# Properties

 Label 72.8.d.b.37.5 Level $72$ Weight $8$ Character 72.37 Analytic conductor $22.492$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$72 = 2^{3} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 72.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$22.4917218349$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ Defining polynomial: $$x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768$$ x^6 - 3*x^5 - 10*x^4 - 24*x^3 - 320*x^2 - 3072*x + 32768 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{15}$$ Twist minimal: no (minimal twist has level 8) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 37.5 Root $$-4.85268 - 2.90715i$$ of defining polynomial Character $$\chi$$ $$=$$ 72.37 Dual form 72.8.d.b.37.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(9.70536 - 5.81430i) q^{2} +(60.3879 - 112.860i) q^{4} +324.492i q^{5} -956.960 q^{7} +(-70.1132 - 1446.46i) q^{8} +O(q^{10})$$ $$q+(9.70536 - 5.81430i) q^{2} +(60.3879 - 112.860i) q^{4} +324.492i q^{5} -956.960 q^{7} +(-70.1132 - 1446.46i) q^{8} +(1886.69 + 3149.31i) q^{10} +5452.20i q^{11} +6289.38i q^{13} +(-9287.64 + 5564.05i) q^{14} +(-9090.60 - 13630.7i) q^{16} -34587.3 q^{17} +14595.6i q^{19} +(36622.0 + 19595.4i) q^{20} +(31700.7 + 52915.6i) q^{22} +24667.5 q^{23} -27169.8 q^{25} +(36568.3 + 61040.6i) q^{26} +(-57788.8 + 108002. i) q^{28} +171116. i q^{29} +111688. q^{31} +(-167481. - 79435.5i) q^{32} +(-335682. + 201101. i) q^{34} -310526. i q^{35} +103636. i q^{37} +(84863.4 + 141656. i) q^{38} +(469363. - 22751.1i) q^{40} -71691.3 q^{41} +328419. i q^{43} +(615334. + 329247. i) q^{44} +(239406. - 143424. i) q^{46} -119043. q^{47} +92230.3 q^{49} +(-263693. + 157973. i) q^{50} +(709817. + 379802. i) q^{52} -1.04011e6i q^{53} -1.76919e6 q^{55} +(67095.6 + 1.38420e6i) q^{56} +(994918. + 1.66074e6i) q^{58} -225984. i q^{59} -1.55268e6i q^{61} +(1.08398e6 - 649390. i) q^{62} +(-2.08732e6 + 202831. i) q^{64} -2.04085e6 q^{65} -316375. i q^{67} +(-2.08865e6 + 3.90351e6i) q^{68} +(-1.80549e6 - 3.01376e6i) q^{70} -538965. q^{71} -2.68512e6 q^{73} +(602570. + 1.00582e6i) q^{74} +(1.64726e6 + 881400. i) q^{76} -5.21754e6i q^{77} +8.22632e6 q^{79} +(4.42305e6 - 2.94982e6i) q^{80} +(-695790. + 416834. i) q^{82} -5.89510e6i q^{83} -1.12233e7i q^{85} +(1.90952e6 + 3.18742e6i) q^{86} +(7.88638e6 - 382271. i) q^{88} -437005. q^{89} -6.01868e6i q^{91} +(1.48962e6 - 2.78396e6i) q^{92} +(-1.15536e6 + 692152. i) q^{94} -4.73616e6 q^{95} -7.84322e6 q^{97} +(895128. - 536254. i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10})$$ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 $$6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100})$$ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 - 1656 * q^10 - 12048 * q^14 + 35344 * q^16 - 1452 * q^17 + 114768 * q^20 + 152860 * q^22 + 1296 * q^23 - 39314 * q^25 + 316968 * q^26 - 480800 * q^28 - 89280 * q^31 - 817056 * q^32 - 1009108 * q^34 - 974124 * q^38 + 954464 * q^40 - 521244 * q^41 + 1096344 * q^44 + 929840 * q^46 - 1566432 * q^47 - 511050 * q^49 + 148626 * q^50 + 823952 * q^52 - 3270256 * q^55 + 2468928 * q^56 + 3130744 * q^58 + 7055808 * q^62 - 4792768 * q^64 - 1416480 * q^65 - 6608040 * q^68 - 7406912 * q^70 + 7597104 * q^71 + 2089564 * q^73 - 7744200 * q^74 + 9241288 * q^76 + 16015904 * q^79 + 12600384 * q^80 + 10715932 * q^82 + 5639076 * q^86 + 1541200 * q^88 - 2169084 * q^89 - 669600 * q^92 + 15503712 * q^94 - 48537936 * q^95 - 1088308 * q^97 + 14983242 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$$.

 $$n$$ $$37$$ $$55$$ $$65$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 9.70536 5.81430i 0.857840 0.513916i
$$3$$ 0 0
$$4$$ 60.3879 112.860i 0.471781 0.881716i
$$5$$ 324.492i 1.16094i 0.814283 + 0.580468i $$0.197130\pi$$
−0.814283 + 0.580468i $$0.802870\pi$$
$$6$$ 0 0
$$7$$ −956.960 −1.05451 −0.527255 0.849707i $$-0.676779\pi$$
−0.527255 + 0.849707i $$0.676779\pi$$
$$8$$ −70.1132 1446.46i −0.0484155 0.998827i
$$9$$ 0 0
$$10$$ 1886.69 + 3149.31i 0.596624 + 0.995898i
$$11$$ 5452.20i 1.23509i 0.786537 + 0.617544i $$0.211872\pi$$
−0.786537 + 0.617544i $$0.788128\pi$$
$$12$$ 0 0
$$13$$ 6289.38i 0.793973i 0.917824 + 0.396987i $$0.129944\pi$$
−0.917824 + 0.396987i $$0.870056\pi$$
$$14$$ −9287.64 + 5564.05i −0.904602 + 0.541930i
$$15$$ 0 0
$$16$$ −9090.60 13630.7i −0.554846 0.831953i
$$17$$ −34587.3 −1.70744 −0.853720 0.520733i $$-0.825659\pi$$
−0.853720 + 0.520733i $$0.825659\pi$$
$$18$$ 0 0
$$19$$ 14595.6i 0.488186i 0.969752 + 0.244093i $$0.0784903\pi$$
−0.969752 + 0.244093i $$0.921510\pi$$
$$20$$ 36622.0 + 19595.4i 1.02362 + 0.547707i
$$21$$ 0 0
$$22$$ 31700.7 + 52915.6i 0.634731 + 1.05951i
$$23$$ 24667.5 0.422743 0.211372 0.977406i $$-0.432207\pi$$
0.211372 + 0.977406i $$0.432207\pi$$
$$24$$ 0 0
$$25$$ −27169.8 −0.347774
$$26$$ 36568.3 + 61040.6i 0.408036 + 0.681102i
$$27$$ 0 0
$$28$$ −57788.8 + 108002.i −0.497497 + 0.929779i
$$29$$ 171116.i 1.30286i 0.758710 + 0.651429i $$0.225830\pi$$
−0.758710 + 0.651429i $$0.774170\pi$$
$$30$$ 0 0
$$31$$ 111688. 0.673352 0.336676 0.941620i $$-0.390697\pi$$
0.336676 + 0.941620i $$0.390697\pi$$
$$32$$ −167481. 79435.5i −0.903524 0.428539i
$$33$$ 0 0
$$34$$ −335682. + 201101.i −1.46471 + 0.877480i
$$35$$ 310526.i 1.22422i
$$36$$ 0 0
$$37$$ 103636.i 0.336360i 0.985756 + 0.168180i $$0.0537890\pi$$
−0.985756 + 0.168180i $$0.946211\pi$$
$$38$$ 84863.4 + 141656.i 0.250887 + 0.418786i
$$39$$ 0 0
$$40$$ 469363. 22751.1i 1.15958 0.0562074i
$$41$$ −71691.3 −0.162451 −0.0812256 0.996696i $$-0.525883\pi$$
−0.0812256 + 0.996696i $$0.525883\pi$$
$$42$$ 0 0
$$43$$ 328419.i 0.629925i 0.949104 + 0.314962i $$0.101992\pi$$
−0.949104 + 0.314962i $$0.898008\pi$$
$$44$$ 615334. + 329247.i 1.08900 + 0.582690i
$$45$$ 0 0
$$46$$ 239406. 143424.i 0.362646 0.217255i
$$47$$ −119043. −0.167248 −0.0836241 0.996497i $$-0.526650\pi$$
−0.0836241 + 0.996497i $$0.526650\pi$$
$$48$$ 0 0
$$49$$ 92230.3 0.111992
$$50$$ −263693. + 157973.i −0.298334 + 0.178727i
$$51$$ 0 0
$$52$$ 709817. + 379802.i 0.700059 + 0.374581i
$$53$$ 1.04011e6i 0.959648i −0.877365 0.479824i $$-0.840700\pi$$
0.877365 0.479824i $$-0.159300\pi$$
$$54$$ 0 0
$$55$$ −1.76919e6 −1.43386
$$56$$ 67095.6 + 1.38420e6i 0.0510547 + 1.05327i
$$57$$ 0 0
$$58$$ 994918. + 1.66074e6i 0.669559 + 1.11764i
$$59$$ 225984.i 0.143250i −0.997432 0.0716250i $$-0.977182\pi$$
0.997432 0.0716250i $$-0.0228185\pi$$
$$60$$ 0 0
$$61$$ 1.55268e6i 0.875843i −0.899013 0.437922i $$-0.855715\pi$$
0.899013 0.437922i $$-0.144285\pi$$
$$62$$ 1.08398e6 649390.i 0.577629 0.346047i
$$63$$ 0 0
$$64$$ −2.08732e6 + 202831.i −0.995312 + 0.0967175i
$$65$$ −2.04085e6 −0.921753
$$66$$ 0 0
$$67$$ 316375.i 0.128511i −0.997933 0.0642555i $$-0.979533\pi$$
0.997933 0.0642555i $$-0.0204673\pi$$
$$68$$ −2.08865e6 + 3.90351e6i −0.805537 + 1.50548i
$$69$$ 0 0
$$70$$ −1.80549e6 3.01376e6i −0.629146 1.05019i
$$71$$ −538965. −0.178713 −0.0893566 0.996000i $$-0.528481\pi$$
−0.0893566 + 0.996000i $$0.528481\pi$$
$$72$$ 0 0
$$73$$ −2.68512e6 −0.807856 −0.403928 0.914791i $$-0.632355\pi$$
−0.403928 + 0.914791i $$0.632355\pi$$
$$74$$ 602570. + 1.00582e6i 0.172861 + 0.288543i
$$75$$ 0 0
$$76$$ 1.64726e6 + 881400.i 0.430442 + 0.230317i
$$77$$ 5.21754e6i 1.30241i
$$78$$ 0 0
$$79$$ 8.22632e6 1.87720 0.938600 0.345007i $$-0.112123\pi$$
0.938600 + 0.345007i $$0.112123\pi$$
$$80$$ 4.42305e6 2.94982e6i 0.965845 0.644141i
$$81$$ 0 0
$$82$$ −695790. + 416834.i −0.139357 + 0.0834863i
$$83$$ 5.89510e6i 1.13167i −0.824520 0.565833i $$-0.808555\pi$$
0.824520 0.565833i $$-0.191445\pi$$
$$84$$ 0 0
$$85$$ 1.12233e7i 1.98223i
$$86$$ 1.90952e6 + 3.18742e6i 0.323728 + 0.540375i
$$87$$ 0 0
$$88$$ 7.88638e6 382271.i 1.23364 0.0597974i
$$89$$ −437005. −0.0657085 −0.0328542 0.999460i $$-0.510460\pi$$
−0.0328542 + 0.999460i $$0.510460\pi$$
$$90$$ 0 0
$$91$$ 6.01868e6i 0.837253i
$$92$$ 1.48962e6 2.78396e6i 0.199442 0.372740i
$$93$$ 0 0
$$94$$ −1.15536e6 + 692152.i −0.143472 + 0.0859516i
$$95$$ −4.73616e6 −0.566753
$$96$$ 0 0
$$97$$ −7.84322e6 −0.872556 −0.436278 0.899812i $$-0.643704\pi$$
−0.436278 + 0.899812i $$0.643704\pi$$
$$98$$ 895128. 536254.i 0.0960713 0.0575545i
$$99$$ 0 0
$$100$$ −1.64073e6 + 3.06638e6i −0.164073 + 0.306638i
$$101$$ 6.19757e6i 0.598545i −0.954168 0.299272i $$-0.903256\pi$$
0.954168 0.299272i $$-0.0967439\pi$$
$$102$$ 0 0
$$103$$ −6.59816e6 −0.594966 −0.297483 0.954727i $$-0.596147\pi$$
−0.297483 + 0.954727i $$0.596147\pi$$
$$104$$ 9.09731e6 440968.i 0.793042 0.0384406i
$$105$$ 0 0
$$106$$ −6.04748e6 1.00946e7i −0.493179 0.823225i
$$107$$ 512845.i 0.0404709i 0.999795 + 0.0202354i $$0.00644158\pi$$
−0.999795 + 0.0202354i $$0.993558\pi$$
$$108$$ 0 0
$$109$$ 1.95882e7i 1.44878i 0.689393 + 0.724388i $$0.257877\pi$$
−0.689393 + 0.724388i $$0.742123\pi$$
$$110$$ −1.71707e7 + 1.02866e7i −1.23002 + 0.736883i
$$111$$ 0 0
$$112$$ 8.69934e6 + 1.30441e7i 0.585091 + 0.877303i
$$113$$ −1.88876e7 −1.23141 −0.615705 0.787977i $$-0.711129\pi$$
−0.615705 + 0.787977i $$0.711129\pi$$
$$114$$ 0 0
$$115$$ 8.00438e6i 0.490778i
$$116$$ 1.93121e7 + 1.03333e7i 1.14875 + 0.614663i
$$117$$ 0 0
$$118$$ −1.31394e6 2.19325e6i −0.0736185 0.122886i
$$119$$ 3.30987e7 1.80051
$$120$$ 0 0
$$121$$ −1.02394e7 −0.525441
$$122$$ −9.02772e6 1.50693e7i −0.450110 0.751334i
$$123$$ 0 0
$$124$$ 6.74463e6 1.26051e7i 0.317675 0.593706i
$$125$$ 1.65345e7i 0.757193i
$$126$$ 0 0
$$127$$ 3.96314e7 1.71683 0.858413 0.512959i $$-0.171451\pi$$
0.858413 + 0.512959i $$0.171451\pi$$
$$128$$ −1.90789e7 + 1.41048e7i −0.804114 + 0.594475i
$$129$$ 0 0
$$130$$ −1.98072e7 + 1.18661e7i −0.790717 + 0.473703i
$$131$$ 3.65337e7i 1.41986i 0.704274 + 0.709928i $$0.251273\pi$$
−0.704274 + 0.709928i $$0.748727\pi$$
$$132$$ 0 0
$$133$$ 1.39675e7i 0.514797i
$$134$$ −1.83950e6 3.07053e6i −0.0660439 0.110242i
$$135$$ 0 0
$$136$$ 2.42503e6 + 5.00290e7i 0.0826666 + 1.70544i
$$137$$ 2.56967e7 0.853799 0.426899 0.904299i $$-0.359606\pi$$
0.426899 + 0.904299i $$0.359606\pi$$
$$138$$ 0 0
$$139$$ 5.23001e7i 1.65177i 0.563836 + 0.825886i $$0.309325\pi$$
−0.563836 + 0.825886i $$0.690675\pi$$
$$140$$ −3.50458e7 1.87520e7i −1.07941 0.577563i
$$141$$ 0 0
$$142$$ −5.23085e6 + 3.13370e6i −0.153307 + 0.0918436i
$$143$$ −3.42910e7 −0.980626
$$144$$ 0 0
$$145$$ −5.55256e7 −1.51254
$$146$$ −2.60601e7 + 1.56121e7i −0.693011 + 0.415170i
$$147$$ 0 0
$$148$$ 1.16963e7 + 6.25836e6i 0.296574 + 0.158688i
$$149$$ 1.80406e7i 0.446785i −0.974729 0.223392i $$-0.928287\pi$$
0.974729 0.223392i $$-0.0717131\pi$$
$$150$$ 0 0
$$151$$ 3.87385e7 0.915637 0.457818 0.889046i $$-0.348631\pi$$
0.457818 + 0.889046i $$0.348631\pi$$
$$152$$ 2.11120e7 1.02335e6i 0.487614 0.0236358i
$$153$$ 0 0
$$154$$ −3.03363e7 5.06381e7i −0.669331 1.11726i
$$155$$ 3.62420e7i 0.781719i
$$156$$ 0 0
$$157$$ 5.12341e7i 1.05660i −0.849058 0.528300i $$-0.822830\pi$$
0.849058 0.528300i $$-0.177170\pi$$
$$158$$ 7.98393e7 4.78302e7i 1.61034 0.964723i
$$159$$ 0 0
$$160$$ 2.57762e7 5.43460e7i 0.497506 1.04893i
$$161$$ −2.36058e7 −0.445787
$$162$$ 0 0
$$163$$ 8.57572e7i 1.55101i 0.631343 + 0.775504i $$0.282504\pi$$
−0.631343 + 0.775504i $$0.717496\pi$$
$$164$$ −4.32929e6 + 8.09105e6i −0.0766413 + 0.143236i
$$165$$ 0 0
$$166$$ −3.42759e7 5.72141e7i −0.581581 0.970789i
$$167$$ 1.05871e8 1.75901 0.879503 0.475893i $$-0.157875\pi$$
0.879503 + 0.475893i $$0.157875\pi$$
$$168$$ 0 0
$$169$$ 2.31923e7 0.369606
$$170$$ −6.52555e7 1.08926e8i −1.01870 1.70044i
$$171$$ 0 0
$$172$$ 3.70652e7 + 1.98325e7i 0.555415 + 0.297186i
$$173$$ 1.98148e7i 0.290956i 0.989361 + 0.145478i $$0.0464720\pi$$
−0.989361 + 0.145478i $$0.953528\pi$$
$$174$$ 0 0
$$175$$ 2.60005e7 0.366731
$$176$$ 7.43175e7 4.95638e7i 1.02753 0.685284i
$$177$$ 0 0
$$178$$ −4.24129e6 + 2.54088e6i −0.0563674 + 0.0337686i
$$179$$ 2.97800e7i 0.388096i 0.980992 + 0.194048i $$0.0621618\pi$$
−0.980992 + 0.194048i $$0.937838\pi$$
$$180$$ 0 0
$$181$$ 3.96227e6i 0.0496671i −0.999692 0.0248335i $$-0.992094\pi$$
0.999692 0.0248335i $$-0.00790558\pi$$
$$182$$ −3.49944e7 5.84135e7i −0.430278 0.718230i
$$183$$ 0 0
$$184$$ −1.72951e6 3.56804e7i −0.0204674 0.422248i
$$185$$ −3.36290e7 −0.390493
$$186$$ 0 0
$$187$$ 1.88577e8i 2.10884i
$$188$$ −7.18876e6 + 1.34352e7i −0.0789045 + 0.147465i
$$189$$ 0 0
$$190$$ −4.59662e7 + 2.75375e7i −0.486184 + 0.291264i
$$191$$ 4.80105e7 0.498562 0.249281 0.968431i $$-0.419806\pi$$
0.249281 + 0.968431i $$0.419806\pi$$
$$192$$ 0 0
$$193$$ −4.72502e6 −0.0473100 −0.0236550 0.999720i $$-0.507530\pi$$
−0.0236550 + 0.999720i $$0.507530\pi$$
$$194$$ −7.61212e7 + 4.56028e7i −0.748514 + 0.448420i
$$195$$ 0 0
$$196$$ 5.56959e6 1.04091e7i 0.0528357 0.0987452i
$$197$$ 1.14882e8i 1.07058i 0.844668 + 0.535290i $$0.179798\pi$$
−0.844668 + 0.535290i $$0.820202\pi$$
$$198$$ 0 0
$$199$$ 1.20933e7 0.108782 0.0543911 0.998520i $$-0.482678\pi$$
0.0543911 + 0.998520i $$0.482678\pi$$
$$200$$ 1.90496e6 + 3.93000e7i 0.0168377 + 0.347366i
$$201$$ 0 0
$$202$$ −3.60345e7 6.01496e7i −0.307602 0.513456i
$$203$$ 1.63751e8i 1.37388i
$$204$$ 0 0
$$205$$ 2.32632e7i 0.188596i
$$206$$ −6.40375e7 + 3.83636e7i −0.510386 + 0.305763i
$$207$$ 0 0
$$208$$ 8.57287e7 5.71742e7i 0.660548 0.440533i
$$209$$ −7.95784e7 −0.602953
$$210$$ 0 0
$$211$$ 1.95850e8i 1.43527i 0.696418 + 0.717636i $$0.254776\pi$$
−0.696418 + 0.717636i $$0.745224\pi$$
$$212$$ −1.17386e8 6.28098e7i −0.846137 0.452743i
$$213$$ 0 0
$$214$$ 2.98183e6 + 4.97734e6i 0.0207986 + 0.0347176i
$$215$$ −1.06569e8 −0.731302
$$216$$ 0 0
$$217$$ −1.06881e8 −0.710057
$$218$$ 1.13891e8 + 1.90110e8i 0.744549 + 1.24282i
$$219$$ 0 0
$$220$$ −1.06838e8 + 1.99671e8i −0.676466 + 1.26426i
$$221$$ 2.17532e8i 1.35566i
$$222$$ 0 0
$$223$$ 1.08024e8 0.652311 0.326156 0.945316i $$-0.394247\pi$$
0.326156 + 0.945316i $$0.394247\pi$$
$$224$$ 1.60272e8 + 7.60167e7i 0.952775 + 0.451898i
$$225$$ 0 0
$$226$$ −1.83311e8 + 1.09818e8i −1.05635 + 0.632841i
$$227$$ 1.61144e8i 0.914374i 0.889371 + 0.457187i $$0.151143\pi$$
−0.889371 + 0.457187i $$0.848857\pi$$
$$228$$ 0 0
$$229$$ 5.27173e7i 0.290088i −0.989425 0.145044i $$-0.953668\pi$$
0.989425 0.145044i $$-0.0463323\pi$$
$$230$$ 4.65399e7 + 7.76854e7i 0.252219 + 0.421010i
$$231$$ 0 0
$$232$$ 2.47511e8 1.19975e7i 1.30133 0.0630786i
$$233$$ 1.79423e8 0.929249 0.464625 0.885508i $$-0.346189\pi$$
0.464625 + 0.885508i $$0.346189\pi$$
$$234$$ 0 0
$$235$$ 3.86285e7i 0.194165i
$$236$$ −2.55044e7 1.36467e7i −0.126306 0.0675826i
$$237$$ 0 0
$$238$$ 3.21234e8 1.92445e8i 1.54455 0.925312i
$$239$$ 8.42441e7 0.399160 0.199580 0.979882i $$-0.436042\pi$$
0.199580 + 0.979882i $$0.436042\pi$$
$$240$$ 0 0
$$241$$ −2.12302e8 −0.977000 −0.488500 0.872564i $$-0.662456\pi$$
−0.488500 + 0.872564i $$0.662456\pi$$
$$242$$ −9.93766e7 + 5.95347e7i −0.450745 + 0.270033i
$$243$$ 0 0
$$244$$ −1.75234e8 9.37629e7i −0.772245 0.413206i
$$245$$ 2.99280e7i 0.130016i
$$246$$ 0 0
$$247$$ −9.17975e7 −0.387607
$$248$$ −7.83083e6 1.61552e8i −0.0326007 0.672563i
$$249$$ 0 0
$$250$$ 9.61366e7 + 1.60473e8i 0.389134 + 0.649551i
$$251$$ 1.18102e8i 0.471411i −0.971825 0.235706i $$-0.924260\pi$$
0.971825 0.235706i $$-0.0757401\pi$$
$$252$$ 0 0
$$253$$ 1.34492e8i 0.522125i
$$254$$ 3.84637e8 2.30429e8i 1.47276 0.882304i
$$255$$ 0 0
$$256$$ −1.03157e8 + 2.47823e8i −0.384291 + 0.923212i
$$257$$ −1.27463e8 −0.468402 −0.234201 0.972188i $$-0.575247\pi$$
−0.234201 + 0.972188i $$0.575247\pi$$
$$258$$ 0 0
$$259$$ 9.91755e7i 0.354695i
$$260$$ −1.23243e8 + 2.30330e8i −0.434865 + 0.812724i
$$261$$ 0 0
$$262$$ 2.12418e8 + 3.54573e8i 0.729687 + 1.21801i
$$263$$ −4.33125e8 −1.46814 −0.734071 0.679073i $$-0.762382\pi$$
−0.734071 + 0.679073i $$0.762382\pi$$
$$264$$ 0 0
$$265$$ 3.37506e8 1.11409
$$266$$ −8.12109e7 1.35559e8i −0.264563 0.441614i
$$267$$ 0 0
$$268$$ −3.57060e7 1.91052e7i −0.113310 0.0606290i
$$269$$ 3.44748e8i 1.07986i −0.841709 0.539931i $$-0.818450\pi$$
0.841709 0.539931i $$-0.181550\pi$$
$$270$$ 0 0
$$271$$ −4.42513e8 −1.35062 −0.675311 0.737533i $$-0.735990\pi$$
−0.675311 + 0.737533i $$0.735990\pi$$
$$272$$ 3.14419e8 + 4.71450e8i 0.947366 + 1.42051i
$$273$$ 0 0
$$274$$ 2.49396e8 1.49408e8i 0.732423 0.438781i
$$275$$ 1.48135e8i 0.429531i
$$276$$ 0 0
$$277$$ 3.18148e8i 0.899395i 0.893181 + 0.449697i $$0.148468\pi$$
−0.893181 + 0.449697i $$0.851532\pi$$
$$278$$ 3.04088e8 + 5.07591e8i 0.848873 + 1.41696i
$$279$$ 0 0
$$280$$ −4.49162e8 + 2.17719e7i −1.22278 + 0.0592713i
$$281$$ −1.28497e8 −0.345478 −0.172739 0.984968i $$-0.555262\pi$$
−0.172739 + 0.984968i $$0.555262\pi$$
$$282$$ 0 0
$$283$$ 3.98970e8i 1.04637i −0.852218 0.523187i $$-0.824743\pi$$
0.852218 0.523187i $$-0.175257\pi$$
$$284$$ −3.25470e7 + 6.08274e7i −0.0843134 + 0.157574i
$$285$$ 0 0
$$286$$ −3.32806e8 + 1.99378e8i −0.841221 + 0.503960i
$$287$$ 6.86057e7 0.171306
$$288$$ 0 0
$$289$$ 7.85942e8 1.91535
$$290$$ −5.38896e8 + 3.22842e8i −1.29751 + 0.777316i
$$291$$ 0 0
$$292$$ −1.62149e8 + 3.03042e8i −0.381131 + 0.712299i
$$293$$ 2.00958e8i 0.466732i −0.972389 0.233366i $$-0.925026\pi$$
0.972389 0.233366i $$-0.0749741\pi$$
$$294$$ 0 0
$$295$$ 7.33298e7 0.166304
$$296$$ 1.49905e8 7.26625e6i 0.335965 0.0162850i
$$297$$ 0 0
$$298$$ −1.04893e8 1.75090e8i −0.229610 0.383270i
$$299$$ 1.55143e8i 0.335647i
$$300$$ 0 0
$$301$$ 3.14284e8i 0.664262i
$$302$$ 3.75971e8 2.25237e8i 0.785470 0.470560i
$$303$$ 0 0
$$304$$ 1.98949e8 1.32683e8i 0.406148 0.270868i
$$305$$ 5.03830e8 1.01680
$$306$$ 0 0
$$307$$ 1.58918e7i 0.0313465i 0.999877 + 0.0156733i $$0.00498916\pi$$
−0.999877 + 0.0156733i $$0.995011\pi$$
$$308$$ −5.88850e8 3.15077e8i −1.14836 0.614453i
$$309$$ 0 0
$$310$$ 2.10722e8 + 3.51741e8i 0.401738 + 0.670591i
$$311$$ −4.87710e8 −0.919391 −0.459695 0.888077i $$-0.652041\pi$$
−0.459695 + 0.888077i $$0.652041\pi$$
$$312$$ 0 0
$$313$$ −3.24731e8 −0.598576 −0.299288 0.954163i $$-0.596749\pi$$
−0.299288 + 0.954163i $$0.596749\pi$$
$$314$$ −2.97890e8 4.97245e8i −0.543003 0.906394i
$$315$$ 0 0
$$316$$ 4.96770e8 9.28419e8i 0.885627 1.65516i
$$317$$ 1.06084e9i 1.87043i 0.354086 + 0.935213i $$0.384792\pi$$
−0.354086 + 0.935213i $$0.615208\pi$$
$$318$$ 0 0
$$319$$ −9.32958e8 −1.60914
$$320$$ −6.58171e7 6.77318e8i −0.112283 1.15549i
$$321$$ 0 0
$$322$$ −2.29102e8 + 1.37251e8i −0.382414 + 0.229097i
$$323$$ 5.04824e8i 0.833548i
$$324$$ 0 0
$$325$$ 1.70881e8i 0.276123i
$$326$$ 4.98618e8 + 8.32304e8i 0.797088 + 1.33052i
$$327$$ 0 0
$$328$$ 5.02651e6 + 1.03698e8i 0.00786516 + 0.162261i
$$329$$ 1.13919e8 0.176365
$$330$$ 0 0
$$331$$ 2.88487e8i 0.437249i −0.975809 0.218624i $$-0.929843\pi$$
0.975809 0.218624i $$-0.0701569\pi$$
$$332$$ −6.65319e8 3.55993e8i −0.997808 0.533898i
$$333$$ 0 0
$$334$$ 1.02751e9 6.15563e8i 1.50895 0.903982i
$$335$$ 1.02661e8 0.149193
$$336$$ 0 0
$$337$$ −1.10595e8 −0.157410 −0.0787051 0.996898i $$-0.525079\pi$$
−0.0787051 + 0.996898i $$0.525079\pi$$
$$338$$ 2.25089e8 1.34847e8i 0.317063 0.189947i
$$339$$ 0 0
$$340$$ −1.26666e9 6.77751e8i −1.74776 0.935177i
$$341$$ 6.08948e8i 0.831649i
$$342$$ 0 0
$$343$$ 6.99837e8 0.936414
$$344$$ 4.75044e8 2.30265e7i 0.629186 0.0304981i
$$345$$ 0 0
$$346$$ 1.15209e8 + 1.92309e8i 0.149527 + 0.249594i
$$347$$ 1.10651e9i 1.42168i −0.703352 0.710841i $$-0.748314\pi$$
0.703352 0.710841i $$-0.251686\pi$$
$$348$$ 0 0
$$349$$ 1.38337e9i 1.74201i 0.491278 + 0.871003i $$0.336530\pi$$
−0.491278 + 0.871003i $$0.663470\pi$$
$$350$$ 2.52344e8 1.51174e8i 0.314597 0.188469i
$$351$$ 0 0
$$352$$ 4.33099e8 9.13138e8i 0.529283 1.11593i
$$353$$ 2.47617e8 0.299618 0.149809 0.988715i $$-0.452134\pi$$
0.149809 + 0.988715i $$0.452134\pi$$
$$354$$ 0 0
$$355$$ 1.74890e8i 0.207475i
$$356$$ −2.63898e7 + 4.93202e7i −0.0310000 + 0.0579362i
$$357$$ 0 0
$$358$$ 1.73150e8 + 2.89026e8i 0.199449 + 0.332925i
$$359$$ 1.38641e9 1.58148 0.790738 0.612155i $$-0.209697\pi$$
0.790738 + 0.612155i $$0.209697\pi$$
$$360$$ 0 0
$$361$$ 6.80839e8 0.761674
$$362$$ −2.30378e7 3.84552e7i −0.0255247 0.0426064i
$$363$$ 0 0
$$364$$ −6.79267e8 3.63456e8i −0.738219 0.395000i
$$365$$ 8.71299e8i 0.937869i
$$366$$ 0 0
$$367$$ −7.49367e8 −0.791341 −0.395670 0.918393i $$-0.629488\pi$$
−0.395670 + 0.918393i $$0.629488\pi$$
$$368$$ −2.24242e8 3.36235e8i −0.234558 0.351703i
$$369$$ 0 0
$$370$$ −3.26381e8 + 1.95529e8i −0.334980 + 0.200680i
$$371$$ 9.95340e8i 1.01196i
$$372$$ 0 0
$$373$$ 1.49519e9i 1.49181i −0.666051 0.745906i $$-0.732017\pi$$
0.666051 0.745906i $$-0.267983\pi$$
$$374$$ −1.09644e9 1.83021e9i −1.08377 1.80905i
$$375$$ 0 0
$$376$$ 8.34649e6 + 1.72191e8i 0.00809741 + 0.167052i
$$377$$ −1.07621e9 −1.03443
$$378$$ 0 0
$$379$$ 7.92096e7i 0.0747379i 0.999302 + 0.0373689i $$0.0118977\pi$$
−0.999302 + 0.0373689i $$0.988102\pi$$
$$380$$ −2.86007e8 + 5.34522e8i −0.267383 + 0.499715i
$$381$$ 0 0
$$382$$ 4.65959e8 2.79147e8i 0.427687 0.256219i
$$383$$ −4.80285e8 −0.436820 −0.218410 0.975857i $$-0.570087\pi$$
−0.218410 + 0.975857i $$0.570087\pi$$
$$384$$ 0 0
$$385$$ 1.69305e9 1.51202
$$386$$ −4.58580e7 + 2.74726e7i −0.0405844 + 0.0243134i
$$387$$ 0 0
$$388$$ −4.73636e8 + 8.85183e8i −0.411655 + 0.769346i
$$389$$ 1.07150e9i 0.922928i 0.887159 + 0.461464i $$0.152676\pi$$
−0.887159 + 0.461464i $$0.847324\pi$$
$$390$$ 0 0
$$391$$ −8.53180e8 −0.721809
$$392$$ −6.46656e6 1.33407e8i −0.00542216 0.111861i
$$393$$ 0 0
$$394$$ 6.67957e8 + 1.11497e9i 0.550189 + 0.918387i
$$395$$ 2.66937e9i 2.17931i
$$396$$ 0 0
$$397$$ 2.03185e9i 1.62976i 0.579627 + 0.814882i $$0.303198\pi$$
−0.579627 + 0.814882i $$0.696802\pi$$
$$398$$ 1.17369e8 7.03138e7i 0.0933178 0.0559049i
$$399$$ 0 0
$$400$$ 2.46990e8 + 3.70344e8i 0.192961 + 0.289331i
$$401$$ 2.57759e9 1.99622 0.998111 0.0614301i $$-0.0195661\pi$$
0.998111 + 0.0614301i $$0.0195661\pi$$
$$402$$ 0 0
$$403$$ 7.02451e8i 0.534624i
$$404$$ −6.99455e8 3.74258e8i −0.527746 0.282382i
$$405$$ 0 0
$$406$$ −9.52097e8 1.58926e9i −0.706057 1.17857i
$$407$$ −5.65044e8 −0.415434
$$408$$ 0 0
$$409$$ 3.30242e8 0.238672 0.119336 0.992854i $$-0.461923\pi$$
0.119336 + 0.992854i $$0.461923\pi$$
$$410$$ −1.35259e8 2.25778e8i −0.0969223 0.161785i
$$411$$ 0 0
$$412$$ −3.98449e8 + 7.44666e8i −0.280693 + 0.524591i
$$413$$ 2.16257e8i 0.151059i
$$414$$ 0 0
$$415$$ 1.91291e9 1.31379
$$416$$ 4.99600e8 1.05335e9i 0.340248 0.717374i
$$417$$ 0 0
$$418$$ −7.72337e8 + 4.62692e8i −0.517237 + 0.309867i
$$419$$ 5.80021e7i 0.0385207i −0.999815 0.0192604i $$-0.993869\pi$$
0.999815 0.0192604i $$-0.00613114\pi$$
$$420$$ 0 0
$$421$$ 1.90609e8i 0.124496i 0.998061 + 0.0622480i $$0.0198270\pi$$
−0.998061 + 0.0622480i $$0.980173\pi$$
$$422$$ 1.13873e9 + 1.90079e9i 0.737610 + 1.23123i
$$423$$ 0 0
$$424$$ −1.50447e9 + 7.29251e7i −0.958523 + 0.0464619i
$$425$$ 9.39731e8 0.593803
$$426$$ 0 0
$$427$$ 1.48585e9i 0.923586i
$$428$$ 5.78795e7 + 3.09696e7i 0.0356838 + 0.0190934i
$$429$$ 0 0
$$430$$ −1.03429e9 + 6.19625e8i −0.627341 + 0.375828i
$$431$$ −2.42923e9 −1.46150 −0.730749 0.682646i $$-0.760829\pi$$
−0.730749 + 0.682646i $$0.760829\pi$$
$$432$$ 0 0
$$433$$ −2.37902e9 −1.40828 −0.704141 0.710060i $$-0.748668\pi$$
−0.704141 + 0.710060i $$0.748668\pi$$
$$434$$ −1.03732e9 + 6.21440e8i −0.609116 + 0.364910i
$$435$$ 0 0
$$436$$ 2.21071e9 + 1.18289e9i 1.27741 + 0.683504i
$$437$$ 3.60037e8i 0.206378i
$$438$$ 0 0
$$439$$ −1.33161e9 −0.751194 −0.375597 0.926783i $$-0.622562\pi$$
−0.375597 + 0.926783i $$0.622562\pi$$
$$440$$ 1.24044e8 + 2.55906e9i 0.0694210 + 1.43218i
$$441$$ 0 0
$$442$$ −1.26480e9 2.11123e9i −0.696696 1.16294i
$$443$$ 5.02643e8i 0.274692i −0.990523 0.137346i $$-0.956143\pi$$
0.990523 0.137346i $$-0.0438573\pi$$
$$444$$ 0 0
$$445$$ 1.41805e8i 0.0762834i
$$446$$ 1.04842e9 6.28086e8i 0.559579 0.335233i
$$447$$ 0 0
$$448$$ 1.99748e9 1.94102e8i 1.04957 0.101990i
$$449$$ −3.14785e9 −1.64116 −0.820580 0.571531i $$-0.806350\pi$$
−0.820580 + 0.571531i $$0.806350\pi$$
$$450$$ 0 0
$$451$$ 3.90876e8i 0.200641i
$$452$$ −1.14058e9 + 2.13165e9i −0.580955 + 1.08575i
$$453$$ 0 0
$$454$$ 9.36939e8 + 1.56396e9i 0.469911 + 0.784387i
$$455$$ 1.95301e9 0.971998
$$456$$ 0 0
$$457$$ −2.68422e9 −1.31556 −0.657782 0.753209i $$-0.728505\pi$$
−0.657782 + 0.753209i $$0.728505\pi$$
$$458$$ −3.06514e8 5.11641e8i −0.149081 0.248849i
$$459$$ 0 0
$$460$$ 9.03372e8 + 4.83368e8i 0.432727 + 0.231540i
$$461$$ 1.30434e9i 0.620065i −0.950726 0.310033i $$-0.899660\pi$$
0.950726 0.310033i $$-0.100340\pi$$
$$462$$ 0 0
$$463$$ 2.86853e9 1.34315 0.671577 0.740934i $$-0.265617\pi$$
0.671577 + 0.740934i $$0.265617\pi$$
$$464$$ 2.33243e9 1.55554e9i 1.08392 0.722886i
$$465$$ 0 0
$$466$$ 1.74136e9 1.04322e9i 0.797148 0.477556i
$$467$$ 5.96519e8i 0.271029i −0.990775 0.135514i $$-0.956731\pi$$
0.990775 0.135514i $$-0.0432687\pi$$
$$468$$ 0 0
$$469$$ 3.02758e8i 0.135516i
$$470$$ −2.24597e8 3.74903e8i −0.0997843 0.166562i
$$471$$ 0 0
$$472$$ −3.26875e8 + 1.58444e7i −0.143082 + 0.00693553i
$$473$$ −1.79061e9 −0.778012
$$474$$ 0 0
$$475$$ 3.96561e8i 0.169778i
$$476$$ 1.99876e9 3.73550e9i 0.849447 1.58754i
$$477$$ 0 0
$$478$$ 8.17619e8 4.89820e8i 0.342416 0.205135i
$$479$$ 2.16068e9 0.898289 0.449144 0.893459i $$-0.351729\pi$$
0.449144 + 0.893459i $$0.351729\pi$$
$$480$$ 0 0
$$481$$ −6.51805e8 −0.267061
$$482$$ −2.06047e9 + 1.23439e9i −0.838110 + 0.502096i
$$483$$ 0 0
$$484$$ −6.18334e8 + 1.15561e9i −0.247893 + 0.463290i
$$485$$ 2.54506e9i 1.01298i
$$486$$ 0 0
$$487$$ 1.41934e8 0.0556847 0.0278424 0.999612i $$-0.491136\pi$$
0.0278424 + 0.999612i $$0.491136\pi$$
$$488$$ −2.24588e9 + 1.08863e8i −0.874816 + 0.0424044i
$$489$$ 0 0
$$490$$ 1.74010e8 + 2.90462e8i 0.0668172 + 0.111533i
$$491$$ 2.38677e9i 0.909966i −0.890500 0.454983i $$-0.849645\pi$$
0.890500 0.454983i $$-0.150355\pi$$
$$492$$ 0 0
$$493$$ 5.91843e9i 2.22455i
$$494$$ −8.90927e8 + 5.33738e8i −0.332505 + 0.199197i
$$495$$ 0 0
$$496$$ −1.01532e9 1.52239e9i −0.373607 0.560197i
$$497$$ 5.15769e8 0.188455
$$498$$ 0 0
$$499$$ 5.23900e9i 1.88754i −0.330601 0.943771i $$-0.607251\pi$$
0.330601 0.943771i $$-0.392749\pi$$
$$500$$ 1.86608e9 + 9.98486e8i 0.667629 + 0.357229i
$$501$$ 0 0
$$502$$ −6.86681e8 1.14622e9i −0.242266 0.404396i
$$503$$ 3.63292e9 1.27282 0.636411 0.771350i $$-0.280418\pi$$
0.636411 + 0.771350i $$0.280418\pi$$
$$504$$ 0 0
$$505$$ 2.01106e9 0.694872
$$506$$ 7.81976e8 + 1.30529e9i 0.268328 + 0.447900i
$$507$$ 0 0
$$508$$ 2.39326e9 4.47278e9i 0.809965 1.51375i
$$509$$ 2.58693e9i 0.869505i −0.900550 0.434753i $$-0.856836\pi$$
0.900550 0.434753i $$-0.143164\pi$$
$$510$$ 0 0
$$511$$ 2.56955e9 0.851892
$$512$$ 4.39735e8 + 3.00500e9i 0.144793 + 0.989462i
$$513$$ 0 0
$$514$$ −1.23708e9 + 7.41108e8i −0.401814 + 0.240719i
$$515$$ 2.14105e9i 0.690718i
$$516$$ 0 0
$$517$$ 6.49047e8i 0.206566i
$$518$$ −5.76636e8 9.62533e8i −0.182283 0.304272i
$$519$$ 0 0
$$520$$ 1.43091e8 + 2.95200e9i 0.0446272 + 0.920672i
$$521$$ −1.08542e8 −0.0336253 −0.0168127 0.999859i $$-0.505352\pi$$
−0.0168127 + 0.999859i $$0.505352\pi$$
$$522$$ 0 0
$$523$$ 6.10725e9i 1.86676i 0.358884 + 0.933382i $$0.383157\pi$$
−0.358884 + 0.933382i $$0.616843\pi$$
$$524$$ 4.12318e9 + 2.20620e9i 1.25191 + 0.669861i
$$525$$ 0 0
$$526$$ −4.20363e9 + 2.51832e9i −1.25943 + 0.754502i
$$527$$ −3.86300e9 −1.14971
$$528$$ 0 0
$$529$$ −2.79634e9 −0.821288
$$530$$ 3.27561e9 1.96236e9i 0.955712 0.572549i
$$531$$ 0 0
$$532$$ −1.57636e9 8.43465e8i −0.453905 0.242871i
$$533$$ 4.50894e8i 0.128982i
$$534$$ 0 0
$$535$$ −1.66414e8 −0.0469841
$$536$$ −4.57623e8 + 2.21821e7i −0.128360 + 0.00622193i
$$537$$ 0 0
$$538$$ −2.00446e9 3.34590e9i −0.554958 0.926349i
$$539$$ 5.02858e8i 0.138320i
$$540$$ 0 0
$$541$$ 5.39345e8i 0.146445i 0.997316 + 0.0732227i $$0.0233284\pi$$
−0.997316 + 0.0732227i $$0.976672\pi$$
$$542$$ −4.29475e9 + 2.57290e9i −1.15862 + 0.694106i
$$543$$ 0 0
$$544$$ 5.79270e9 + 2.74746e9i 1.54271 + 0.731704i
$$545$$ −6.35620e9 −1.68194
$$546$$ 0 0
$$547$$ 8.82287e7i 0.0230491i 0.999934 + 0.0115246i $$0.00366846\pi$$
−0.999934 + 0.0115246i $$0.996332\pi$$
$$548$$ 1.55177e9 2.90012e9i 0.402806 0.752808i
$$549$$ 0 0
$$550$$ −8.61304e8 1.43771e9i −0.220743 0.368469i
$$551$$ −2.49754e9 −0.636037
$$552$$ 0 0
$$553$$ −7.87226e9 −1.97953
$$554$$ 1.84981e9 + 3.08774e9i 0.462213 + 0.771537i
$$555$$ 0 0
$$556$$ 5.90257e9 + 3.15829e9i 1.45639 + 0.779274i
$$557$$ 5.57233e8i 0.136629i 0.997664 + 0.0683147i $$0.0217622\pi$$
−0.997664 + 0.0683147i $$0.978238\pi$$
$$558$$ 0 0
$$559$$ −2.06555e9 −0.500143
$$560$$ −4.23269e9 + 2.82286e9i −1.01849 + 0.679254i
$$561$$ 0 0
$$562$$ −1.24711e9 + 7.47119e8i −0.296365 + 0.177547i
$$563$$ 1.17012e9i 0.276344i 0.990408 + 0.138172i $$0.0441227\pi$$
−0.990408 + 0.138172i $$0.955877\pi$$
$$564$$ 0 0
$$565$$ 6.12887e9i 1.42959i
$$566$$ −2.31973e9 3.87214e9i −0.537749 0.897623i
$$567$$ 0 0
$$568$$ 3.77886e7 + 7.79590e8i 0.00865250 + 0.178504i
$$569$$ 2.39181e9 0.544295 0.272147 0.962256i $$-0.412266\pi$$
0.272147 + 0.962256i $$0.412266\pi$$
$$570$$ 0 0
$$571$$ 3.15823e9i 0.709933i −0.934879 0.354966i $$-0.884492\pi$$
0.934879 0.354966i $$-0.115508\pi$$
$$572$$ −2.07076e9 + 3.87007e9i −0.462640 + 0.864634i
$$573$$ 0 0
$$574$$ 6.65843e8 3.98894e8i 0.146954 0.0880371i
$$575$$ −6.70211e8 −0.147019
$$576$$ 0 0
$$577$$ 4.03435e9 0.874296 0.437148 0.899390i $$-0.355989\pi$$
0.437148 + 0.899390i $$0.355989\pi$$
$$578$$ 7.62785e9 4.56970e9i 1.64306 0.984329i
$$579$$ 0 0
$$580$$ −3.35308e9 + 6.26660e9i −0.713585 + 1.33363i
$$581$$ 5.64138e9i 1.19335i
$$582$$ 0 0
$$583$$ 5.67087e9 1.18525
$$584$$ 1.88262e8 + 3.88391e9i 0.0391128 + 0.806908i
$$585$$ 0 0
$$586$$ −1.16843e9 1.95037e9i −0.239861 0.400382i
$$587$$ 2.72240e9i 0.555544i 0.960647 + 0.277772i $$0.0895960\pi$$
−0.960647 + 0.277772i $$0.910404\pi$$
$$588$$ 0 0
$$589$$ 1.63016e9i 0.328721i
$$590$$ 7.11692e8 4.26361e8i 0.142662 0.0854664i
$$591$$ 0 0
$$592$$ 1.41263e9 9.42113e8i 0.279836 0.186628i
$$593$$ 2.29251e9 0.451460 0.225730 0.974190i $$-0.427523\pi$$
0.225730 + 0.974190i $$0.427523\pi$$
$$594$$ 0 0
$$595$$ 1.07402e10i 2.09028i
$$596$$ −2.03605e9 1.08943e9i −0.393937 0.210784i
$$597$$ 0 0
$$598$$ 9.02047e8 + 1.50572e9i 0.172494 + 0.287932i
$$599$$ 3.58734e9 0.681991 0.340995 0.940065i $$-0.389236\pi$$
0.340995 + 0.940065i $$0.389236\pi$$
$$600$$ 0 0
$$601$$ 8.20369e9 1.54152 0.770759 0.637127i $$-0.219877\pi$$
0.770759 + 0.637127i $$0.219877\pi$$
$$602$$ −1.82734e9 3.05024e9i −0.341375 0.569831i
$$603$$ 0 0
$$604$$ 2.33934e9 4.37201e9i 0.431980 0.807332i
$$605$$ 3.32259e9i 0.610004i
$$606$$ 0 0
$$607$$ −4.60087e9 −0.834986 −0.417493 0.908680i $$-0.637091\pi$$
−0.417493 + 0.908680i $$0.637091\pi$$
$$608$$ 1.15941e9 2.44449e9i 0.209207 0.441088i
$$609$$ 0 0
$$610$$ 4.88985e9 2.92942e9i 0.872251 0.522549i
$$611$$ 7.48707e8i 0.132791i
$$612$$ 0 0
$$613$$ 8.55728e9i 1.50046i 0.661178 + 0.750229i $$0.270057\pi$$
−0.661178 + 0.750229i $$0.729943\pi$$
$$614$$ 9.23998e7 + 1.54236e8i 0.0161095 + 0.0268903i
$$615$$ 0 0
$$616$$ −7.54695e9 + 3.65819e8i −1.30089 + 0.0630570i
$$617$$ 2.58089e9 0.442355 0.221178 0.975234i $$-0.429010\pi$$
0.221178 + 0.975234i $$0.429010\pi$$
$$618$$ 0 0
$$619$$ 5.26641e9i 0.892478i 0.894914 + 0.446239i $$0.147237\pi$$
−0.894914 + 0.446239i $$0.852763\pi$$
$$620$$ 4.09026e9 + 2.18858e9i 0.689255 + 0.368800i
$$621$$ 0 0
$$622$$ −4.73340e9 + 2.83569e9i −0.788690 + 0.472490i
$$623$$ 4.18197e8 0.0692903
$$624$$ 0 0
$$625$$ −7.48796e9 −1.22683
$$626$$ −3.15164e9 + 1.88809e9i −0.513483 + 0.307618i
$$627$$ 0 0
$$628$$ −5.78226e9 3.09392e9i −0.931621 0.498483i
$$629$$ 3.58449e9i 0.574314i
$$630$$ 0 0
$$631$$ 8.32515e9 1.31914 0.659568 0.751645i $$-0.270739\pi$$
0.659568 + 0.751645i $$0.270739\pi$$
$$632$$ −5.76773e8 1.18990e10i −0.0908857 1.87500i
$$633$$ 0 0
$$634$$ 6.16801e9 + 1.02958e10i 0.961242 + 1.60453i
$$635$$ 1.28601e10i 1.99313i
$$636$$ 0 0
$$637$$ 5.80071e8i 0.0889187i
$$638$$ −9.05469e9 + 5.42449e9i −1.38039 + 0.826965i
$$639$$ 0 0
$$640$$ −4.57691e9 6.19093e9i −0.690148 0.933526i
$$641$$ −4.26190e9 −0.639146 −0.319573 0.947562i $$-0.603540\pi$$
−0.319573 + 0.947562i $$0.603540\pi$$
$$642$$ 0 0
$$643$$ 1.26588e10i 1.87782i −0.344167 0.938908i $$-0.611839\pi$$
0.344167 0.938908i $$-0.388161\pi$$
$$644$$ −1.42550e9 + 2.66414e9i −0.210314 + 0.393058i
$$645$$ 0 0
$$646$$ −2.93519e9 4.89949e9i −0.428374 0.715052i
$$647$$ 7.38061e9 1.07134 0.535670 0.844427i $$-0.320059\pi$$
0.535670 + 0.844427i $$0.320059\pi$$
$$648$$ 0 0
$$649$$ 1.23211e9 0.176926
$$650$$ −9.93555e8 1.65846e9i −0.141904 0.236870i
$$651$$ 0 0
$$652$$ 9.67853e9 + 5.17870e9i 1.36755 + 0.731735i
$$653$$ 3.21579e9i 0.451951i 0.974133 + 0.225975i $$0.0725569\pi$$
−0.974133 + 0.225975i $$0.927443\pi$$
$$654$$ 0 0
$$655$$ −1.18549e10 −1.64836
$$656$$ 6.51717e8 + 9.77204e8i 0.0901354 + 0.135152i
$$657$$ 0 0
$$658$$ 1.10563e9 6.62362e8i 0.151293 0.0906368i
$$659$$ 5.17004e9i 0.703711i −0.936054 0.351856i $$-0.885551\pi$$
0.936054 0.351856i $$-0.114449\pi$$
$$660$$ 0 0
$$661$$ 1.95604e9i 0.263435i −0.991287 0.131717i $$-0.957951\pi$$
0.991287 0.131717i $$-0.0420491\pi$$
$$662$$ −1.67735e9 2.79987e9i −0.224709 0.375090i
$$663$$ 0 0
$$664$$ −8.52701e9 + 4.13325e8i −1.13034 + 0.0547902i
$$665$$ 4.53232e9 0.597647
$$666$$ 0 0
$$667$$ 4.22099e9i 0.550775i
$$668$$ 6.39330e9 1.19485e10i 0.829865 1.55094i
$$669$$ 0 0
$$670$$ 9.96362e8 5.96902e8i 0.127984 0.0766727i
$$671$$ 8.46551e9 1.08174
$$672$$ 0 0
$$673$$ 1.54679e9 0.195605 0.0978024 0.995206i $$-0.468819\pi$$
0.0978024 + 0.995206i $$0.468819\pi$$
$$674$$ −1.07337e9 + 6.43035e8i −0.135033 + 0.0808956i
$$675$$ 0 0
$$676$$ 1.40053e9 2.61747e9i 0.174373 0.325888i
$$677$$ 8.55209e9i 1.05928i 0.848222 + 0.529642i $$0.177674\pi$$
−0.848222 + 0.529642i $$0.822326\pi$$
$$678$$ 0 0
$$679$$ 7.50565e9 0.920119
$$680$$ −1.62340e10 + 7.86900e8i −1.97990 + 0.0959707i
$$681$$ 0 0
$$682$$ 3.54061e9 + 5.91006e9i 0.427398 + 0.713422i
$$683$$ 7.26976e9i 0.873067i −0.899688 0.436534i $$-0.856206\pi$$
0.899688 0.436534i $$-0.143794\pi$$
$$684$$ 0 0
$$685$$ 8.33837e9i 0.991206i
$$686$$ 6.79217e9 4.06906e9i 0.803293 0.481238i
$$687$$ 0 0
$$688$$ 4.47658e9 2.98552e9i 0.524068 0.349511i
$$689$$ 6.54162e9 0.761935
$$690$$ 0 0
$$691$$ 5.19893e9i 0.599434i −0.954028 0.299717i $$-0.903108\pi$$
0.954028 0.299717i $$-0.0968922\pi$$
$$692$$ 2.23629e9 + 1.19657e9i 0.256541 + 0.137268i
$$693$$ 0 0
$$694$$ −6.43358e9 1.07391e10i −0.730626 1.21958i
$$695$$ −1.69709e10 −1.91760
$$696$$ 0 0
$$697$$ 2.47961e9 0.277376
$$698$$ 8.04333e9 + 1.34261e10i 0.895245 + 1.49436i
$$699$$ 0 0
$$700$$ 1.57011e9 2.93440e9i 0.173017 0.323353i
$$701$$ 1.35221e10i 1.48262i 0.671163 + 0.741310i $$0.265795\pi$$
−0.671163 + 0.741310i $$0.734205\pi$$
$$702$$ 0 0
$$703$$ −1.51263e9 −0.164206
$$704$$ −1.10588e9 1.13805e10i −0.119455 1.22930i
$$705$$ 0 0
$$706$$ 2.40321e9 1.43972e9i 0.257025 0.153979i
$$707$$ 5.93083e9i 0.631172i
$$708$$ 0 0
$$709$$ 1.05901e10i 1.11594i 0.829862 + 0.557969i $$0.188419\pi$$
−0.829862 + 0.557969i $$0.811581\pi$$
$$710$$ −1.01686e9 1.69737e9i −0.106625 0.177980i
$$711$$ 0 0
$$712$$ 3.06398e7 + 6.32109e8i 0.00318131 + 0.0656314i
$$713$$ 2.75507e9 0.284655
$$714$$ 0 0
$$715$$ 1.11271e10i 1.13845i
$$716$$ 3.36096e9 + 1.79835e9i 0.342191 + 0.183096i
$$717$$ 0 0
$$718$$ 1.34556e10 8.06102e9i 1.35665 0.812746i
$$719$$ −1.49161e10 −1.49659 −0.748297 0.663363i $$-0.769128\pi$$
−0.748297 + 0.663363i $$0.769128\pi$$
$$720$$ 0 0
$$721$$ 6.31417e9 0.627398
$$722$$ 6.60779e9 3.95860e9i 0.653395 0.391437i
$$723$$ 0 0
$$724$$ −4.47180e8 2.39273e8i −0.0437923 0.0234320i
$$725$$ 4.64919e9i 0.453100i
$$726$$ 0 0
$$727$$ −8.90159e9 −0.859206 −0.429603 0.903018i $$-0.641346\pi$$
−0.429603 + 0.903018i $$0.641346\pi$$
$$728$$ −8.70577e9 + 4.21989e8i −0.836271 + 0.0405361i
$$729$$ 0 0
$$730$$ −5.06599e9 8.45627e9i −0.481986 0.804542i
$$731$$ 1.13591e10i 1.07556i
$$732$$ 0 0
$$733$$ 7.99792e9i 0.750090i −0.927007 0.375045i $$-0.877627\pi$$
0.927007 0.375045i $$-0.122373\pi$$
$$734$$ −7.27288e9 + 4.35704e9i −0.678844 + 0.406683i
$$735$$ 0 0
$$736$$ −4.13132e9 1.95947e9i −0.381959 0.181162i
$$737$$ 1.72494e9 0.158722
$$738$$ 0 0
$$739$$ 1.03852e10i 0.946588i 0.880905 + 0.473294i $$0.156935\pi$$
−0.880905 + 0.473294i $$0.843065\pi$$
$$740$$ −2.03078e9 + 3.79536e9i −0.184227 + 0.344304i
$$741$$ 0 0
$$742$$ 5.78720e9 + 9.66013e9i 0.520062 + 0.868099i
$$743$$ 3.73477e9 0.334044 0.167022 0.985953i $$-0.446585\pi$$
0.167022 + 0.985953i $$0.446585\pi$$
$$744$$ 0 0
$$745$$ 5.85402e9 0.518689
$$746$$ −8.69345e9 1.45113e10i −0.766666 1.27974i
$$747$$ 0 0
$$748$$ −2.12827e10 1.13878e10i −1.85940 0.994908i
$$749$$ 4.90772e8i 0.0426770i
$$750$$ 0 0
$$751$$ −1.34330e10 −1.15726 −0.578631 0.815589i $$-0.696413\pi$$
−0.578631 + 0.815589i $$0.696413\pi$$
$$752$$ 1.08217e9 + 1.62264e9i 0.0927970 + 0.139143i
$$753$$ 0 0
$$754$$ −1.04450e10 + 6.25741e9i −0.887379 + 0.531612i
$$755$$ 1.25703e10i 1.06300i
$$756$$ 0 0
$$757$$ 6.78007e9i 0.568065i −0.958815 0.284033i $$-0.908328\pi$$
0.958815 0.284033i $$-0.0916724\pi$$
$$758$$ 4.60548e8 + 7.68758e8i 0.0384090 + 0.0641132i
$$759$$ 0 0
$$760$$ 3.32068e8 + 6.85065e9i 0.0274397 + 0.566089i
$$761$$ −8.01137e9 −0.658962 −0.329481 0.944162i $$-0.606874\pi$$
−0.329481 + 0.944162i $$0.606874\pi$$
$$762$$ 0 0
$$763$$ 1.87451e10i 1.52775i
$$764$$ 2.89925e9 5.41845e9i 0.235212 0.439590i
$$765$$ 0 0
$$766$$ −4.66133e9 + 2.79252e9i −0.374722 + 0.224489i
$$767$$ 1.42130e9 0.113737
$$768$$ 0 0
$$769$$ 1.46553e10 1.16213 0.581063 0.813858i $$-0.302637\pi$$
0.581063 + 0.813858i $$0.302637\pi$$
$$770$$ 1.64316e10 9.84389e9i 1.29707 0.777051i
$$771$$ 0 0
$$772$$ −2.85334e8 + 5.33264e8i −0.0223199 + 0.0417140i
$$773$$ 2.33296e10i 1.81668i −0.418233 0.908340i $$-0.637350\pi$$
0.418233 0.908340i $$-0.362650\pi$$
$$774$$ 0 0
$$775$$ −3.03456e9 −0.234174
$$776$$ 5.49913e8 + 1.13449e10i 0.0422453 + 0.871533i
$$777$$ 0 0
$$778$$ 6.23001e9 + 1.03993e10i 0.474307 + 0.791725i
$$779$$