# Properties

 Label 1728.3.q.i.1601.2 Level $1728$ Weight $3$ Character 1728.1601 Analytic conductor $47.085$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1728 = 2^{6} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1728.q (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$47.0845896815$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.19269881856.9 Defining polynomial: $$x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144$$ x^8 - 2*x^7 + 15*x^6 - 2*x^5 + 133*x^4 - 84*x^3 + 276*x^2 + 144*x + 144 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 72) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1601.2 Root $$-0.331167 + 0.573598i$$ of defining polynomial Character $$\chi$$ $$=$$ 1728.1601 Dual form 1728.3.q.i.449.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.0440114 + 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +O(q^{10})$$ $$q+(-0.0440114 + 0.0254100i) q^{5} +(-4.52944 + 7.84521i) q^{7} +(-3.29117 - 1.90016i) q^{11} +(-0.216902 - 0.375686i) q^{13} -26.2355i q^{17} +34.2225 q^{19} +(-29.9930 + 17.3164i) q^{23} +(-12.4987 + 21.6484i) q^{25} +(14.0316 + 8.10114i) q^{29} +(17.1675 + 29.7350i) q^{31} -0.460372i q^{35} -29.2761 q^{37} +(-48.7026 + 28.1185i) q^{41} +(-3.94539 + 6.83362i) q^{43} +(-33.4489 - 19.3117i) q^{47} +(-16.5316 - 28.6335i) q^{49} -50.5273i q^{53} +0.193132 q^{55} +(8.54743 - 4.93486i) q^{59} +(36.5718 - 63.3442i) q^{61} +(0.0190923 + 0.0110230i) q^{65} +(-12.6797 - 21.9618i) q^{67} -97.8262i q^{71} -77.0599 q^{73} +(29.8143 - 17.2133i) q^{77} +(42.1389 - 72.9868i) q^{79} +(-40.6763 - 23.4845i) q^{83} +(0.666644 + 1.15466i) q^{85} -108.587i q^{89} +3.92978 q^{91} +(-1.50618 + 0.869593i) q^{95} +(-32.4021 + 56.1221i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 6 q^{5} - 6 q^{7}+O(q^{10})$$ 8 * q - 6 * q^5 - 6 * q^7 $$8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100})$$ 8 * q - 6 * q^5 - 6 * q^7 - 36 * q^11 - 14 * q^13 + 4 * q^19 - 102 * q^23 + 10 * q^25 - 114 * q^29 + 50 * q^31 - 120 * q^37 - 264 * q^41 - 28 * q^43 + 150 * q^47 + 94 * q^49 + 244 * q^55 + 108 * q^59 - 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 + 66 * q^77 - 26 * q^79 - 246 * q^83 + 224 * q^85 + 108 * q^91 - 456 * q^95 - 236 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$703$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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 0
$$4$$ 0 0
$$5$$ −0.0440114 + 0.0254100i −0.00880228 + 0.00508200i −0.504395 0.863473i $$-0.668284\pi$$
0.495592 + 0.868555i $$0.334951\pi$$
$$6$$ 0 0
$$7$$ −4.52944 + 7.84521i −0.647062 + 1.12074i 0.336759 + 0.941591i $$0.390669\pi$$
−0.983821 + 0.179154i $$0.942664\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −3.29117 1.90016i −0.299198 0.172742i 0.342885 0.939377i $$-0.388596\pi$$
−0.642082 + 0.766636i $$0.721929\pi$$
$$12$$ 0 0
$$13$$ −0.216902 0.375686i −0.0166848 0.0288989i 0.857562 0.514380i $$-0.171978\pi$$
−0.874247 + 0.485481i $$0.838645\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 26.2355i 1.54327i −0.636068 0.771633i $$-0.719440\pi$$
0.636068 0.771633i $$-0.280560\pi$$
$$18$$ 0 0
$$19$$ 34.2225 1.80118 0.900592 0.434666i $$-0.143133\pi$$
0.900592 + 0.434666i $$0.143133\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −29.9930 + 17.3164i −1.30404 + 0.752889i −0.981095 0.193528i $$-0.938007\pi$$
−0.322947 + 0.946417i $$0.604674\pi$$
$$24$$ 0 0
$$25$$ −12.4987 + 21.6484i −0.499948 + 0.865936i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 14.0316 + 8.10114i 0.483848 + 0.279350i 0.722019 0.691874i $$-0.243214\pi$$
−0.238171 + 0.971223i $$0.576548\pi$$
$$30$$ 0 0
$$31$$ 17.1675 + 29.7350i 0.553790 + 0.959193i 0.997997 + 0.0632685i $$0.0201524\pi$$
−0.444206 + 0.895925i $$0.646514\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.460372i 0.0131535i
$$36$$ 0 0
$$37$$ −29.2761 −0.791247 −0.395623 0.918413i $$-0.629471\pi$$
−0.395623 + 0.918413i $$0.629471\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −48.7026 + 28.1185i −1.18787 + 0.685816i −0.957822 0.287363i $$-0.907221\pi$$
−0.230047 + 0.973180i $$0.573888\pi$$
$$42$$ 0 0
$$43$$ −3.94539 + 6.83362i −0.0917533 + 0.158921i −0.908249 0.418430i $$-0.862580\pi$$
0.816496 + 0.577352i $$0.195914\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −33.4489 19.3117i −0.711678 0.410887i 0.100004 0.994987i $$-0.468114\pi$$
−0.811682 + 0.584100i $$0.801448\pi$$
$$48$$ 0 0
$$49$$ −16.5316 28.6335i −0.337379 0.584358i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 50.5273i 0.953344i −0.879081 0.476672i $$-0.841843\pi$$
0.879081 0.476672i $$-0.158157\pi$$
$$54$$ 0 0
$$55$$ 0.193132 0.00351149
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 8.54743 4.93486i 0.144872 0.0836417i −0.425812 0.904812i $$-0.640012\pi$$
0.570684 + 0.821170i $$0.306678\pi$$
$$60$$ 0 0
$$61$$ 36.5718 63.3442i 0.599537 1.03843i −0.393352 0.919388i $$-0.628685\pi$$
0.992889 0.119041i $$-0.0379821\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0.0190923 + 0.0110230i 0.000293728 + 0.000169584i
$$66$$ 0 0
$$67$$ −12.6797 21.9618i −0.189249 0.327789i 0.755751 0.654859i $$-0.227272\pi$$
−0.945000 + 0.327070i $$0.893939\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 97.8262i 1.37783i −0.724840 0.688917i $$-0.758086\pi$$
0.724840 0.688917i $$-0.241914\pi$$
$$72$$ 0 0
$$73$$ −77.0599 −1.05561 −0.527807 0.849364i $$-0.676986\pi$$
−0.527807 + 0.849364i $$0.676986\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 29.8143 17.2133i 0.387199 0.223549i
$$78$$ 0 0
$$79$$ 42.1389 72.9868i 0.533404 0.923883i −0.465835 0.884872i $$-0.654246\pi$$
0.999239 0.0390112i $$-0.0124208\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −40.6763 23.4845i −0.490076 0.282946i 0.234530 0.972109i $$-0.424645\pi$$
−0.724606 + 0.689163i $$0.757978\pi$$
$$84$$ 0 0
$$85$$ 0.666644 + 1.15466i 0.00784287 + 0.0135843i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 108.587i 1.22008i −0.792371 0.610039i $$-0.791154\pi$$
0.792371 0.610039i $$-0.208846\pi$$
$$90$$ 0 0
$$91$$ 3.92978 0.0431844
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −1.50618 + 0.869593i −0.0158545 + 0.00915361i
$$96$$ 0 0
$$97$$ −32.4021 + 56.1221i −0.334043 + 0.578579i −0.983300 0.181990i $$-0.941746\pi$$
0.649258 + 0.760568i $$0.275080\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −168.478 97.2705i −1.66809 0.963075i −0.968664 0.248373i $$-0.920104\pi$$
−0.699430 0.714701i $$-0.746563\pi$$
$$102$$ 0 0
$$103$$ 12.4420 + 21.5502i 0.120796 + 0.209225i 0.920082 0.391726i $$-0.128122\pi$$
−0.799286 + 0.600951i $$0.794789\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 23.2306i 0.217108i 0.994091 + 0.108554i $$0.0346221\pi$$
−0.994091 + 0.108554i $$0.965378\pi$$
$$108$$ 0 0
$$109$$ −157.077 −1.44108 −0.720538 0.693416i $$-0.756105\pi$$
−0.720538 + 0.693416i $$0.756105\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 32.5614 18.7994i 0.288154 0.166366i −0.348955 0.937140i $$-0.613463\pi$$
0.637109 + 0.770774i $$0.280130\pi$$
$$114$$ 0 0
$$115$$ 0.880021 1.52424i 0.00765236 0.0132543i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 205.823 + 118.832i 1.72961 + 0.998589i
$$120$$ 0 0
$$121$$ −53.2788 92.2816i −0.440321 0.762658i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 2.54087i 0.0203269i
$$126$$ 0 0
$$127$$ −48.4364 −0.381389 −0.190694 0.981649i $$-0.561074\pi$$
−0.190694 + 0.981649i $$0.561074\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.0274376 + 0.0158411i −0.000209447 + 0.000120924i −0.500105 0.865965i $$-0.666705\pi$$
0.499895 + 0.866086i $$0.333372\pi$$
$$132$$ 0 0
$$133$$ −155.009 + 268.483i −1.16548 + 2.01867i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −0.913705 0.527528i −0.00666938 0.00385057i 0.496662 0.867944i $$-0.334559\pi$$
−0.503331 + 0.864094i $$0.667892\pi$$
$$138$$ 0 0
$$139$$ 45.3655 + 78.5754i 0.326371 + 0.565290i 0.981789 0.189976i $$-0.0608410\pi$$
−0.655418 + 0.755266i $$0.727508\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1.64860i 0.0115286i
$$144$$ 0 0
$$145$$ −0.823399 −0.00567862
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 15.1086 8.72295i 0.101400 0.0585433i −0.448442 0.893812i $$-0.648021\pi$$
0.549842 + 0.835268i $$0.314688\pi$$
$$150$$ 0 0
$$151$$ −40.8713 + 70.7912i −0.270671 + 0.468816i −0.969034 0.246928i $$-0.920579\pi$$
0.698363 + 0.715744i $$0.253912\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −1.51113 0.872452i −0.00974923 0.00562872i
$$156$$ 0 0
$$157$$ −96.4835 167.114i −0.614544 1.06442i −0.990464 0.137770i $$-0.956007\pi$$
0.375920 0.926652i $$-0.377327\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 313.735i 1.94866i
$$162$$ 0 0
$$163$$ −165.401 −1.01473 −0.507364 0.861732i $$-0.669380\pi$$
−0.507364 + 0.861732i $$0.669380\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −215.643 + 124.502i −1.29128 + 0.745520i −0.978881 0.204432i $$-0.934465\pi$$
−0.312398 + 0.949951i $$0.601132\pi$$
$$168$$ 0 0
$$169$$ 84.4059 146.195i 0.499443 0.865061i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −117.476 67.8248i −0.679052 0.392051i 0.120446 0.992720i $$-0.461568\pi$$
−0.799498 + 0.600669i $$0.794901\pi$$
$$174$$ 0 0
$$175$$ −113.224 196.110i −0.646995 1.12063i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 95.4526i 0.533255i −0.963800 0.266627i $$-0.914091\pi$$
0.963800 0.266627i $$-0.0859093\pi$$
$$180$$ 0 0
$$181$$ −58.9249 −0.325552 −0.162776 0.986663i $$-0.552045\pi$$
−0.162776 + 0.986663i $$0.552045\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.28848 0.743906i 0.00696477 0.00402111i
$$186$$ 0 0
$$187$$ −49.8517 + 86.3457i −0.266587 + 0.461742i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 164.852 + 95.1775i 0.863101 + 0.498311i 0.865049 0.501687i $$-0.167287\pi$$
−0.00194880 + 0.999998i $$0.500620\pi$$
$$192$$ 0 0
$$193$$ 5.29645 + 9.17373i 0.0274428 + 0.0475323i 0.879421 0.476046i $$-0.157930\pi$$
−0.851978 + 0.523578i $$0.824597\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 215.874i 1.09581i −0.836541 0.547904i $$-0.815426\pi$$
0.836541 0.547904i $$-0.184574\pi$$
$$198$$ 0 0
$$199$$ 146.668 0.737026 0.368513 0.929623i $$-0.379867\pi$$
0.368513 + 0.929623i $$0.379867\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −127.110 + 73.3872i −0.626159 + 0.361513i
$$204$$ 0 0
$$205$$ 1.42898 2.47506i 0.00697063 0.0120735i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −112.632 65.0282i −0.538910 0.311140i
$$210$$ 0 0
$$211$$ −54.8335 94.9744i −0.259874 0.450116i 0.706334 0.707879i $$-0.250348\pi$$
−0.966208 + 0.257763i $$0.917014\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0.401009i 0.00186516i
$$216$$ 0 0
$$217$$ −311.036 −1.43335
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −9.85631 + 5.69054i −0.0445987 + 0.0257491i
$$222$$ 0 0
$$223$$ −73.8403 + 127.895i −0.331123 + 0.573521i −0.982732 0.185033i $$-0.940761\pi$$
0.651610 + 0.758554i $$0.274094\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 346.255 + 199.911i 1.52535 + 0.880664i 0.999548 + 0.0300589i $$0.00956949\pi$$
0.525806 + 0.850605i $$0.323764\pi$$
$$228$$ 0 0
$$229$$ −39.1692 67.8430i −0.171044 0.296258i 0.767741 0.640760i $$-0.221381\pi$$
−0.938785 + 0.344503i $$0.888047\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 352.995i 1.51500i 0.652835 + 0.757500i $$0.273580\pi$$
−0.652835 + 0.757500i $$0.726420\pi$$
$$234$$ 0 0
$$235$$ 1.96284 0.00835251
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 279.549 161.397i 1.16966 0.675303i 0.216060 0.976380i $$-0.430679\pi$$
0.953600 + 0.301077i $$0.0973461\pi$$
$$240$$ 0 0
$$241$$ −105.601 + 182.907i −0.438180 + 0.758949i −0.997549 0.0699691i $$-0.977710\pi$$
0.559370 + 0.828918i $$0.311043\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1.45516 + 0.840135i 0.00593941 + 0.00342912i
$$246$$ 0 0
$$247$$ −7.42293 12.8569i −0.0300524 0.0520522i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 206.824i 0.824001i 0.911184 + 0.412001i $$0.135170\pi$$
−0.911184 + 0.412001i $$0.864830\pi$$
$$252$$ 0 0
$$253$$ 131.616 0.520222
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −20.7432 + 11.9761i −0.0807127 + 0.0465995i −0.539813 0.841785i $$-0.681505\pi$$
0.459100 + 0.888384i $$0.348172\pi$$
$$258$$ 0 0
$$259$$ 132.604 229.678i 0.511986 0.886786i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −119.369 68.9175i −0.453873 0.262044i 0.255592 0.966785i $$-0.417730\pi$$
−0.709464 + 0.704741i $$0.751063\pi$$
$$264$$ 0 0
$$265$$ 1.28390 + 2.22377i 0.00484489 + 0.00839160i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 249.461i 0.927366i 0.886001 + 0.463683i $$0.153472\pi$$
−0.886001 + 0.463683i $$0.846528\pi$$
$$270$$ 0 0
$$271$$ −72.6700 −0.268155 −0.134078 0.990971i $$-0.542807\pi$$
−0.134078 + 0.990971i $$0.542807\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 82.2709 47.4991i 0.299167 0.172724i
$$276$$ 0 0
$$277$$ 182.021 315.270i 0.657117 1.13816i −0.324242 0.945974i $$-0.605109\pi$$
0.981359 0.192185i $$-0.0615574\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −241.120 139.211i −0.858077 0.495411i 0.00529060 0.999986i $$-0.498316\pi$$
−0.863368 + 0.504575i $$0.831649\pi$$
$$282$$ 0 0
$$283$$ −13.7745 23.8581i −0.0486732 0.0843044i 0.840662 0.541560i $$-0.182166\pi$$
−0.889336 + 0.457255i $$0.848833\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 509.443i 1.77506i
$$288$$ 0 0
$$289$$ −399.303 −1.38167
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 342.145 197.537i 1.16773 0.674189i 0.214585 0.976705i $$-0.431160\pi$$
0.953144 + 0.302517i $$0.0978267\pi$$
$$294$$ 0 0
$$295$$ −0.250789 + 0.434380i −0.000850133 + 0.00147247i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 13.0111 + 7.51195i 0.0435153 + 0.0251236i
$$300$$ 0 0
$$301$$ −35.7408 61.9049i −0.118740 0.205664i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 3.71715i 0.0121874i
$$306$$ 0 0
$$307$$ −122.443 −0.398836 −0.199418 0.979915i $$-0.563905\pi$$
−0.199418 + 0.979915i $$0.563905\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −420.591 + 242.829i −1.35238 + 0.780799i −0.988583 0.150677i $$-0.951855\pi$$
−0.363801 + 0.931477i $$0.618521\pi$$
$$312$$ 0 0
$$313$$ 5.15434 8.92759i 0.0164676 0.0285226i −0.857674 0.514194i $$-0.828091\pi$$
0.874142 + 0.485671i $$0.161425\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −144.879 83.6462i −0.457033 0.263868i 0.253763 0.967266i $$-0.418332\pi$$
−0.710796 + 0.703398i $$0.751665\pi$$
$$318$$ 0 0
$$319$$ −30.7869 53.3245i −0.0965107 0.167162i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 897.845i 2.77971i
$$324$$ 0 0
$$325$$ 10.8440 0.0333661
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 303.009 174.942i 0.921000 0.531740i
$$330$$ 0 0
$$331$$ 52.2422 90.4861i 0.157831 0.273372i −0.776255 0.630419i $$-0.782883\pi$$
0.934086 + 0.357047i $$0.116216\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.11610 + 0.644381i 0.00333164 + 0.00192352i
$$336$$ 0 0
$$337$$ 196.086 + 339.631i 0.581858 + 1.00781i 0.995259 + 0.0972586i $$0.0310074\pi$$
−0.413401 + 0.910549i $$0.635659\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 130.484i 0.382651i
$$342$$ 0 0
$$343$$ −144.370 −0.420903
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −247.220 + 142.732i −0.712449 + 0.411333i −0.811967 0.583703i $$-0.801603\pi$$
0.0995180 + 0.995036i $$0.468270\pi$$
$$348$$ 0 0
$$349$$ −151.562 + 262.514i −0.434276 + 0.752189i −0.997236 0.0742956i $$-0.976329\pi$$
0.562960 + 0.826484i $$0.309663\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −308.183 177.929i −0.873039 0.504049i −0.00468222 0.999989i $$-0.501490\pi$$
−0.868357 + 0.495940i $$0.834824\pi$$
$$354$$ 0 0
$$355$$ 2.48576 + 4.30547i 0.00700215 + 0.0121281i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 148.171i 0.412733i 0.978475 + 0.206367i $$0.0661639\pi$$
−0.978475 + 0.206367i $$0.933836\pi$$
$$360$$ 0 0
$$361$$ 810.179 2.24426
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.39151 1.95809i 0.00929181 0.00536463i
$$366$$ 0 0
$$367$$ 123.772 214.380i 0.337254 0.584141i −0.646661 0.762777i $$-0.723835\pi$$
0.983915 + 0.178636i $$0.0571686\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 396.397 + 228.860i 1.06846 + 0.616873i
$$372$$ 0 0
$$373$$ 224.520 + 388.881i 0.601931 + 1.04258i 0.992528 + 0.122014i $$0.0389353\pi$$
−0.390597 + 0.920562i $$0.627731\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 7.02862i 0.0186436i
$$378$$ 0 0
$$379$$ 618.282 1.63135 0.815675 0.578510i $$-0.196366\pi$$
0.815675 + 0.578510i $$0.196366\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −370.803 + 214.083i −0.968155 + 0.558965i −0.898673 0.438619i $$-0.855468\pi$$
−0.0694818 + 0.997583i $$0.522135\pi$$
$$384$$ 0 0
$$385$$ −0.874780 + 1.51516i −0.00227216 + 0.00393549i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 585.313 + 337.930i 1.50466 + 0.868716i 0.999985 + 0.00540555i $$0.00172065\pi$$
0.504674 + 0.863310i $$0.331613\pi$$
$$390$$ 0 0
$$391$$ 454.306 + 786.881i 1.16191 + 2.01248i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 4.28300i 0.0108430i
$$396$$ 0 0
$$397$$ −209.902 −0.528721 −0.264361 0.964424i $$-0.585161\pi$$
−0.264361 + 0.964424i $$0.585161\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −175.023 + 101.050i −0.436467 + 0.251994i −0.702098 0.712080i $$-0.747753\pi$$
0.265631 + 0.964075i $$0.414420\pi$$
$$402$$ 0 0
$$403$$ 7.44734 12.8992i 0.0184797 0.0320079i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 96.3528 + 55.6293i 0.236739 + 0.136681i
$$408$$ 0 0
$$409$$ −291.252 504.464i −0.712108 1.23341i −0.964064 0.265669i $$-0.914407\pi$$
0.251957 0.967739i $$-0.418926\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 89.4085i 0.216486i
$$414$$ 0 0
$$415$$ 2.38696 0.00575172
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −675.460 + 389.977i −1.61208 + 0.930733i −0.623189 + 0.782071i $$0.714163\pi$$
−0.988888 + 0.148662i $$0.952503\pi$$
$$420$$ 0 0
$$421$$ 84.1068 145.677i 0.199779 0.346027i −0.748678 0.662934i $$-0.769311\pi$$
0.948457 + 0.316907i $$0.102644\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 567.957 + 327.910i 1.33637 + 0.771553i
$$426$$ 0 0
$$427$$ 331.299 + 573.827i 0.775876 + 1.34386i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 182.732i 0.423973i 0.977273 + 0.211986i $$0.0679933\pi$$
−0.977273 + 0.211986i $$0.932007\pi$$
$$432$$ 0 0
$$433$$ 447.193 1.03278 0.516389 0.856354i $$-0.327276\pi$$
0.516389 + 0.856354i $$0.327276\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −1026.43 + 592.612i −2.34882 + 1.35609i
$$438$$ 0 0
$$439$$ −98.6108 + 170.799i −0.224626 + 0.389063i −0.956207 0.292691i $$-0.905449\pi$$
0.731581 + 0.681754i $$0.238783\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −244.803 141.337i −0.552603 0.319045i 0.197568 0.980289i $$-0.436696\pi$$
−0.750171 + 0.661244i $$0.770029\pi$$
$$444$$ 0 0
$$445$$ 2.75919 + 4.77906i 0.00620043 + 0.0107395i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 349.046i 0.777386i 0.921367 + 0.388693i $$0.127073\pi$$
−0.921367 + 0.388693i $$0.872927\pi$$
$$450$$ 0 0
$$451$$ 213.718 0.473877
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −0.172955 + 0.0998556i −0.000380121 + 0.000219463i
$$456$$ 0 0
$$457$$ −40.2987 + 69.7995i −0.0881811 + 0.152734i −0.906742 0.421685i $$-0.861439\pi$$
0.818561 + 0.574419i $$0.194772\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 495.135 + 285.866i 1.07405 + 0.620100i 0.929284 0.369366i $$-0.120425\pi$$
0.144761 + 0.989467i $$0.453759\pi$$
$$462$$ 0 0
$$463$$ −139.837 242.205i −0.302024 0.523120i 0.674571 0.738210i $$-0.264329\pi$$
−0.976594 + 0.215090i $$0.930996\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 506.702i 1.08501i −0.840051 0.542507i $$-0.817475\pi$$
0.840051 0.542507i $$-0.182525\pi$$
$$468$$ 0 0
$$469$$ 229.727 0.489823
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 25.9699 14.9938i 0.0549048 0.0316993i
$$474$$ 0 0
$$475$$ −427.737 + 740.862i −0.900499 + 1.55971i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −217.596 125.629i −0.454271 0.262274i 0.255361 0.966846i $$-0.417806\pi$$
−0.709632 + 0.704572i $$0.751139\pi$$
$$480$$ 0 0
$$481$$ 6.35006 + 10.9986i 0.0132018 + 0.0228662i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 3.29335i 0.00679041i
$$486$$ 0 0
$$487$$ 313.224 0.643170 0.321585 0.946881i $$-0.395784\pi$$
0.321585 + 0.946881i $$0.395784\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −533.397 + 307.957i −1.08635 + 0.627204i −0.932602 0.360906i $$-0.882467\pi$$
−0.153747 + 0.988110i $$0.549134\pi$$
$$492$$ 0 0
$$493$$ 212.538 368.126i 0.431111 0.746706i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 767.467 + 443.098i 1.54420 + 0.891544i
$$498$$ 0 0
$$499$$ −412.029 713.654i −0.825709 1.43017i −0.901377 0.433036i $$-0.857442\pi$$
0.0756679 0.997133i $$-0.475891\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 175.718i 0.349340i −0.984627 0.174670i $$-0.944114\pi$$
0.984627 0.174670i $$-0.0558858\pi$$
$$504$$ 0 0
$$505$$ 9.88657 0.0195774
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −314.934 + 181.827i −0.618730 + 0.357224i −0.776374 0.630272i $$-0.782943\pi$$
0.157644 + 0.987496i $$0.449610\pi$$
$$510$$ 0 0
$$511$$ 349.038 604.551i 0.683049 1.18307i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.09518 0.632301i −0.00212656 0.00122777i
$$516$$ 0 0
$$517$$ 73.3907 + 127.116i 0.141955 + 0.245873i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 458.709i 0.880440i 0.897890 + 0.440220i $$0.145099\pi$$
−0.897890 + 0.440220i $$0.854901\pi$$
$$522$$ 0 0
$$523$$ −458.289 −0.876270 −0.438135 0.898909i $$-0.644361\pi$$
−0.438135 + 0.898909i $$0.644361\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 780.113 450.398i 1.48029 0.854646i
$$528$$ 0 0
$$529$$ 335.219 580.616i 0.633683 1.09757i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 21.1274 + 12.1979i 0.0396387 + 0.0228854i
$$534$$ 0 0
$$535$$ −0.590289 1.02241i −0.00110334 0.00191105i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 125.651i 0.233118i
$$540$$ 0 0
$$541$$ 824.876 1.52472 0.762362 0.647150i $$-0.224039\pi$$
0.762362 + 0.647150i $$0.224039\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 6.91319 3.99133i 0.0126847 0.00732354i
$$546$$ 0 0
$$547$$ −16.8719 + 29.2230i −0.0308444 + 0.0534241i −0.881036 0.473050i $$-0.843153\pi$$
0.850191 + 0.526474i $$0.176486\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 480.196 + 277.241i 0.871499 + 0.503160i
$$552$$ 0 0
$$553$$ 381.731 + 661.178i 0.690291 + 1.19562i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 541.032i 0.971332i −0.874145 0.485666i $$-0.838577\pi$$
0.874145 0.485666i $$-0.161423\pi$$
$$558$$ 0 0
$$559$$ 3.42306 0.00612354
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 97.8909 56.5173i 0.173874 0.100386i −0.410537 0.911844i $$-0.634659\pi$$
0.584411 + 0.811458i $$0.301326\pi$$
$$564$$ 0 0
$$565$$ −0.955383 + 1.65477i −0.00169094 + 0.00292880i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −236.524 136.557i −0.415684 0.239995i 0.277545 0.960713i $$-0.410479\pi$$
−0.693229 + 0.720717i $$0.743813\pi$$
$$570$$ 0 0
$$571$$ 122.654 + 212.443i 0.214806 + 0.372054i 0.953212 0.302301i $$-0.0977548\pi$$
−0.738407 + 0.674356i $$0.764421\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 865.733i 1.50562i
$$576$$ 0 0
$$577$$ 632.666 1.09648 0.548238 0.836323i $$-0.315299\pi$$
0.548238 + 0.836323i $$0.315299\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 368.482 212.743i 0.634220 0.366167i
$$582$$ 0 0
$$583$$ −96.0099 + 166.294i −0.164682 + 0.285238i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 980.129 + 565.878i 1.66973 + 0.964017i 0.967784 + 0.251782i $$0.0810167\pi$$
0.701942 + 0.712234i $$0.252317\pi$$
$$588$$ 0 0
$$589$$ 587.515 + 1017.61i 0.997478 + 1.72768i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 180.213i 0.303900i 0.988388 + 0.151950i $$0.0485553\pi$$
−0.988388 + 0.151950i $$0.951445\pi$$
$$594$$ 0 0
$$595$$ −12.0781 −0.0202993
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −566.086 + 326.830i −0.945052 + 0.545626i −0.891541 0.452941i $$-0.850375\pi$$
−0.0535119 + 0.998567i $$0.517041\pi$$
$$600$$ 0 0
$$601$$ −178.947 + 309.945i −0.297749 + 0.515716i −0.975621 0.219464i $$-0.929569\pi$$
0.677872 + 0.735180i $$0.262902\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 4.68975 + 2.70763i 0.00775164 + 0.00447541i
$$606$$ 0 0
$$607$$ −320.064 554.367i −0.527288 0.913290i −0.999494 0.0318015i $$-0.989876\pi$$
0.472206 0.881488i $$-0.343458\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 16.7550i 0.0274223i
$$612$$ 0 0
$$613$$ −246.093 −0.401457 −0.200729 0.979647i $$-0.564331\pi$$
−0.200729 + 0.979647i $$0.564331\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −309.912 + 178.928i −0.502289 + 0.289997i −0.729658 0.683812i $$-0.760321\pi$$
0.227369 + 0.973809i $$0.426987\pi$$
$$618$$ 0 0
$$619$$ −40.5053 + 70.1573i −0.0654368 + 0.113340i −0.896888 0.442258i $$-0.854177\pi$$
0.831451 + 0.555598i $$0.187511\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 851.888 + 491.838i 1.36740 + 0.789467i
$$624$$ 0 0
$$625$$ −312.403 541.098i −0.499845 0.865757i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 768.075i 1.22110i
$$630$$ 0 0
$$631$$ 252.241 0.399748 0.199874 0.979822i $$-0.435947\pi$$
0.199874 + 0.979822i $$0.435947\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 2.13175 1.23077i 0.00335709 0.00193822i
$$636$$ 0 0
$$637$$ −7.17147 + 12.4214i −0.0112582 + 0.0194998i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 843.278 + 486.867i 1.31557 + 0.759542i 0.983012 0.183542i $$-0.0587563\pi$$
0.332554 + 0.943084i $$0.392090\pi$$
$$642$$ 0 0
$$643$$ −341.530 591.547i −0.531151 0.919980i −0.999339 0.0363512i $$-0.988426\pi$$
0.468188 0.883629i $$-0.344907\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 390.640i 0.603771i 0.953344 + 0.301885i $$0.0976160\pi$$
−0.953344 + 0.301885i $$0.902384\pi$$
$$648$$ 0 0
$$649$$ −37.5081 −0.0577937
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 542.529 313.230i 0.830826 0.479678i −0.0233093 0.999728i $$-0.507420\pi$$
0.854135 + 0.520051i $$0.174087\pi$$
$$654$$ 0 0
$$655$$ 0.000805043 0.00139438i 1.22907e−6 2.12882e-6i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −51.4518 29.7057i −0.0780755 0.0450769i 0.460454 0.887684i $$-0.347687\pi$$
−0.538530 + 0.842607i $$0.681020\pi$$
$$660$$ 0 0
$$661$$ −425.950 737.767i −0.644402 1.11614i −0.984439 0.175725i $$-0.943773\pi$$
0.340037 0.940412i $$-0.389560\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 15.7551i 0.0236918i
$$666$$ 0 0
$$667$$ −561.132 −0.841277
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −240.728 + 138.985i −0.358760 + 0.207130i
$$672$$ 0 0
$$673$$ 210.489 364.577i 0.312762 0.541720i −0.666197 0.745776i $$-0.732079\pi$$
0.978959 + 0.204056i $$0.0654124\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 313.326 + 180.899i 0.462816 + 0.267207i 0.713227 0.700933i $$-0.247233\pi$$
−0.250412 + 0.968139i $$0.580566\pi$$
$$678$$ 0 0
$$679$$ −293.527 508.403i −0.432293 0.748753i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 705.769i 1.03334i −0.856186 0.516668i $$-0.827172\pi$$
0.856186 0.516668i $$-0.172828\pi$$
$$684$$ 0 0
$$685$$ 0.0536179 7.82743e−5
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −18.9824 + 10.9595i −0.0275506 + 0.0159063i
$$690$$ 0 0
$$691$$ 345.384 598.222i 0.499832 0.865734i −0.500168 0.865928i $$-0.666728\pi$$
1.00000 0.000194148i $$6.17992e-5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −3.99320 2.30547i −0.00574561 0.00331723i
$$696$$ 0 0
$$697$$ 737.703 + 1277.74i 1.05840 + 1.83320i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1213.04i 1.73045i 0.501384 + 0.865225i $$0.332824\pi$$
−0.501384 + 0.865225i $$0.667176\pi$$
$$702$$ 0 0
$$703$$ −1001.90 −1.42518
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1526.22 881.161i 2.15872 1.24634i
$$708$$ 0 0
$$709$$ −226.667 + 392.598i −0.319699 + 0.553735i −0.980425 0.196892i $$-0.936915\pi$$
0.660726 + 0.750627i $$0.270249\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1029.81 594.560i −1.44433 0.833885i
$$714$$ 0 0
$$715$$ −0.0418908 0.0725570i −5.85885e−5 0.000101478i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 418.833i 0.582522i −0.956644 0.291261i $$-0.905925\pi$$
0.956644 0.291261i $$-0.0940748\pi$$
$$720$$ 0 0
$$721$$ −225.421 −0.312650
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −350.753 + 202.508i −0.483798 + 0.279321i
$$726$$ 0 0
$$727$$ −376.166 + 651.539i −0.517423 + 0.896203i 0.482372 + 0.875966i $$0.339775\pi$$
−0.999795 + 0.0202365i $$0.993558\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 179.284 + 103.509i 0.245258 + 0.141600i
$$732$$ 0 0
$$733$$ −255.863 443.168i −0.349063 0.604595i 0.637020 0.770847i $$-0.280167\pi$$
−0.986083 + 0.166252i $$0.946833\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 96.3737i 0.130765i
$$738$$ 0 0
$$739$$ −466.830 −0.631705 −0.315853 0.948808i $$-0.602290\pi$$
−0.315853 + 0.948808i $$0.602290\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −546.320 + 315.418i −0.735290 + 0.424520i −0.820354 0.571856i $$-0.806224\pi$$
0.0850643 + 0.996375i $$0.472890\pi$$
$$744$$ 0 0
$$745$$ −0.443300 + 0.767818i −0.000595034 + 0.00103063i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −182.249 105.222i −0.243323 0.140483i
$$750$$ 0 0
$$751$$ −90.7172 157.127i −0.120795 0.209223i 0.799286 0.600950i $$-0.205211\pi$$
−0.920081 + 0.391727i $$0.871878\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 4.15416i 0.00550220i
$$756$$ 0 0
$$757$$ 1381.82 1.82539 0.912696 0.408640i $$-0.133997\pi$$
0.912696 + 0.408640i $$0.133997\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 590.093 340.690i 0.775418 0.447688i −0.0593862 0.998235i $$-0.518914\pi$$
0.834804 + 0.550548i $$0.185581\pi$$
$$762$$ 0 0
$$763$$ 711.471 1232.30i 0.932466 1.61508i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −3.70791 2.14076i −0.00483430 0.00279109i
$$768$$ 0 0
$$769$$ −45.1754 78.2461i −0.0587457 0.101750i 0.835157 0.550012i $$-0.185377\pi$$
−0.893903 + 0.448261i $$0.852043\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 87.4025i 0.113069i 0.998401 + 0.0565346i $$0.0180051\pi$$
−0.998401 + 0.0565346i $$0.981995\pi$$
$$774$$ 0 0
$$775$$ −858.286 −1.10747
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1666.72 + 962.284i −2.13957 + 1.23528i
$$780$$ 0 0
$$781$$ −185.885 + 321.963i −0.238010 + 0.412245i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 8.49274 + 4.90329i 0.0108188 + 0.00624622i
$$786$$ 0 0
$$787$$ 366.731 + 635.196i 0.465986 + 0.807111i 0.999245 0.0388408i $$-0.0123665\pi$$
−0.533260 + 0.845951i $$0.679033\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 340.602i 0.430597i
$$792$$ 0 0
$$793$$ −31.7300 −0.0400126
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 853.500 492.768i 1.07089 0.618279i 0.142466 0.989800i $$-0.454497\pi$$
0.928425 + 0.371521i $$0.121164\pi$$
$$798$$ 0 0
$$799$$ −506.653 + 877.549i