# Properties

 Label 128.4.e.b.97.3 Level $128$ Weight $4$ Character 128.97 Analytic conductor $7.552$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 128.e (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.55224448073$$ 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: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$2^{20}$$ Twist minimal: no (minimal twist has level 16) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 97.3 Root $$-1.62580 - 1.16481i$$ of defining polynomial Character $$\chi$$ $$=$$ 128.97 Dual form 128.4.e.b.33.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.756776 + 0.756776i) q^{3} +(-8.22587 - 8.22587i) q^{5} +2.67171i q^{7} +25.8546i q^{9} +O(q^{10})$$ $$q+(-0.756776 + 0.756776i) q^{3} +(-8.22587 - 8.22587i) q^{5} +2.67171i q^{7} +25.8546i q^{9} +(45.2213 + 45.2213i) q^{11} +(-35.3968 + 35.3968i) q^{13} +12.4503 q^{15} -72.4991 q^{17} +(-19.4427 + 19.4427i) q^{19} +(-2.02188 - 2.02188i) q^{21} +139.462i q^{23} +10.3299i q^{25} +(-39.9991 - 39.9991i) q^{27} +(-66.0434 + 66.0434i) q^{29} +188.682 q^{31} -68.4447 q^{33} +(21.9771 - 21.9771i) q^{35} +(84.0653 + 84.0653i) q^{37} -53.5748i q^{39} -104.629i q^{41} +(31.4857 + 31.4857i) q^{43} +(212.676 - 212.676i) q^{45} -488.151 q^{47} +335.862 q^{49} +(54.8656 - 54.8656i) q^{51} +(-149.560 - 149.560i) q^{53} -743.968i q^{55} -29.4275i q^{57} +(-284.698 - 284.698i) q^{59} +(228.069 - 228.069i) q^{61} -69.0758 q^{63} +582.338 q^{65} +(-139.151 + 139.151i) q^{67} +(-105.541 - 105.541i) q^{69} +453.655i q^{71} +259.747i q^{73} +(-7.81740 - 7.81740i) q^{75} +(-120.818 + 120.818i) q^{77} +323.190 q^{79} -637.533 q^{81} +(563.897 - 563.897i) q^{83} +(596.368 + 596.368i) q^{85} -99.9602i q^{87} -866.853i q^{89} +(-94.5697 - 94.5697i) q^{91} +(-142.790 + 142.790i) q^{93} +319.866 q^{95} -936.077 q^{97} +(-1169.18 + 1169.18i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q + 2q^{3} + 2q^{5} + O(q^{10})$$ $$10q + 2q^{3} + 2q^{5} - 18q^{11} + 2q^{13} - 124q^{15} - 4q^{17} + 26q^{19} - 52q^{21} - 184q^{27} + 202q^{29} + 368q^{31} - 4q^{33} - 476q^{35} + 10q^{37} + 838q^{43} - 194q^{45} - 944q^{47} + 94q^{49} + 1500q^{51} + 378q^{53} - 1706q^{59} - 910q^{61} + 2628q^{63} - 492q^{65} - 1942q^{67} - 580q^{69} + 2954q^{75} + 268q^{77} - 4416q^{79} + 482q^{81} + 2562q^{83} + 12q^{85} - 3332q^{91} + 2192q^{93} + 6900q^{95} - 4q^{97} - 4958q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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
$$3$$ −0.756776 + 0.756776i −0.145642 + 0.145642i −0.776168 0.630526i $$-0.782839\pi$$
0.630526 + 0.776168i $$0.282839\pi$$
$$4$$ 0 0
$$5$$ −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 $$0.977021\pi$$
$$8$$ 0 0
$$9$$ 25.8546i 0.957577i
$$10$$ 0 0
$$11$$ 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 −0.975440 0.220264i $$-0.929308\pi$$
0.220264 + 0.975440i $$0.429308\pi$$
$$14$$ 0 0
$$15$$ 12.4503 0.214310
$$16$$ 0 0
$$17$$ −72.4991 −1.03433 −0.517165 0.855886i $$-0.673013\pi$$
−0.517165 + 0.855886i $$0.673013\pi$$
$$18$$ 0 0
$$19$$ −19.4427 + 19.4427i −0.234761 + 0.234761i −0.814676 0.579916i $$-0.803085\pi$$
0.579916 + 0.814676i $$0.303085\pi$$
$$20$$ 0 0
$$21$$ −2.02188 2.02188i −0.0210100 0.0210100i
$$22$$ 0 0
$$23$$ 139.462i 1.26434i 0.774830 + 0.632170i $$0.217835\pi$$
−0.774830 + 0.632170i $$0.782165\pi$$
$$24$$ 0 0
$$25$$ 10.3299i 0.0826390i
$$26$$ 0 0
$$27$$ −39.9991 39.9991i −0.285105 0.285105i
$$28$$ 0 0
$$29$$ −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 $$0.315928\pi$$
$$32$$ 0 0
$$33$$ −68.4447 −0.361051
$$34$$ 0 0
$$35$$ 21.9771 21.9771i 0.106137 0.106137i
$$36$$ 0 0
$$37$$ 84.0653 + 84.0653i 0.373520 + 0.373520i 0.868758 0.495237i $$-0.164919\pi$$
−0.495237 + 0.868758i $$0.664919\pi$$
$$38$$ 0 0
$$39$$ 53.5748i 0.219970i
$$40$$ 0 0
$$41$$ 104.629i 0.398545i −0.979944 0.199272i $$-0.936142\pi$$
0.979944 0.199272i $$-0.0638578\pi$$
$$42$$ 0 0
$$43$$ 31.4857 + 31.4857i 0.111663 + 0.111663i 0.760731 0.649067i $$-0.224841\pi$$
−0.649067 + 0.760731i $$0.724841\pi$$
$$44$$ 0 0
$$45$$ 212.676 212.676i 0.704532 0.704532i
$$46$$ 0 0
$$47$$ −488.151 −1.51498 −0.757491 0.652846i $$-0.773575\pi$$
−0.757491 + 0.652846i $$0.773575\pi$$
$$48$$ 0 0
$$49$$ 335.862 0.979189
$$50$$ 0 0
$$51$$ 54.8656 54.8656i 0.150641 0.150641i
$$52$$ 0 0
$$53$$ −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
$$56$$ 0 0
$$57$$ 29.4275i 0.0683819i
$$58$$ 0 0
$$59$$ −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 −0.426010 0.904719i $$-0.640081\pi$$
0.904719 + 0.426010i $$0.140081\pi$$
$$62$$ 0 0
$$63$$ −69.0758 −0.138139
$$64$$ 0 0
$$65$$ 582.338 1.11123
$$66$$ 0 0
$$67$$ −139.151 + 139.151i −0.253730 + 0.253730i −0.822498 0.568768i $$-0.807420\pi$$
0.568768 + 0.822498i $$0.307420\pi$$
$$68$$ 0 0
$$69$$ −105.541 105.541i −0.184140 0.184140i
$$70$$ 0 0
$$71$$ 453.655i 0.758294i 0.925336 + 0.379147i $$0.123783\pi$$
−0.925336 + 0.379147i $$0.876217\pi$$
$$72$$ 0 0
$$73$$ 259.747i 0.416454i 0.978081 + 0.208227i $$0.0667692\pi$$
−0.978081 + 0.208227i $$0.933231\pi$$
$$74$$ 0 0
$$75$$ −7.81740 7.81740i −0.0120357 0.0120357i
$$76$$ 0 0
$$77$$ −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 $$0.426082\pi$$
$$80$$ 0 0
$$81$$ −637.533 −0.874531
$$82$$ 0 0
$$83$$ 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
$$86$$ 0 0
$$87$$ 99.9602i 0.123182i
$$88$$ 0 0
$$89$$ 866.853i 1.03243i −0.856459 0.516215i $$-0.827341\pi$$
0.856459 0.516215i $$-0.172659\pi$$
$$90$$ 0 0
$$91$$ −94.5697 94.5697i −0.108941 0.108941i
$$92$$ 0 0
$$93$$ −142.790 + 142.790i −0.159211 + 0.159211i
$$94$$ 0 0
$$95$$ 319.866 0.345448
$$96$$ 0 0
$$97$$ −936.077 −0.979837 −0.489919 0.871768i $$-0.662974\pi$$
−0.489919 + 0.871768i $$0.662974\pi$$
$$98$$ 0 0
$$99$$ −1169.18 + 1169.18i −1.18694 + 1.18694i
$$100$$ 0 0
$$101$$ 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 $$0.768842\pi$$
$$104$$ 0 0
$$105$$ 33.2635i 0.0309160i
$$106$$ 0 0
$$107$$ 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 −0.901328 0.433138i $$-0.857406\pi$$
0.433138 + 0.901328i $$0.357406\pi$$
$$110$$ 0 0
$$111$$ −127.237 −0.108800
$$112$$ 0 0
$$113$$ −67.2680 −0.0560003 −0.0280002 0.999608i $$-0.508914\pi$$
−0.0280002 + 0.999608i $$0.508914\pi$$
$$114$$ 0 0
$$115$$ 1147.19 1147.19i 0.930230 0.930230i
$$116$$ 0 0
$$117$$ −915.168 915.168i −0.723140 0.723140i
$$118$$ 0 0
$$119$$ 193.696i 0.149211i
$$120$$ 0 0
$$121$$ 2758.92i 2.07282i
$$122$$ 0 0
$$123$$ 79.1808 + 79.1808i 0.0580447 + 0.0580447i
$$124$$ 0 0
$$125$$ −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 $$0.268421\pi$$
$$128$$ 0 0
$$129$$ −47.6552 −0.0325257
$$130$$ 0 0
$$131$$ −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
$$134$$ 0 0
$$135$$ 658.054i 0.419528i
$$136$$ 0 0
$$137$$ 477.234i 0.297612i −0.988866 0.148806i $$-0.952457\pi$$
0.988866 0.148806i $$-0.0475430\pi$$
$$138$$ 0 0
$$139$$ 1513.89 + 1513.89i 0.923788 + 0.923788i 0.997295 0.0735064i $$-0.0234189\pi$$
−0.0735064 + 0.997295i $$0.523419\pi$$
$$140$$ 0 0
$$141$$ 369.421 369.421i 0.220644 0.220644i
$$142$$ 0 0
$$143$$ −3201.37 −1.87211
$$144$$ 0 0
$$145$$ 1086.53 0.622285
$$146$$ 0 0
$$147$$ −254.172 + 254.172i −0.142611 + 0.142611i
$$148$$ 0 0
$$149$$ −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 $$-0.299304\pi$$
$$152$$ 0 0
$$153$$ 1874.43i 0.990451i
$$154$$ 0 0
$$155$$ −1552.07 1552.07i −0.804293 0.804293i
$$156$$ 0 0
$$157$$ 1509.01 1509.01i 0.767082 0.767082i −0.210510 0.977592i $$-0.567512\pi$$
0.977592 + 0.210510i $$0.0675125\pi$$
$$158$$ 0 0
$$159$$ 226.368 0.112906
$$160$$ 0 0
$$161$$ −372.601 −0.182392
$$162$$ 0 0
$$163$$ 1425.19 1425.19i 0.684844 0.684844i −0.276244 0.961088i $$-0.589090\pi$$
0.961088 + 0.276244i $$0.0890898\pi$$
$$164$$ 0 0
$$165$$ 563.017 + 563.017i 0.265641 + 0.265641i
$$166$$ 0 0
$$167$$ 792.415i 0.367179i 0.983003 + 0.183590i $$0.0587717\pi$$
−0.983003 + 0.183590i $$0.941228\pi$$
$$168$$ 0 0
$$169$$ 308.861i 0.140583i
$$170$$ 0 0
$$171$$ −502.682 502.682i −0.224802 0.224802i
$$172$$ 0 0
$$173$$ 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
$$176$$ 0 0
$$177$$ 430.905 0.182988
$$178$$ 0 0
$$179$$ −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 $$0.0249157\pi$$
0.0781951 + 0.996938i $$0.475084\pi$$
$$182$$ 0 0
$$183$$ 345.194i 0.139440i
$$184$$ 0 0
$$185$$ 1383.02i 0.549631i
$$186$$ 0 0
$$187$$ −3278.50 3278.50i −1.28207 1.28207i
$$188$$ 0 0
$$189$$ 106.866 106.866i 0.0411288 0.0411288i
$$190$$ 0 0
$$191$$ 3216.39 1.21848 0.609240 0.792986i $$-0.291475\pi$$
0.609240 + 0.792986i $$0.291475\pi$$
$$192$$ 0 0
$$193$$ 2852.57 1.06390 0.531950 0.846776i $$-0.321459\pi$$
0.531950 + 0.846776i $$0.321459\pi$$
$$194$$ 0 0
$$195$$ −440.700 + 440.700i −0.161842 + 0.161842i
$$196$$ 0 0
$$197$$ −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 $$-0.0424845\pi$$
$$200$$ 0 0
$$201$$ 210.612i 0.0739074i
$$202$$ 0 0
$$203$$ −176.449 176.449i −0.0610062 0.0610062i
$$204$$ 0 0
$$205$$ −860.666 + 860.666i −0.293227 + 0.293227i
$$206$$ 0 0
$$207$$ −3605.73 −1.21070
$$208$$ 0 0
$$209$$ −1758.44 −0.581981
$$210$$ 0 0
$$211$$ 2227.13 2227.13i 0.726645 0.726645i −0.243305 0.969950i $$-0.578231\pi$$
0.969950 + 0.243305i $$0.0782315\pi$$
$$212$$ 0 0
$$213$$ −343.315 343.315i −0.110439 0.110439i
$$214$$ 0 0
$$215$$ 517.995i 0.164311i
$$216$$ 0 0
$$217$$ 504.102i 0.157699i
$$218$$ 0 0
$$219$$ −196.570 196.570i −0.0606530 0.0606530i
$$220$$ 0 0
$$221$$ 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 $$0.517121\pi$$
$$224$$ 0 0
$$225$$ −267.075 −0.0791332
$$226$$ 0 0
$$227$$ −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 0.882664 0.470005i $$-0.155748\pi$$
−0.470005 + 0.882664i $$0.655748\pi$$
$$230$$ 0 0
$$231$$ 182.864i 0.0520847i
$$232$$ 0 0
$$233$$ 926.479i 0.260496i 0.991481 + 0.130248i $$0.0415774\pi$$
−0.991481 + 0.130248i $$0.958423\pi$$
$$234$$ 0 0
$$235$$ 4015.47 + 4015.47i 1.11464 + 1.11464i
$$236$$ 0 0
$$237$$ −244.583 + 244.583i −0.0670352 + 0.0670352i
$$238$$ 0 0
$$239$$ −792.472 −0.214480 −0.107240 0.994233i $$-0.534201\pi$$
−0.107240 + 0.994233i $$0.534201\pi$$
$$240$$ 0 0
$$241$$ 1449.01 0.387299 0.193650 0.981071i $$-0.437967\pi$$
0.193650 + 0.981071i $$0.437967\pi$$
$$242$$ 0 0
$$243$$ 1562.44 1562.44i 0.412473 0.412473i
$$244$$ 0 0
$$245$$ −2762.76 2762.76i −0.720433 0.720433i
$$246$$ 0 0
$$247$$ 1376.42i 0.354572i
$$248$$ 0 0
$$249$$ 853.487i 0.217219i
$$250$$ 0 0
$$251$$ 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
$$254$$ 0 0
$$255$$ −902.634 −0.221667
$$256$$ 0 0
$$257$$ −4708.87 −1.14292 −0.571461 0.820629i $$-0.693623\pi$$
−0.571461 + 0.820629i $$0.693623\pi$$
$$258$$ 0 0
$$259$$ −224.598 + 224.598i −0.0538835 + 0.0538835i
$$260$$ 0 0
$$261$$ −1707.53 1707.53i −0.404955 0.404955i
$$262$$ 0 0
$$263$$ 2967.82i 0.695830i 0.937526 + 0.347915i $$0.113110\pi$$
−0.937526 + 0.347915i $$0.886890\pi$$
$$264$$ 0 0
$$265$$ 2460.53i 0.570374i
$$266$$ 0 0
$$267$$ 656.013 + 656.013i 0.150365 + 0.150365i
$$268$$ 0 0
$$269$$ 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 $$0.141212\pi$$
$$272$$ 0 0
$$273$$ 143.136 0.0317326
$$274$$ 0 0
$$275$$ −467.130 + 467.130i −0.102433 + 0.102433i
$$276$$ 0 0
$$277$$ −482.477 482.477i −0.104654 0.104654i 0.652841 0.757495i $$-0.273577\pi$$
−0.757495 + 0.652841i $$0.773577\pi$$
$$278$$ 0 0
$$279$$ 4878.29i 1.04679i
$$280$$ 0 0
$$281$$ 5899.10i 1.25235i 0.779682 + 0.626175i $$0.215381\pi$$
−0.779682 + 0.626175i $$0.784619\pi$$
$$282$$ 0 0
$$283$$ 679.897 + 679.897i 0.142812 + 0.142812i 0.774898 0.632086i $$-0.217801\pi$$
−0.632086 + 0.774898i $$0.717801\pi$$
$$284$$ 0 0
$$285$$ −242.067 + 242.067i −0.0503116 + 0.0503116i
$$286$$ 0 0
$$287$$ 279.538 0.0574935
$$288$$ 0 0
$$289$$ 343.118 0.0698388
$$290$$ 0 0
$$291$$ 708.401 708.401i 0.142705 0.142705i
$$292$$ 0 0
$$293$$ 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
$$296$$ 0 0
$$297$$ 3617.62i 0.706786i
$$298$$ 0 0
$$299$$ −4936.50 4936.50i −0.954799 0.954799i
$$300$$ 0 0
$$301$$ −84.1205 + 84.1205i −0.0161084 + 0.0161084i
$$302$$ 0 0
$$303$$ −2.40419 −0.000455831
$$304$$ 0 0
$$305$$ −3752.13 −0.704415
$$306$$ 0 0
$$307$$ −2735.56 + 2735.56i −0.508556 + 0.508556i −0.914083 0.405527i $$-0.867088\pi$$
0.405527 + 0.914083i $$0.367088\pi$$
$$308$$ 0 0
$$309$$ −1050.62 1050.62i −0.193423 0.193423i
$$310$$ 0 0
$$311$$ 5796.70i 1.05692i −0.848960 0.528458i $$-0.822771\pi$$
0.848960 0.528458i $$-0.177229\pi$$
$$312$$ 0 0
$$313$$ 8362.62i 1.51017i −0.655627 0.755085i $$-0.727596\pi$$
0.655627 0.755085i $$-0.272404\pi$$
$$314$$ 0 0
$$315$$ 568.209 + 568.209i 0.101635 + 0.101635i
$$316$$ 0 0
$$317$$ 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
$$320$$ 0 0
$$321$$ −1243.42 −0.216203
$$322$$ 0 0
$$323$$ 1409.58 1409.58i 0.242820 0.242820i
$$324$$ 0 0
$$325$$ −365.644 365.644i −0.0624071 0.0624071i
$$326$$ 0 0
$$327$$ 806.416i 0.136376i
$$328$$ 0 0
$$329$$ 1304.20i 0.218549i
$$330$$ 0 0
$$331$$ −2687.86 2687.86i −0.446339 0.446339i 0.447797 0.894135i $$-0.352209\pi$$
−0.894135 + 0.447797i $$0.852209\pi$$
$$332$$ 0 0
$$333$$ −2173.47 + 2173.47i −0.357675 + 0.357675i
$$334$$ 0 0
$$335$$ 2289.27 0.373361
$$336$$ 0 0
$$337$$ −1795.31 −0.290199 −0.145099 0.989417i $$-0.546350\pi$$
−0.145099 + 0.989417i $$0.546350\pi$$
$$338$$ 0 0
$$339$$ 50.9068 50.9068i 0.00815598 0.00815598i
$$340$$ 0 0
$$341$$ 8532.42 + 8532.42i 1.35500 + 1.35500i
$$342$$ 0 0
$$343$$ 1813.72i 0.285515i
$$344$$ 0 0
$$345$$ 1736.34i 0.270960i
$$346$$ 0 0
$$347$$ 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 $$-0.455580\pi$$
0.990279 0.139097i $$-0.0444200\pi$$
$$350$$ 0 0
$$351$$ 2831.68 0.430609
$$352$$ 0 0
$$353$$ 10644.3 1.60493 0.802466 0.596698i $$-0.203521\pi$$
0.802466 + 0.596698i $$0.203521\pi$$
$$354$$ 0 0
$$355$$ 3731.70 3731.70i 0.557911 0.557911i
$$356$$ 0 0
$$357$$ 146.585 + 146.585i 0.0217313 + 0.0217313i
$$358$$ 0 0
$$359$$ 7459.42i 1.09664i −0.836269 0.548319i $$-0.815268\pi$$
0.836269 0.548319i $$-0.184732\pi$$
$$360$$ 0 0
$$361$$ 6102.96i 0.889775i
$$362$$ 0 0
$$363$$ −2087.89 2087.89i −0.301889 0.301889i
$$364$$ 0 0
$$365$$ 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 $$0.646645\pi$$
$$368$$ 0 0
$$369$$ 2705.14 0.381637
$$370$$ 0 0
$$371$$ 399.582 399.582i 0.0559171 0.0559171i
$$372$$ 0 0
$$373$$ −8911.86 8911.86i −1.23710 1.23710i −0.961180 0.275921i $$-0.911017\pi$$
−0.275921 0.961180i $$-0.588983\pi$$
$$374$$ 0 0
$$375$$ 1427.68i 0.196600i
$$376$$ 0 0
$$377$$ 4675.45i 0.638721i
$$378$$ 0 0
$$379$$ −1184.03 1184.03i −0.160473 0.160473i 0.622303 0.782776i $$-0.286197\pi$$
−0.782776 + 0.622303i $$0.786197\pi$$
$$380$$ 0 0
$$381$$ −1440.59 + 1440.59i −0.193711 + 0.193711i
$$382$$ 0 0
$$383$$ −2880.38 −0.384283 −0.192142 0.981367i $$-0.561543\pi$$
−0.192142 + 0.981367i $$0.561543\pi$$
$$384$$ 0 0
$$385$$ 1987.66 0.263119
$$386$$ 0 0
$$387$$ −814.050 + 814.050i −0.106926 + 0.106926i
$$388$$ 0 0
$$389$$ −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
$$392$$ 0 0
$$393$$ 1390.09i 0.178424i
$$394$$ 0 0
$$395$$ −2658.52 2658.52i −0.338645 0.338645i
$$396$$ 0 0
$$397$$ 4257.80 4257.80i 0.538270 0.538270i −0.384751 0.923020i $$-0.625713\pi$$
0.923020 + 0.384751i $$0.125713\pi$$
$$398$$ 0 0
$$399$$ 78.6216 0.00986467
$$400$$ 0 0
$$401$$ 12722.6 1.58437 0.792187 0.610278i $$-0.208942\pi$$
0.792187 + 0.610278i $$0.208942\pi$$
$$402$$ 0 0
$$403$$ −6678.72 + 6678.72i −0.825535 + 0.825535i
$$404$$ 0 0
$$405$$ 5244.26 + 5244.26i 0.643431 + 0.643431i
$$406$$ 0 0
$$407$$ 7603.08i 0.925972i
$$408$$ 0 0
$$409$$ 232.991i 0.0281678i −0.999901 0.0140839i $$-0.995517\pi$$
0.999901 0.0140839i $$-0.00448320\pi$$
$$410$$ 0 0
$$411$$ 361.159 + 361.159i 0.0433447 + 0.0433447i
$$412$$ 0 0
$$413$$ 760.629 760.629i 0.0906250 0.0906250i
$$414$$ 0 0
$$415$$ −9277.08 −1.09734
$$416$$ 0 0
$$417$$ −2291.35 −0.269084
$$418$$ 0 0
$$419$$ 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 0.999298 0.0374725i $$-0.0119307\pi$$
−0.0374725 + 0.999298i $$0.511931\pi$$
$$422$$ 0 0
$$423$$ 12620.9i 1.45071i
$$424$$ 0 0
$$425$$ 748.907i 0.0854760i
$$426$$ 0 0
$$427$$ 609.333 + 609.333i 0.0690579 + 0.0690579i
$$428$$ 0 0
$$429$$ 2422.72 2422.72i 0.272657 0.272657i
$$430$$ 0 0
$$431$$ 8737.57 0.976506 0.488253 0.872702i $$-0.337634\pi$$
0.488253 + 0.872702i $$0.337634\pi$$
$$432$$ 0 0
$$433$$ −11627.5 −1.29049 −0.645247 0.763974i $$-0.723245\pi$$
−0.645247 + 0.763974i $$0.723245\pi$$
$$434$$ 0 0
$$435$$ −822.260 + 822.260i −0.0906306 + 0.0906306i
$$436$$ 0 0
$$437$$ −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 $$0.592080\pi$$
$$440$$ 0 0
$$441$$ 8683.57i 0.937649i
$$442$$ 0 0
$$443$$ 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
$$446$$ 0 0
$$447$$ 568.116 0.0601140
$$448$$ 0 0
$$449$$ −12926.5 −1.35867 −0.679334 0.733830i $$-0.737731\pi$$
−0.679334 + 0.733830i $$0.737731\pi$$
$$450$$ 0 0
$$451$$ 4731.46 4731.46i 0.494004 0.494004i
$$452$$ 0 0
$$453$$ 2268.45 + 2268.45i 0.235278 + 0.235278i
$$454$$ 0 0
$$455$$ 1555.84i 0.160305i
$$456$$ 0 0
$$457$$ 9320.32i 0.954018i −0.878898 0.477009i $$-0.841721\pi$$
0.878898 0.477009i $$-0.158279\pi$$
$$458$$ 0 0
$$459$$ 2899.90 + 2899.90i 0.294892 + 0.294892i
$$460$$ 0 0
$$461$$ −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 $$0.385080\pi$$
$$464$$ 0 0
$$465$$ 2349.14 0.234277
$$466$$ 0 0
$$467$$ −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
$$470$$ 0 0
$$471$$ 2283.96i 0.223438i
$$472$$ 0 0
$$473$$ 2847.65i 0.276818i
$$474$$ 0 0
$$475$$ −200.840 200.840i −0.0194004 0.0194004i
$$476$$ 0 0
$$477$$ 3866.82 3866.82i 0.371173 0.371173i
$$478$$ 0 0
$$479$$ −587.317 −0.0560234 −0.0280117 0.999608i $$-0.508918\pi$$
−0.0280117 + 0.999608i $$0.508918\pi$$
$$480$$ 0 0
$$481$$ −5951.28 −0.564148
$$482$$ 0 0
$$483$$ 281.975 281.975i 0.0265638 0.0265638i
$$484$$ 0 0
$$485$$ 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 $$0.872738\pi$$
$$488$$ 0 0
$$489$$ 2157.10i 0.199483i
$$490$$ 0 0
$$491$$ −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
$$494$$ 0 0
$$495$$ 19235.0 1.74656
$$496$$ 0 0
$$497$$ −1212.03 −0.109390
$$498$$ 0 0
$$499$$ −11364.5 + 11364.5i −1.01952 + 1.01952i −0.0197191 + 0.999806i $$0.506277\pi$$
−0.999806 + 0.0197191i $$0.993723\pi$$
$$500$$ 0 0
$$501$$ −599.681 599.681i −0.0534766 0.0534766i
$$502$$ 0 0
$$503$$ 12570.2i 1.11427i 0.830421 + 0.557137i $$0.188100\pi$$
−0.830421 + 0.557137i $$0.811900\pi$$
$$504$$ 0 0
$$505$$ 26.1326i 0.00230274i
$$506$$ 0 0
$$507$$ 233.738 + 233.738i 0.0204747 + 0.0204747i
$$508$$ 0 0
$$509$$ −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
$$512$$ 0 0
$$513$$ 1555.38 0.133863
$$514$$ 0 0
$$515$$ 11419.8 11419.8i 0.977122 0.977122i
$$516$$ 0 0
$$517$$ −22074.8 22074.8i −1.87785 1.87785i
$$518$$ 0 0
$$519$$ 1170.87i 0.0990283i
$$520$$ 0 0
$$521$$ 6612.98i 0.556085i 0.960569 + 0.278042i $$0.0896856\pi$$
−0.960569 + 0.278042i $$0.910314\pi$$
$$522$$ 0 0
$$523$$ −5129.30 5129.30i −0.428850 0.428850i 0.459387 0.888236i $$-0.348069\pi$$
−0.888236 + 0.459387i $$0.848069\pi$$
$$524$$ 0 0
$$525$$ 20.8858 20.8858i 0.00173625 0.00173625i
$$526$$ 0 0
$$527$$ −13679.3 −1.13070
$$528$$ 0 0
$$529$$ −7282.60 −0.598553
$$530$$ 0 0
$$531$$ 7360.75 7360.75i 0.601562 0.601562i
$$532$$ 0 0
$$533$$ 3703.53 + 3703.53i 0.300972 + 0.300972i
$$534$$ 0 0
$$535$$ 13515.5i 1.09220i
$$536$$ 0 0
$$537$$ 644.849i 0.0518199i
$$538$$ 0 0
$$539$$ 15188.1 + 15188.1i 1.21372 + 1.21372i
$$540$$ 0 0
$$541$$ 10968.5 10968.5i 0.871672 0.871672i −0.120983 0.992655i $$-0.538605\pi$$
0.992655 + 0.120983i $$0.0386047\pi$$
$$542$$ 0 0
$$543$$ −3962.57 −0.313168
$$544$$ 0 0
$$545$$ 8765.44 0.688936
$$546$$ 0 0
$$547$$ −13088.8 + 13088.8i −1.02311 + 1.02311i −0.0233784 + 0.999727i $$0.507442\pi$$
−0.999727 + 0.0233784i $$0.992558\pi$$
$$548$$ 0 0
$$549$$ 5896.63 + 5896.63i 0.458401 + 0.458401i
$$550$$ 0 0
$$551$$ 2568.12i 0.198558i
$$552$$ 0 0
$$553$$ 863.469i 0.0663986i
$$554$$ 0 0
$$555$$ 1046.64 + 1046.64i 0.0800491 + 0.0800491i
$$556$$ 0 0
$$557$$ −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
$$560$$ 0 0
$$561$$ 4962.18 0.373446
$$562$$ 0 0
$$563$$ 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
$$566$$ 0 0
$$567$$ 1703.30i 0.126159i
$$568$$ 0 0
$$569$$ 2806.05i 0.206741i −0.994643 0.103371i $$-0.967037\pi$$
0.994643 0.103371i $$-0.0329628\pi$$
$$570$$ 0 0
$$571$$ 12038.8 + 12038.8i 0.882324 + 0.882324i 0.993770 0.111446i $$-0.0355483\pi$$
−0.111446 + 0.993770i $$0.535548\pi$$
$$572$$ 0 0
$$573$$ −2434.08 + 2434.08i −0.177461 + 0.177461i
$$574$$ 0 0
$$575$$ −1440.62 −0.104484
$$576$$ 0 0
$$577$$ 7206.84 0.519973 0.259987 0.965612i $$-0.416282\pi$$
0.259987 + 0.965612i $$0.416282\pi$$
$$578$$ 0 0
$$579$$ −2158.76 + 2158.76i −0.154948 + 0.154948i
$$580$$ 0 0
$$581$$ 1506.57 + 1506.57i 0.107578 + 0.107578i
$$582$$ 0 0
$$583$$ 13526.6i 0.960918i
$$584$$ 0 0
$$585$$ 15056.1i 1.06409i
$$586$$ 0 0
$$587$$ −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
$$590$$ 0 0
$$591$$ 2435.33 0.169503
$$592$$ 0 0
$$593$$ −4758.60 −0.329531 −0.164766 0.986333i $$-0.552687\pi$$
−0.164766 + 0.986333i $$0.552687\pi$$
$$594$$ 0 0
$$595$$ −1593.32 + 1593.32i −0.109781 + 0.109781i
$$596$$ 0 0
$$597$$ 565.414 + 565.414i 0.0387619 + 0.0387619i
$$598$$ 0 0
$$599$$ 14256.4i 0.972455i −0.873832 0.486227i $$-0.838373\pi$$
0.873832 0.486227i $$-0.161627\pi$$
$$600$$ 0 0
$$601$$ 10385.2i 0.704862i −0.935838 0.352431i $$-0.885355\pi$$
0.935838 0.352431i $$-0.114645\pi$$
$$602$$ 0 0
$$603$$ −3597.68 3597.68i −0.242966 0.242966i
$$604$$ 0 0
$$605$$ 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 $$0.682745\pi$$
$$608$$ 0 0
$$609$$ 267.064 0.0177701
$$610$$ 0 0
$$611$$ 17279.0 17279.0i 1.14408 1.14408i
$$612$$ 0 0
$$613$$ 500.502 + 500.502i 0.0329773 + 0.0329773i 0.723403 0.690426i $$-0.242577\pi$$
−0.690426 + 0.723403i $$0.742577\pi$$
$$614$$ 0 0
$$615$$ 1302.66i 0.0854121i
$$616$$ 0 0
$$617$$ 11575.9i 0.755316i −0.925945 0.377658i $$-0.876729\pi$$
0.925945 0.377658i $$-0.123271\pi$$
$$618$$ 0 0
$$619$$ −18356.1 18356.1i −1.19191 1.19191i −0.976530 0.215380i $$-0.930901\pi$$
−0.215380 0.976530i $$-0.569099\pi$$
$$620$$ 0 0
$$621$$ 5578.34 5578.34i 0.360469 0.360469i
$$622$$ 0 0
$$623$$ 2315.98 0.148937
$$624$$ 0 0
$$625$$ 16809.5 1.07581
$$626$$ 0 0
$$627$$ 1330.75 1330.75i 0.0847607 0.0847607i
$$628$$ 0 0
$$629$$ −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 $$0.895463\pi$$
$$632$$ 0 0
$$633$$ 3370.88i 0.211660i
$$634$$ 0 0
$$635$$ −15658.7 15658.7i −0.978578 0.978578i
$$636$$ 0 0
$$637$$ −11888.4 + 11888.4i −0.739461 + 0.739461i
$$638$$ 0 0
$$639$$ −11729.0 −0.726125
$$640$$ 0 0
$$641$$ 19804.4 1.22032 0.610162 0.792277i $$-0.291104\pi$$
0.610162 + 0.792277i $$0.291104\pi$$
$$642$$ 0 0
$$643$$ −15680.7 + 15680.7i −0.961723 + 0.961723i −0.999294 0.0375712i $$-0.988038\pi$$
0.0375712 + 0.999294i $$0.488038\pi$$
$$644$$ 0 0
$$645$$ 392.006 + 392.006i 0.0239306 + 0.0239306i
$$646$$ 0 0
$$647$$ 9232.26i 0.560985i 0.959856 + 0.280493i $$0.0904978\pi$$
−0.959856 + 0.280493i $$0.909502\pi$$
$$648$$ 0 0
$$649$$ 25748.8i 1.55736i
$$650$$ 0 0
$$651$$ −381.492 381.492i −0.0229675 0.0229675i
$$652$$ 0 0
$$653$$ 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
$$656$$ 0 0
$$657$$ −6715.66 −0.398786
$$658$$ 0 0
$$659$$ −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 0.904245 0.427013i $$-0.140434\pi$$
−0.427013 + 0.904245i $$0.640434\pi$$
$$662$$ 0 0
$$663$$ 3884.13i 0.227522i
$$664$$ 0 0
$$665$$ 854.587i 0.0498338i
$$666$$ 0 0
$$667$$ −9210.54 9210.54i −0.534683 0.534683i
$$668$$ 0 0
$$669$$ 270.966 270.966i 0.0156594 0.0156594i
$$670$$ 0 0
$$671$$ 20627.1 1.18674
$$672$$ 0 0
$$673$$ −28428.2 −1.62827 −0.814135 0.580676i $$-0.802788\pi$$
−0.814135 + 0.580676i $$0.802788\pi$$
$$674$$ 0 0
$$675$$ 413.186 413.186i 0.0235608 0.0235608i
$$676$$ 0 0
$$677$$ 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
$$680$$ 0 0
$$681$$ 5229.92i 0.294289i
$$682$$ 0 0
$$683$$ 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
$$686$$ 0 0
$$687$$ −2164.42 −0.120201
$$688$$ 0 0
$$689$$ 10587.9 0.585439
$$690$$ 0 0
$$691$$ 20859.7 20859.7i 1.14839 1.14839i 0.161527 0.986868i $$-0.448358\pi$$
0.986868 0.161527i $$-0.0516418\pi$$
$$692$$ 0 0
$$693$$ −3123.70 3123.70i −0.171226 0.171226i
$$694$$ 0 0
$$695$$ 24906.1i 1.35934i
$$696$$ 0 0
$$697$$ 7585.52i 0.412227i
$$698$$ 0 0
$$699$$ −701.137 701.137i −0.0379391 0.0379391i
$$700$$ 0 0
$$701$$ −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
$$704$$ 0 0
$$705$$ −6077.62 −0.324676
$$706$$ 0 0
$$707$$ −4.24384 + 4.24384i −0.000225751 + 0.000225751i
$$708$$ 0 0
$$709$$ −4559.45 4559.45i −0.241515 0.241515i 0.575962 0.817477i $$-0.304628\pi$$
−0.817477 + 0.575962i $$0.804628\pi$$
$$710$$ 0 0
$$711$$ 8355.95i 0.440749i
$$712$$ 0 0
$$713$$ 26313.9i 1.38214i
$$714$$ 0 0
$$715$$ 26334.1 + 26334.1i 1.37740 + 1.37740i
$$716$$ 0 0
$$717$$ 599.724 599.724i 0.0312372 0.0312372i
$$718$$ 0 0
$$719$$ −6494.67 −0.336871 −0.168436 0.985713i $$-0.553872\pi$$
−0.168436 + 0.985713i $$0.553872\pi$$
$$720$$ 0 0
$$721$$ −3709.08 −0.191586
$$722$$ 0 0
$$723$$ −1096.58 + 1096.58i −0.0564069 + 0.0564069i
$$724$$ 0 0
$$725$$ −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 $$0.781296\pi$$
$$728$$ 0 0
$$729$$ 14848.5i 0.754384i
$$730$$ 0 0
$$731$$ −2282.68 2282.68i −0.115497 0.115497i
$$732$$ 0 0
$$733$$ 14914.3 14914.3i 0.751533 0.751533i −0.223232 0.974765i $$-0.571661\pi$$
0.974765 + 0.223232i $$0.0716607\pi$$
$$734$$ 0 0
$$735$$ 4181.58 0.209850
$$736$$ 0 0
$$737$$ −12585.1 −0.629008
$$738$$ 0 0
$$739$$ −8451.86 + 8451.86i −0.420713 + 0.420713i −0.885449 0.464737i $$-0.846149\pi$$
0.464737 + 0.885449i $$0.346149\pi$$
$$740$$ 0 0
$$741$$ 1041.64 + 1041.64i 0.0516404 + 0.0516404i
$$742$$ 0 0
$$743$$ 5622.43i 0.277614i 0.990319 + 0.138807i $$0.0443267\pi$$
−0.990319 + 0.138807i $$0.955673\pi$$
$$744$$ 0 0
$$745$$ 6175.21i 0.303681i
$$746$$ 0 0
$$747$$ 14579.3 + 14579.3i 0.714095 + 0.714095i
$$748$$ 0 0
$$749$$ −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 $$0.787378\pi$$
$$752$$ 0 0
$$753$$ −5418.58 −0.262236
$$754$$ 0 0
$$755$$ −24657.2 + 24657.2i −1.18857 + 1.18857i
$$756$$ 0 0
$$757$$ −12692.8 12692.8i −0.609418 0.609418i 0.333376 0.942794i $$-0.391812\pi$$
−0.942794 + 0.333376i $$0.891812\pi$$
$$758$$ 0 0
$$759$$ 9545.42i 0.456491i
$$760$$ 0 0
$$761$$ 13108.2i 0.624404i 0.950016 + 0.312202i $$0.101067\pi$$
−0.950016 + 0.312202i $$0.898933\pi$$
$$762$$ 0 0
$$763$$ −1423.48 1423.48i −0.0675404 0.0675404i
$$764$$ 0 0
$$765$$ −15418.8 + 15418.8i −0.728718 + 0.728718i
$$766$$ 0 0
$$767$$ 20154.8 0.948822
$$768$$ 0 0
$$769$$ 23661.2 1.10955 0.554776 0.832000i $$-0.312804\pi$$
0.554776 + 0.832000i $$0.312804\pi$$
$$770$$ 0 0
$$771$$ 3563.56 3563.56i 0.166457 0.166457i
$$772$$ 0 0
$$773$$ −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
$$776$$ 0 0
$$777$$ 339.940i 0.0156954i
$$778$$ 0 0
$$779$$ 2034.27 + 2034.27i 0.0935627 + 0.0935627i
$$780$$ 0 0
$$781$$ −20514.8 + 20514.8i −0.939921 + 0.939921i
$$782$$ 0 0
$$783$$ 5283.35 0.241139
$$784$$ 0 0
$$785$$ −24825.8 −1.12875
$$786$$ 0 0
$$787$$ 20890.9 20890.9i 0.946226 0.946226i −0.0524002 0.998626i $$-0.516687\pi$$
0.998626 + 0.0524002i $$0.0166872\pi$$
$$788$$ 0 0
$$789$$ −2245.97 2245.97i −0.101342 0.101342i
$$790$$ 0 0
$$791$$ 179.720i 0.00807853i
$$792$$ 0 0
$$793$$ 16145.8i 0.723020i
$$794$$ 0 0
$$795$$ −1862.07 1862.07i −0.0830702 0.0830702i
$$796$$ 0 0
$$797$$ 6834.83 6834.83i 0.303767