$$748$$ −16399.5 33269.7i −0.801638 1.62628i
$$749$$ −2194.88 + 2194.88i −0.107075 + 0.107075i
$$750$$ 0 0
$$751$$ −32314.9 −1.57016 −0.785079 0.619396i $$-0.787378\pi$$
−0.785079 + 0.619396i $$0.787378\pi$$
$$752$$ 24779.0 + 19027.4i 1.20159 + 0.922685i
$$753$$ 0 0
$$754$$ −13047.3 2155.30i −0.630181 0.104100i
$$755$$ −24657.2 + 24657.2i −1.18857 + 1.18857i
$$756$$ 0 0
$$757$$ 12692.8 + 12692.8i 0.609418 + 0.609418i 0.942794 0.333376i $$-0.108188\pi$$
−0.333376 + 0.942794i $$0.608188\pi$$
$$758$$ −3849.97 + 2758.34i −0.184482 + 0.132173i
$$759$$ 0 0
$$760$$ −3413.53 + 6382.21i −0.162923 + 0.304615i
$$761$$ 13108.2i 0.624404i −0.950016 0.312202i $$-0.898933\pi$$
0.950016 0.312202i $$-0.101067\pi$$
$$762$$ 0 0
$$763$$ 1423.48 + 1423.48i 0.0675404 + 0.0675404i
$$764$$ 24364.1 + 8275.27i 1.15375 + 0.391870i
$$765$$ 0 0
$$766$$ −1327.81 + 8038.01i −0.0626314 + 0.379145i
$$767$$ −20154.8 −0.948822
$$768$$ 0 0
$$769$$ 23661.2 1.10955 0.554776 0.832000i $$-0.312804\pi$$
0.554776 + 0.832000i $$0.312804\pi$$
$$770$$ −916.280 + 5546.79i −0.0428837 + 0.259601i
$$771$$ 0 0
$$772$$ −21608.2 7339.24i −1.00738 0.342157i
$$773$$ −21370.5 21370.5i −0.994362 0.994362i 0.00562228 0.999984i $$-0.498210\pi$$
−0.999984 + 0.00562228i $$0.998210\pi$$
$$774$$ 0 0
$$775$$ 1949.06i 0.0903384i
$$776$$ −9989.59 + 18677.3i −0.462120 + 0.864018i
$$777$$ 0 0
$$778$$ 30058.5 21535.6i 1.38515 0.992402i
$$779$$ 2034.27 + 2034.27i 0.0935627 + 0.0935627i
$$780$$ 0 0
$$781$$ 20514.8 20514.8i 0.939921 0.939921i
$$782$$ 28215.4 + 4660.94i 1.29026 + 0.213139i
$$783$$ 0 0
$$784$$ 17048.7 + 13091.4i 0.776633 + 0.596366i
$$785$$ 24825.8 1.12875
$$786$$ 0 0