# Properties

 Label 882.4.g.v.361.1 Level $882$ Weight $4$ Character 882.361 Analytic conductor $52.040$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 14) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.361 Dual form 882.4.g.v.667.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.00000 + 10.3923i) q^{5} -8.00000 q^{8} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.00000 + 10.3923i) q^{5} -8.00000 q^{8} +(-12.0000 + 20.7846i) q^{10} +(24.0000 - 41.5692i) q^{11} -56.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(57.0000 - 98.7269i) q^{17} +(1.00000 + 1.73205i) q^{19} -48.0000 q^{20} +96.0000 q^{22} +(-60.0000 - 103.923i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(-56.0000 - 96.9948i) q^{26} +54.0000 q^{29} +(118.000 - 204.382i) q^{31} +(16.0000 - 27.7128i) q^{32} +228.000 q^{34} +(-73.0000 - 126.440i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-48.0000 - 83.1384i) q^{40} +126.000 q^{41} -376.000 q^{43} +(96.0000 + 166.277i) q^{44} +(120.000 - 207.846i) q^{46} +(6.00000 + 10.3923i) q^{47} -38.0000 q^{50} +(112.000 - 193.990i) q^{52} +(87.0000 - 150.688i) q^{53} +576.000 q^{55} +(54.0000 + 93.5307i) q^{58} +(-69.0000 + 119.512i) q^{59} +(190.000 + 329.090i) q^{61} +472.000 q^{62} +64.0000 q^{64} +(-336.000 - 581.969i) q^{65} +(242.000 - 419.156i) q^{67} +(228.000 + 394.908i) q^{68} -576.000 q^{71} +(-575.000 + 995.929i) q^{73} +(146.000 - 252.879i) q^{74} -8.00000 q^{76} +(-388.000 - 672.036i) q^{79} +(96.0000 - 166.277i) q^{80} +(126.000 + 218.238i) q^{82} +378.000 q^{83} +1368.00 q^{85} +(-376.000 - 651.251i) q^{86} +(-192.000 + 332.554i) q^{88} +(195.000 + 337.750i) q^{89} +480.000 q^{92} +(-12.0000 + 20.7846i) q^{94} +(-12.0000 + 20.7846i) q^{95} +1330.00 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} - 4q^{4} + 12q^{5} - 16q^{8} + O(q^{10})$$ $$2q + 2q^{2} - 4q^{4} + 12q^{5} - 16q^{8} - 24q^{10} + 48q^{11} - 112q^{13} - 16q^{16} + 114q^{17} + 2q^{19} - 96q^{20} + 192q^{22} - 120q^{23} - 19q^{25} - 112q^{26} + 108q^{29} + 236q^{31} + 32q^{32} + 456q^{34} - 146q^{37} - 4q^{38} - 96q^{40} + 252q^{41} - 752q^{43} + 192q^{44} + 240q^{46} + 12q^{47} - 76q^{50} + 224q^{52} + 174q^{53} + 1152q^{55} + 108q^{58} - 138q^{59} + 380q^{61} + 944q^{62} + 128q^{64} - 672q^{65} + 484q^{67} + 456q^{68} - 1152q^{71} - 1150q^{73} + 292q^{74} - 16q^{76} - 776q^{79} + 192q^{80} + 252q^{82} + 756q^{83} + 2736q^{85} - 752q^{86} - 384q^{88} + 390q^{89} + 960q^{92} - 24q^{94} - 24q^{95} + 2660q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.73205i 0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −2.00000 + 3.46410i −0.250000 + 0.433013i
$$5$$ 6.00000 + 10.3923i 0.536656 + 0.929516i 0.999081 + 0.0428575i $$0.0136462\pi$$
−0.462425 + 0.886658i $$0.653021\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ −12.0000 + 20.7846i −0.379473 + 0.657267i
$$11$$ 24.0000 41.5692i 0.657843 1.13942i −0.323330 0.946286i $$-0.604802\pi$$
0.981173 0.193131i $$-0.0618643\pi$$
$$12$$ 0 0
$$13$$ −56.0000 −1.19474 −0.597369 0.801966i $$-0.703787\pi$$
−0.597369 + 0.801966i $$0.703787\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ 57.0000 98.7269i 0.813208 1.40852i −0.0974001 0.995245i $$-0.531053\pi$$
0.910608 0.413272i $$-0.135614\pi$$
$$18$$ 0 0
$$19$$ 1.00000 + 1.73205i 0.0120745 + 0.0209137i 0.872000 0.489507i $$-0.162823\pi$$
−0.859925 + 0.510420i $$0.829490\pi$$
$$20$$ −48.0000 −0.536656
$$21$$ 0 0
$$22$$ 96.0000 0.930330
$$23$$ −60.0000 103.923i −0.543951 0.942150i −0.998672 0.0515165i $$-0.983595\pi$$
0.454721 0.890634i $$-0.349739\pi$$
$$24$$ 0 0
$$25$$ −9.50000 + 16.4545i −0.0760000 + 0.131636i
$$26$$ −56.0000 96.9948i −0.422404 0.731625i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 54.0000 0.345778 0.172889 0.984941i $$-0.444690\pi$$
0.172889 + 0.984941i $$0.444690\pi$$
$$30$$ 0 0
$$31$$ 118.000 204.382i 0.683659 1.18413i −0.290197 0.956967i $$-0.593721\pi$$
0.973856 0.227165i $$-0.0729457\pi$$
$$32$$ 16.0000 27.7128i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 228.000 1.15005
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −73.0000 126.440i −0.324355 0.561799i 0.657027 0.753867i $$-0.271814\pi$$
−0.981382 + 0.192068i $$0.938480\pi$$
$$38$$ −2.00000 + 3.46410i −0.00853797 + 0.0147882i
$$39$$ 0 0
$$40$$ −48.0000 83.1384i −0.189737 0.328634i
$$41$$ 126.000 0.479949 0.239974 0.970779i $$-0.422861\pi$$
0.239974 + 0.970779i $$0.422861\pi$$
$$42$$ 0 0
$$43$$ −376.000 −1.33348 −0.666738 0.745292i $$-0.732310\pi$$
−0.666738 + 0.745292i $$0.732310\pi$$
$$44$$ 96.0000 + 166.277i 0.328921 + 0.569709i
$$45$$ 0 0
$$46$$ 120.000 207.846i 0.384631 0.666201i
$$47$$ 6.00000 + 10.3923i 0.0186211 + 0.0322526i 0.875186 0.483787i $$-0.160739\pi$$
−0.856565 + 0.516040i $$0.827406\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −38.0000 −0.107480
$$51$$ 0 0
$$52$$ 112.000 193.990i 0.298685 0.517337i
$$53$$ 87.0000 150.688i 0.225479 0.390540i −0.730984 0.682394i $$-0.760939\pi$$
0.956463 + 0.291854i $$0.0942721\pi$$
$$54$$ 0 0
$$55$$ 576.000 1.41214
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 54.0000 + 93.5307i 0.122251 + 0.211745i
$$59$$ −69.0000 + 119.512i −0.152255 + 0.263713i −0.932056 0.362314i $$-0.881987\pi$$
0.779801 + 0.626027i $$0.215320\pi$$
$$60$$ 0 0
$$61$$ 190.000 + 329.090i 0.398803 + 0.690748i 0.993579 0.113144i $$-0.0360923\pi$$
−0.594775 + 0.803892i $$0.702759\pi$$
$$62$$ 472.000 0.966840
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ −336.000 581.969i −0.641164 1.11053i
$$66$$ 0 0
$$67$$ 242.000 419.156i 0.441269 0.764300i −0.556515 0.830837i $$-0.687862\pi$$
0.997784 + 0.0665376i $$0.0211952\pi$$
$$68$$ 228.000 + 394.908i 0.406604 + 0.704259i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −576.000 −0.962798 −0.481399 0.876502i $$-0.659871\pi$$
−0.481399 + 0.876502i $$0.659871\pi$$
$$72$$ 0 0
$$73$$ −575.000 + 995.929i −0.921899 + 1.59678i −0.125426 + 0.992103i $$0.540030\pi$$
−0.796473 + 0.604674i $$0.793304\pi$$
$$74$$ 146.000 252.879i 0.229353 0.397252i
$$75$$ 0 0
$$76$$ −8.00000 −0.0120745
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −388.000 672.036i −0.552575 0.957088i −0.998088 0.0618122i $$-0.980312\pi$$
0.445513 0.895275i $$-0.353021\pi$$
$$80$$ 96.0000 166.277i 0.134164 0.232379i
$$81$$ 0 0
$$82$$ 126.000 + 218.238i 0.169687 + 0.293907i
$$83$$ 378.000 0.499890 0.249945 0.968260i $$-0.419587\pi$$
0.249945 + 0.968260i $$0.419587\pi$$
$$84$$ 0 0
$$85$$ 1368.00 1.74565
$$86$$ −376.000 651.251i −0.471455 0.816584i
$$87$$ 0 0
$$88$$ −192.000 + 332.554i −0.232583 + 0.402845i
$$89$$ 195.000 + 337.750i 0.232247 + 0.402263i 0.958469 0.285197i $$-0.0920590\pi$$
−0.726222 + 0.687460i $$0.758726\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 480.000 0.543951
$$93$$ 0 0
$$94$$ −12.0000 + 20.7846i −0.0131671 + 0.0228061i
$$95$$ −12.0000 + 20.7846i −0.0129597 + 0.0224469i
$$96$$ 0 0
$$97$$ 1330.00 1.39218 0.696088 0.717957i $$-0.254922\pi$$
0.696088 + 0.717957i $$0.254922\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −38.0000 65.8179i −0.0380000 0.0658179i
$$101$$ 750.000 1299.04i 0.738889 1.27979i −0.214107 0.976810i $$-0.568684\pi$$
0.952996 0.302983i $$-0.0979826\pi$$
$$102$$ 0 0
$$103$$ 190.000 + 329.090i 0.181760 + 0.314817i 0.942480 0.334263i $$-0.108487\pi$$
−0.760720 + 0.649080i $$0.775154\pi$$
$$104$$ 448.000 0.422404
$$105$$ 0 0
$$106$$ 348.000 0.318875
$$107$$ 318.000 + 550.792i 0.287310 + 0.497636i 0.973167 0.230101i $$-0.0739055\pi$$
−0.685856 + 0.727737i $$0.740572\pi$$
$$108$$ 0 0
$$109$$ −73.0000 + 126.440i −0.0641480 + 0.111108i −0.896316 0.443416i $$-0.853766\pi$$
0.832168 + 0.554524i $$0.187100\pi$$
$$110$$ 576.000 + 997.661i 0.499268 + 0.864757i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −198.000 −0.164834 −0.0824171 0.996598i $$-0.526264\pi$$
−0.0824171 + 0.996598i $$0.526264\pi$$
$$114$$ 0 0
$$115$$ 720.000 1247.08i 0.583829 1.01122i
$$116$$ −108.000 + 187.061i −0.0864444 + 0.149726i
$$117$$ 0 0
$$118$$ −276.000 −0.215321
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −486.500 842.643i −0.365515 0.633090i
$$122$$ −380.000 + 658.179i −0.281997 + 0.488432i
$$123$$ 0 0
$$124$$ 472.000 + 817.528i 0.341829 + 0.592066i
$$125$$ 1272.00 0.910169
$$126$$ 0 0
$$127$$ −376.000 −0.262713 −0.131357 0.991335i $$-0.541933\pi$$
−0.131357 + 0.991335i $$0.541933\pi$$
$$128$$ 64.0000 + 110.851i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 672.000 1163.94i 0.453372 0.785263i
$$131$$ −1065.00 1844.63i −0.710301 1.23028i −0.964744 0.263190i $$-0.915225\pi$$
0.254443 0.967088i $$-0.418108\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 968.000 0.624048
$$135$$ 0 0
$$136$$ −456.000 + 789.815i −0.287512 + 0.497986i
$$137$$ −39.0000 + 67.5500i −0.0243211 + 0.0421254i −0.877930 0.478789i $$-0.841076\pi$$
0.853609 + 0.520915i $$0.174409\pi$$
$$138$$ 0 0
$$139$$ 2338.00 1.42667 0.713333 0.700825i $$-0.247185\pi$$
0.713333 + 0.700825i $$0.247185\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −576.000 997.661i −0.340400 0.589591i
$$143$$ −1344.00 + 2327.88i −0.785951 + 1.36131i
$$144$$ 0 0
$$145$$ 324.000 + 561.184i 0.185564 + 0.321406i
$$146$$ −2300.00 −1.30376
$$147$$ 0 0
$$148$$ 584.000 0.324355
$$149$$ −501.000 867.757i −0.275460 0.477110i 0.694791 0.719212i $$-0.255497\pi$$
−0.970251 + 0.242101i $$0.922163\pi$$
$$150$$ 0 0
$$151$$ 1376.00 2383.30i 0.741571 1.28444i −0.210208 0.977657i $$-0.567414\pi$$
0.951780 0.306783i $$-0.0992525\pi$$
$$152$$ −8.00000 13.8564i −0.00426898 0.00739410i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2832.00 1.46756
$$156$$ 0 0
$$157$$ −260.000 + 450.333i −0.132167 + 0.228920i −0.924512 0.381154i $$-0.875527\pi$$
0.792345 + 0.610074i $$0.208860\pi$$
$$158$$ 776.000 1344.07i 0.390729 0.676763i
$$159$$ 0 0
$$160$$ 384.000 0.189737
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −640.000 1108.51i −0.307538 0.532671i 0.670285 0.742104i $$-0.266172\pi$$
−0.977823 + 0.209432i $$0.932838\pi$$
$$164$$ −252.000 + 436.477i −0.119987 + 0.207824i
$$165$$ 0 0
$$166$$ 378.000 + 654.715i 0.176738 + 0.306119i
$$167$$ 1764.00 0.817380 0.408690 0.912673i $$-0.365986\pi$$
0.408690 + 0.912673i $$0.365986\pi$$
$$168$$ 0 0
$$169$$ 939.000 0.427401
$$170$$ 1368.00 + 2369.45i 0.617181 + 1.06899i
$$171$$ 0 0
$$172$$ 752.000 1302.50i 0.333369 0.577412i
$$173$$ 384.000 + 665.108i 0.168757 + 0.292296i 0.937983 0.346681i $$-0.112691\pi$$
−0.769226 + 0.638977i $$0.779358\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −768.000 −0.328921
$$177$$ 0 0
$$178$$ −390.000 + 675.500i −0.164223 + 0.284443i
$$179$$ 906.000 1569.24i 0.378311 0.655253i −0.612506 0.790466i $$-0.709838\pi$$
0.990817 + 0.135213i $$0.0431718\pi$$
$$180$$ 0 0
$$181$$ 448.000 0.183976 0.0919878 0.995760i $$-0.470678\pi$$
0.0919878 + 0.995760i $$0.470678\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 480.000 + 831.384i 0.192316 + 0.333100i
$$185$$ 876.000 1517.28i 0.348134 0.602986i
$$186$$ 0 0
$$187$$ −2736.00 4738.89i −1.06993 1.85317i
$$188$$ −48.0000 −0.0186211
$$189$$ 0 0
$$190$$ −48.0000 −0.0183278
$$191$$ −1068.00 1849.83i −0.404596 0.700780i 0.589679 0.807638i $$-0.299254\pi$$
−0.994274 + 0.106858i $$0.965921\pi$$
$$192$$ 0 0
$$193$$ −2215.00 + 3836.49i −0.826110 + 1.43086i 0.0749584 + 0.997187i $$0.476118\pi$$
−0.901068 + 0.433677i $$0.857216\pi$$
$$194$$ 1330.00 + 2303.63i 0.492208 + 0.852530i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −198.000 −0.0716087 −0.0358044 0.999359i $$-0.511399\pi$$
−0.0358044 + 0.999359i $$0.511399\pi$$
$$198$$ 0 0
$$199$$ −1142.00 + 1978.00i −0.406805 + 0.704607i −0.994530 0.104454i $$-0.966691\pi$$
0.587725 + 0.809061i $$0.300024\pi$$
$$200$$ 76.0000 131.636i 0.0268701 0.0465403i
$$201$$ 0 0
$$202$$ 3000.00 1.04495
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 756.000 + 1309.43i 0.257567 + 0.446120i
$$206$$ −380.000 + 658.179i −0.128524 + 0.222609i
$$207$$ 0 0
$$208$$ 448.000 + 775.959i 0.149342 + 0.258669i
$$209$$ 96.0000 0.0317725
$$210$$ 0 0
$$211$$ 4412.00 1.43950 0.719750 0.694233i $$-0.244256\pi$$
0.719750 + 0.694233i $$0.244256\pi$$
$$212$$ 348.000 + 602.754i 0.112739 + 0.195270i
$$213$$ 0 0
$$214$$ −636.000 + 1101.58i −0.203159 + 0.351882i
$$215$$ −2256.00 3907.51i −0.715618 1.23949i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −292.000 −0.0907190
$$219$$ 0 0
$$220$$ −1152.00 + 1995.32i −0.353036 + 0.611476i
$$221$$ −3192.00 + 5528.71i −0.971571 + 1.68281i
$$222$$ 0 0
$$223$$ −2072.00 −0.622204 −0.311102 0.950377i $$-0.600698\pi$$
−0.311102 + 0.950377i $$0.600698\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −198.000 342.946i −0.0582777 0.100940i
$$227$$ 183.000 316.965i 0.0535072 0.0926772i −0.838031 0.545622i $$-0.816293\pi$$
0.891538 + 0.452945i $$0.149627\pi$$
$$228$$ 0 0
$$229$$ −188.000 325.626i −0.0542506 0.0939648i 0.837625 0.546246i $$-0.183944\pi$$
−0.891875 + 0.452281i $$0.850610\pi$$
$$230$$ 2880.00 0.825659
$$231$$ 0 0
$$232$$ −432.000 −0.122251
$$233$$ −1131.00 1958.95i −0.318001 0.550794i 0.662070 0.749442i $$-0.269678\pi$$
−0.980071 + 0.198648i $$0.936345\pi$$
$$234$$ 0 0
$$235$$ −72.0000 + 124.708i −0.0199862 + 0.0346172i
$$236$$ −276.000 478.046i −0.0761274 0.131857i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −2592.00 −0.701517 −0.350758 0.936466i $$-0.614076\pi$$
−0.350758 + 0.936466i $$0.614076\pi$$
$$240$$ 0 0
$$241$$ 55.0000 95.2628i 0.0147007 0.0254623i −0.858581 0.512677i $$-0.828654\pi$$
0.873282 + 0.487215i $$0.161987\pi$$
$$242$$ 973.000 1685.29i 0.258458 0.447662i
$$243$$ 0 0
$$244$$ −1520.00 −0.398803
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −56.0000 96.9948i −0.0144259 0.0249864i
$$248$$ −944.000 + 1635.06i −0.241710 + 0.418654i
$$249$$ 0 0
$$250$$ 1272.00 + 2203.17i 0.321793 + 0.557362i
$$251$$ −1890.00 −0.475282 −0.237641 0.971353i $$-0.576374\pi$$
−0.237641 + 0.971353i $$0.576374\pi$$
$$252$$ 0 0
$$253$$ −5760.00 −1.43134
$$254$$ −376.000 651.251i −0.0928832 0.160878i
$$255$$ 0 0
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ −1065.00 1844.63i −0.258494 0.447724i 0.707345 0.706869i $$-0.249893\pi$$
−0.965839 + 0.259144i $$0.916559\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 2688.00 0.641164
$$261$$ 0 0
$$262$$ 2130.00 3689.27i 0.502259 0.869938i
$$263$$ −2496.00 + 4323.20i −0.585209 + 1.01361i 0.409640 + 0.912247i $$0.365654\pi$$
−0.994849 + 0.101365i $$0.967679\pi$$
$$264$$ 0 0
$$265$$ 2088.00 0.484018
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 968.000 + 1676.63i 0.220634 + 0.382150i
$$269$$ −3408.00 + 5902.83i −0.772451 + 1.33793i 0.163764 + 0.986499i $$0.447636\pi$$
−0.936216 + 0.351426i $$0.885697\pi$$
$$270$$ 0 0
$$271$$ 4096.00 + 7094.48i 0.918134 + 1.59025i 0.802247 + 0.596992i $$0.203638\pi$$
0.115887 + 0.993262i $$0.463029\pi$$
$$272$$ −1824.00 −0.406604
$$273$$ 0 0
$$274$$ −156.000 −0.0343953
$$275$$ 456.000 + 789.815i 0.0999921 + 0.173191i
$$276$$ 0 0
$$277$$ −1207.00 + 2090.59i −0.261811 + 0.453470i −0.966723 0.255825i $$-0.917653\pi$$
0.704912 + 0.709294i $$0.250986\pi$$
$$278$$ 2338.00 + 4049.53i 0.504403 + 0.873651i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1962.00 −0.416524 −0.208262 0.978073i $$-0.566781\pi$$
−0.208262 + 0.978073i $$0.566781\pi$$
$$282$$ 0 0
$$283$$ 2701.00 4678.27i 0.567342 0.982665i −0.429486 0.903074i $$-0.641305\pi$$
0.996828 0.0795914i $$-0.0253616\pi$$
$$284$$ 1152.00 1995.32i 0.240699 0.416904i
$$285$$ 0 0
$$286$$ −5376.00 −1.11150
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4041.50 7000.08i −0.822613 1.42481i
$$290$$ −648.000 + 1122.37i −0.131213 + 0.227268i
$$291$$ 0 0
$$292$$ −2300.00 3983.72i −0.460950 0.798388i
$$293$$ −4788.00 −0.954669 −0.477334 0.878722i $$-0.658397\pi$$
−0.477334 + 0.878722i $$0.658397\pi$$
$$294$$ 0 0
$$295$$ −1656.00 −0.326834
$$296$$ 584.000 + 1011.52i 0.114677 + 0.198626i
$$297$$ 0 0
$$298$$ 1002.00 1735.51i 0.194780 0.337368i
$$299$$ 3360.00 + 5819.69i 0.649879 + 1.12562i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 5504.00 1.04874
$$303$$ 0 0
$$304$$ 16.0000 27.7128i 0.00301863 0.00522842i
$$305$$ −2280.00 + 3949.08i −0.428041 + 0.741388i
$$306$$ 0 0
$$307$$ 574.000 0.106710 0.0533549 0.998576i $$-0.483009\pi$$
0.0533549 + 0.998576i $$0.483009\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 2832.00 + 4905.17i 0.518861 + 0.898693i
$$311$$ 4404.00 7627.95i 0.802984 1.39081i −0.114660 0.993405i $$-0.536578\pi$$
0.917644 0.397404i $$-0.130089\pi$$
$$312$$ 0 0
$$313$$ −1385.00 2398.89i −0.250111 0.433205i 0.713445 0.700711i $$-0.247134\pi$$
−0.963556 + 0.267506i $$0.913801\pi$$
$$314$$ −1040.00 −0.186913
$$315$$ 0 0
$$316$$ 3104.00 0.552575
$$317$$ 3783.00 + 6552.35i 0.670266 + 1.16094i 0.977828 + 0.209407i $$0.0671535\pi$$
−0.307562 + 0.951528i $$0.599513\pi$$
$$318$$ 0 0
$$319$$ 1296.00 2244.74i 0.227467 0.393985i
$$320$$ 384.000 + 665.108i 0.0670820 + 0.116190i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 228.000 0.0392763
$$324$$ 0 0
$$325$$ 532.000 921.451i 0.0908002 0.157270i
$$326$$ 1280.00 2217.03i 0.217462 0.376655i
$$327$$ 0 0
$$328$$ −1008.00 −0.169687
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 5660.00 + 9803.41i 0.939884 + 1.62793i 0.765684 + 0.643217i $$0.222401\pi$$
0.174201 + 0.984710i $$0.444266\pi$$
$$332$$ −756.000 + 1309.43i −0.124973 + 0.216459i
$$333$$ 0 0
$$334$$ 1764.00 + 3055.34i 0.288987 + 0.500541i
$$335$$ 5808.00 0.947239
$$336$$ 0 0
$$337$$ −4786.00 −0.773620 −0.386810 0.922159i $$-0.626423\pi$$
−0.386810 + 0.922159i $$0.626423\pi$$
$$338$$ 939.000 + 1626.40i 0.151109 + 0.261729i
$$339$$ 0 0
$$340$$ −2736.00 + 4738.89i −0.436413 + 0.755890i
$$341$$ −5664.00 9810.34i −0.899480 1.55795i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 3008.00 0.471455
$$345$$ 0 0
$$346$$ −768.000 + 1330.22i −0.119329 + 0.206684i
$$347$$ 6324.00 10953.5i 0.978358 1.69457i 0.309980 0.950743i $$-0.399678\pi$$
0.668378 0.743822i $$-0.266989\pi$$
$$348$$ 0 0
$$349$$ −9632.00 −1.47733 −0.738666 0.674071i $$-0.764544\pi$$
−0.738666 + 0.674071i $$0.764544\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −768.000 1330.22i −0.116291 0.201422i
$$353$$ 1695.00 2935.83i 0.255569 0.442658i −0.709481 0.704724i $$-0.751071\pi$$
0.965050 + 0.262066i $$0.0844040\pi$$
$$354$$ 0 0
$$355$$ −3456.00 5985.97i −0.516691 0.894936i
$$356$$ −1560.00 −0.232247
$$357$$ 0 0
$$358$$ 3624.00 0.535012
$$359$$ −5352.00 9269.94i −0.786818 1.36281i −0.927907 0.372812i $$-0.878394\pi$$
0.141089 0.989997i $$-0.454940\pi$$
$$360$$ 0 0
$$361$$ 3427.50 5936.60i 0.499708 0.865520i
$$362$$ 448.000 + 775.959i 0.0650452 + 0.112662i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −13800.0 −1.97897
$$366$$ 0 0
$$367$$ −4292.00 + 7433.96i −0.610465 + 1.05736i 0.380697 + 0.924700i $$0.375684\pi$$
−0.991162 + 0.132656i $$0.957649\pi$$
$$368$$ −960.000 + 1662.77i −0.135988 + 0.235538i
$$369$$ 0 0
$$370$$ 3504.00 0.492336
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1061.00 + 1837.71i 0.147283 + 0.255101i 0.930222 0.366997i $$-0.119614\pi$$
−0.782939 + 0.622098i $$0.786281\pi$$
$$374$$ 5472.00 9477.78i 0.756552 1.31039i
$$375$$ 0 0
$$376$$ −48.0000 83.1384i −0.00658354 0.0114030i
$$377$$ −3024.00 −0.413114
$$378$$ 0 0
$$379$$ −4912.00 −0.665732 −0.332866 0.942974i $$-0.608016\pi$$
−0.332866 + 0.942974i $$0.608016\pi$$
$$380$$ −48.0000 83.1384i −0.00647986 0.0112235i
$$381$$ 0 0
$$382$$ 2136.00 3699.66i 0.286092 0.495526i
$$383$$ −4530.00 7846.19i −0.604366 1.04679i −0.992151 0.125043i $$-0.960093\pi$$
0.387785 0.921750i $$-0.373240\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −8860.00 −1.16830
$$387$$ 0 0
$$388$$ −2660.00 + 4607.26i −0.348044 + 0.602830i
$$389$$ 4497.00 7789.03i 0.586136 1.01522i −0.408597 0.912715i $$-0.633982\pi$$
0.994733 0.102502i $$-0.0326850\pi$$
$$390$$ 0 0
$$391$$ −13680.0 −1.76938
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −198.000 342.946i −0.0253175 0.0438512i
$$395$$ 4656.00 8064.43i 0.593086 1.02725i
$$396$$ 0 0
$$397$$ −6488.00 11237.5i −0.820210 1.42065i −0.905526 0.424291i $$-0.860523\pi$$
0.0853156 0.996354i $$-0.472810\pi$$
$$398$$ −4568.00 −0.575309
$$399$$ 0 0
$$400$$ 304.000 0.0380000
$$401$$ −1761.00 3050.14i −0.219302 0.379842i 0.735293 0.677750i $$-0.237045\pi$$
−0.954595 + 0.297907i $$0.903711\pi$$
$$402$$ 0 0
$$403$$ −6608.00 + 11445.4i −0.816794 + 1.41473i
$$404$$ 3000.00 + 5196.15i 0.369445 + 0.639897i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −7008.00 −0.853498
$$408$$ 0 0
$$409$$ 6355.00 11007.2i 0.768300 1.33073i −0.170185 0.985412i $$-0.554436\pi$$
0.938484 0.345322i $$-0.112230\pi$$
$$410$$ −1512.00 + 2618.86i −0.182128 + 0.315454i
$$411$$ 0 0
$$412$$ −1520.00 −0.181760
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 2268.00 + 3928.29i 0.268269 + 0.464656i
$$416$$ −896.000 + 1551.92i −0.105601 + 0.182906i
$$417$$ 0 0
$$418$$ 96.0000 + 166.277i 0.0112333 + 0.0194566i
$$419$$ 1638.00 0.190982 0.0954911 0.995430i $$-0.469558\pi$$
0.0954911 + 0.995430i $$0.469558\pi$$
$$420$$ 0 0
$$421$$ −12850.0 −1.48758 −0.743789 0.668414i $$-0.766973\pi$$
−0.743789 + 0.668414i $$0.766973\pi$$
$$422$$ 4412.00 + 7641.81i 0.508940 + 0.881510i
$$423$$ 0 0
$$424$$ −696.000 + 1205.51i −0.0797187 + 0.138077i
$$425$$ 1083.00 + 1875.81i 0.123608 + 0.214095i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2544.00 −0.287310
$$429$$ 0 0
$$430$$ 4512.00 7815.01i 0.506019 0.876450i
$$431$$ −4008.00 + 6942.06i −0.447932 + 0.775840i −0.998251 0.0591136i $$-0.981173\pi$$
0.550320 + 0.834954i $$0.314506\pi$$
$$432$$ 0 0
$$433$$ −2198.00 −0.243947 −0.121974 0.992533i $$-0.538922\pi$$
−0.121974 + 0.992533i $$0.538922\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −292.000 505.759i −0.0320740 0.0555538i
$$437$$ 120.000 207.846i 0.0131359 0.0227520i
$$438$$ 0 0
$$439$$ −188.000 325.626i −0.0204391 0.0354015i 0.855625 0.517596i $$-0.173173\pi$$
−0.876064 + 0.482195i $$0.839840\pi$$
$$440$$ −4608.00 −0.499268
$$441$$ 0 0
$$442$$ −12768.0 −1.37401
$$443$$ 3594.00 + 6224.99i 0.385454 + 0.667626i 0.991832 0.127551i $$-0.0407115\pi$$
−0.606378 + 0.795176i $$0.707378\pi$$
$$444$$ 0 0
$$445$$ −2340.00 + 4053.00i −0.249273 + 0.431754i
$$446$$ −2072.00 3588.81i −0.219982 0.381020i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 14670.0 1.54192 0.770958 0.636886i $$-0.219778\pi$$
0.770958 + 0.636886i $$0.219778\pi$$
$$450$$ 0 0
$$451$$ 3024.00 5237.72i 0.315731 0.546862i
$$452$$ 396.000 685.892i 0.0412086 0.0713753i
$$453$$ 0 0
$$454$$ 732.000 0.0756706
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2573.00 + 4456.57i 0.263370 + 0.456169i 0.967135 0.254263i $$-0.0818328\pi$$
−0.703766 + 0.710432i $$0.748499\pi$$
$$458$$ 376.000 651.251i 0.0383610 0.0664432i
$$459$$ 0 0
$$460$$ 2880.00 + 4988.31i 0.291915 + 0.505611i
$$461$$ −1512.00 −0.152757 −0.0763784 0.997079i $$-0.524336\pi$$
−0.0763784 + 0.997079i $$0.524336\pi$$
$$462$$ 0 0
$$463$$ 7184.00 0.721099 0.360549 0.932740i $$-0.382589\pi$$
0.360549 + 0.932740i $$0.382589\pi$$
$$464$$ −432.000 748.246i −0.0432222 0.0748630i
$$465$$ 0 0
$$466$$ 2262.00 3917.90i 0.224861 0.389470i
$$467$$ 8259.00 + 14305.0i 0.818375 + 1.41747i 0.906879 + 0.421391i $$0.138458\pi$$
−0.0885046 + 0.996076i $$0.528209\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −288.000 −0.0282648
$$471$$ 0 0
$$472$$ 552.000 956.092i 0.0538302 0.0932367i
$$473$$ −9024.00 + 15630.0i −0.877218 + 1.51939i
$$474$$ 0 0
$$475$$ −38.0000 −0.00367065
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −2592.00 4489.48i −0.248024 0.429590i
$$479$$ −5046.00 + 8739.93i −0.481331 + 0.833690i −0.999770 0.0214244i $$-0.993180\pi$$
0.518439 + 0.855114i $$0.326513\pi$$
$$480$$ 0 0
$$481$$ 4088.00 + 7080.62i 0.387519 + 0.671203i
$$482$$ 220.000 0.0207899
$$483$$ 0 0
$$484$$ 3892.00 0.365515
$$485$$ 7980.00 + 13821.8i 0.747120 + 1.29405i
$$486$$ 0 0
$$487$$ −3916.00 + 6782.71i −0.364376 + 0.631117i −0.988676 0.150068i $$-0.952051\pi$$
0.624300 + 0.781185i $$0.285384\pi$$
$$488$$ −1520.00 2632.72i −0.140998 0.244216i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 6732.00 0.618759 0.309380 0.950939i $$-0.399879\pi$$
0.309380 + 0.950939i $$0.399879\pi$$
$$492$$ 0 0
$$493$$ 3078.00 5331.25i 0.281189 0.487034i
$$494$$ 112.000 193.990i 0.0102006 0.0176680i
$$495$$ 0 0
$$496$$ −3776.00 −0.341829
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −9334.00 16167.0i −0.837369 1.45037i −0.892087 0.451864i $$-0.850759\pi$$
0.0547176 0.998502i $$-0.482574\pi$$
$$500$$ −2544.00 + 4406.34i −0.227542 + 0.394115i
$$501$$ 0 0
$$502$$ −1890.00 3273.58i −0.168038 0.291049i
$$503$$ −6048.00 −0.536117 −0.268059 0.963403i $$-0.586382\pi$$
−0.268059 + 0.963403i $$0.586382\pi$$
$$504$$ 0 0
$$505$$ 18000.0 1.58612
$$506$$ −5760.00 9976.61i −0.506054 0.876511i
$$507$$ 0 0
$$508$$ 752.000 1302.50i 0.0656784 0.113758i
$$509$$ −5664.00 9810.34i −0.493227 0.854294i 0.506743 0.862097i $$-0.330849\pi$$
−0.999970 + 0.00780356i $$0.997516\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ 2130.00 3689.27i 0.182783 0.316589i
$$515$$ −2280.00 + 3949.08i −0.195085 + 0.337897i
$$516$$ 0 0
$$517$$ 576.000 0.0489989
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 2688.00 + 4655.75i 0.226686 + 0.392631i
$$521$$ 2073.00 3590.54i 0.174318 0.301928i −0.765607 0.643309i $$-0.777561\pi$$
0.939925 + 0.341381i $$0.110895\pi$$
$$522$$ 0 0
$$523$$ −503.000 871.222i −0.0420548 0.0728410i 0.844232 0.535978i $$-0.180057\pi$$
−0.886287 + 0.463137i $$0.846724\pi$$
$$524$$ 8520.00 0.710301
$$525$$ 0 0
$$526$$ −9984.00 −0.827610
$$527$$ −13452.0 23299.5i −1.11191 1.92589i
$$528$$ 0 0
$$529$$ −1116.50 + 1933.83i −0.0917646 + 0.158941i
$$530$$ 2088.00 + 3616.52i 0.171126 + 0.296399i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −7056.00 −0.573413
$$534$$ 0 0
$$535$$ −3816.00 + 6609.51i −0.308374 + 0.534119i
$$536$$ −1936.00 + 3353.25i −0.156012 + 0.270221i
$$537$$ 0 0
$$538$$ −13632.0 −1.09241
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 7361.00 + 12749.6i 0.584980 + 1.01321i 0.994878 + 0.101084i $$0.0322309\pi$$
−0.409898 + 0.912131i $$0.634436\pi$$
$$542$$ −8192.00 + 14189.0i −0.649219 + 1.12448i
$$543$$ 0 0
$$544$$ −1824.00 3159.26i −0.143756 0.248993i
$$545$$ −1752.00 −0.137702
$$546$$ 0 0
$$547$$ −13480.0 −1.05368 −0.526840 0.849964i $$-0.676623\pi$$
−0.526840 + 0.849964i $$0.676623\pi$$
$$548$$ −156.000 270.200i −0.0121606 0.0210627i
$$549$$ 0 0
$$550$$ −912.000 + 1579.63i −0.0707051 + 0.122465i
$$551$$ 54.0000 + 93.5307i 0.00417509 + 0.00723148i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −4828.00 −0.370256
$$555$$ 0 0
$$556$$ −4676.00 + 8099.07i −0.356666 + 0.617764i
$$557$$ 3111.00 5388.41i 0.236656 0.409900i −0.723097 0.690747i $$-0.757282\pi$$
0.959753 + 0.280847i $$0.0906153\pi$$
$$558$$ 0 0
$$559$$ 21056.0 1.59316
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1962.00 3398.28i −0.147263 0.255068i
$$563$$ −2463.00 + 4266.04i −0.184375 + 0.319347i −0.943366 0.331755i $$-0.892359\pi$$
0.758991 + 0.651101i $$0.225693\pi$$
$$564$$ 0 0
$$565$$ −1188.00 2057.68i −0.0884594 0.153216i
$$566$$ 10804.0 0.802343
$$567$$ 0 0
$$568$$ 4608.00 0.340400
$$569$$ 11091.0 + 19210.2i 0.817151 + 1.41535i 0.907773 + 0.419462i $$0.137781\pi$$
−0.0906221 + 0.995885i $$0.528886\pi$$
$$570$$ 0 0
$$571$$ −1648.00 + 2854.42i −0.120782 + 0.209201i −0.920076 0.391739i $$-0.871874\pi$$
0.799294 + 0.600940i $$0.205207\pi$$
$$572$$ −5376.00 9311.51i −0.392975 0.680653i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 2280.00 0.165361
$$576$$ 0 0
$$577$$ −12167.0 + 21073.9i −0.877849 + 1.52048i −0.0241523 + 0.999708i $$0.507689\pi$$
−0.853697 + 0.520771i $$0.825645\pi$$
$$578$$ 8083.00 14000.2i 0.581676 1.00749i
$$579$$ 0 0
$$580$$ −2592.00 −0.185564
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −4176.00 7233.04i −0.296659 0.513829i
$$584$$ 4600.00 7967.43i 0.325941 0.564546i
$$585$$ 0 0
$$586$$ −4788.00 8293.06i −0.337526 0.584613i
$$587$$ 1638.00 0.115175 0.0575873 0.998340i $$-0.481659\pi$$
0.0575873 + 0.998340i $$0.481659\pi$$
$$588$$ 0 0
$$589$$ 472.000 0.0330194
$$590$$ −1656.00 2868.28i −0.115553 0.200144i
$$591$$ 0 0
$$592$$ −1168.00 + 2023.04i −0.0810887 + 0.140450i
$$593$$ 3723.00 + 6448.43i 0.257817 + 0.446552i 0.965657 0.259821i $$-0.0836636\pi$$
−0.707840 + 0.706373i $$0.750330\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 4008.00 0.275460
$$597$$ 0 0
$$598$$ −6720.00 + 11639.4i −0.459534 + 0.795936i
$$599$$ −3252.00 + 5632.63i −0.221825 + 0.384212i −0.955362 0.295437i $$-0.904535\pi$$
0.733537 + 0.679649i $$0.237868\pi$$
$$600$$ 0 0
$$601$$ −16058.0 −1.08988 −0.544941 0.838474i $$-0.683448\pi$$
−0.544941 + 0.838474i $$0.683448\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 5504.00 + 9533.21i 0.370786 + 0.642220i
$$605$$ 5838.00 10111.7i 0.392311 0.679503i
$$606$$ 0 0
$$607$$ 5104.00 + 8840.39i 0.341293 + 0.591137i 0.984673 0.174410i $$-0.0558018\pi$$
−0.643380 + 0.765547i $$0.722468\pi$$
$$608$$ 64.0000 0.00426898
$$609$$ 0 0
$$610$$ −9120.00 −0.605341
$$611$$ −336.000 581.969i −0.0222473 0.0385335i
$$612$$ 0 0
$$613$$ 7487.00 12967.9i 0.493307 0.854432i −0.506663 0.862144i $$-0.669121\pi$$
0.999970 + 0.00771145i $$0.00245465\pi$$
$$614$$ 574.000 + 994.197i 0.0377276 + 0.0653461i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7254.00 −0.473314 −0.236657 0.971593i $$-0.576052\pi$$
−0.236657 + 0.971593i $$0.576052\pi$$
$$618$$ 0 0
$$619$$ 6229.00 10788.9i 0.404466 0.700556i −0.589793 0.807555i $$-0.700791\pi$$
0.994259 + 0.106998i $$0.0341240\pi$$
$$620$$ −5664.00 + 9810.34i −0.366890 + 0.635472i
$$621$$ 0 0
$$622$$ 17616.0 1.13559
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 8819.50 + 15275.8i 0.564448 + 0.977653i
$$626$$ 2770.00 4797.78i 0.176855 0.306322i
$$627$$ 0 0
$$628$$ −1040.00 1801.33i −0.0660836 0.114460i
$$629$$ −16644.0 −1.05507
$$630$$ 0 0
$$631$$ 28352.0 1.78871 0.894354 0.447359i $$-0.147635\pi$$
0.894354 + 0.447359i $$0.147635\pi$$
$$632$$ 3104.00 + 5376.29i 0.195365 + 0.338382i
$$633$$ 0 0
$$634$$ −7566.00 + 13104.7i −0.473950 + 0.820905i
$$635$$ −2256.00 3907.51i −0.140987 0.244196i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 5184.00 0.321687
$$639$$ 0 0
$$640$$ −768.000 + 1330.22i −0.0474342 + 0.0821584i
$$641$$ 13695.0 23720.4i 0.843869 1.46162i −0.0427309 0.999087i $$-0.513606\pi$$
0.886600 0.462537i $$-0.153061\pi$$
$$642$$ 0 0
$$643$$ 21490.0 1.31801 0.659007 0.752137i $$-0.270977\pi$$
0.659007 + 0.752137i $$0.270977\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 228.000 + 394.908i 0.0138863 + 0.0240518i
$$647$$ −8826.00 + 15287.1i −0.536300 + 0.928898i 0.462800 + 0.886463i $$0.346845\pi$$
−0.999099 + 0.0424353i $$0.986488\pi$$
$$648$$ 0 0
$$649$$ 3312.00 + 5736.55i 0.200320 + 0.346964i
$$650$$ 2128.00 0.128411
$$651$$ 0 0
$$652$$ 5120.00 0.307538
$$653$$ −2391.00 4141.33i −0.143288 0.248182i 0.785445 0.618932i $$-0.212434\pi$$
−0.928733 + 0.370749i $$0.879101\pi$$
$$654$$ 0 0
$$655$$ 12780.0 22135.6i 0.762375 1.32047i
$$656$$ −1008.00 1745.91i −0.0599936 0.103912i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 27144.0 1.60452 0.802261 0.596973i $$-0.203630\pi$$
0.802261 + 0.596973i $$0.203630\pi$$
$$660$$ 0 0
$$661$$ −5930.00 + 10271.1i −0.348941 + 0.604384i −0.986062 0.166380i $$-0.946792\pi$$
0.637120 + 0.770764i $$0.280125\pi$$
$$662$$ −11320.0 + 19606.8i −0.664599 + 1.15112i
$$663$$ 0 0
$$664$$ −3024.00 −0.176738
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −3240.00 5611.84i −0.188086 0.325774i
$$668$$ −3528.00 + 6110.68i −0.204345 + 0.353936i
$$669$$ 0 0
$$670$$ 5808.00 + 10059.8i 0.334899 + 0.580063i
$$671$$ 18240.0 1.04940
$$672$$ 0 0
$$673$$ 5546.00 0.317656 0.158828 0.987306i $$-0.449228\pi$$
0.158828 + 0.987306i $$0.449228\pi$$
$$674$$ −4786.00 8289.60i −0.273516 0.473744i
$$675$$ 0 0
$$676$$ −1878.00 + 3252.79i −0.106850 + 0.185070i
$$677$$ 7440.00 + 12886.5i 0.422367 + 0.731561i 0.996170 0.0874320i $$-0.0278660\pi$$
−0.573804 + 0.818993i $$0.694533\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −10944.0 −0.617181
$$681$$ 0 0
$$682$$ 11328.0 19620.7i 0.636029 1.10163i
$$683$$ 10482.0 18155.4i 0.587237 1.01712i −0.407356 0.913269i $$-0.633549\pi$$
0.994593 0.103854i $$-0.0331175\pi$$
$$684$$ 0 0
$$685$$ −936.000 −0.0522084
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 3008.00 + 5210.01i 0.166684 + 0.288706i
$$689$$ −4872.00 + 8438.55i −0.269388 + 0.466594i
$$690$$ 0 0
$$691$$ 6553.00 + 11350.1i 0.360764 + 0.624861i 0.988087 0.153898i $$-0.0491827\pi$$
−0.627323 + 0.778759i $$0.715849\pi$$
$$692$$ −3072.00 −0.168757
$$693$$ 0 0
$$694$$ 25296.0 1.38361
$$695$$ 14028.0 + 24297.2i 0.765629 + 1.32611i
$$696$$ 0 0
$$697$$ 7182.00 12439.6i 0.390298 0.676016i
$$698$$ −9632.00 16683.1i −0.522316 0.904678i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 4590.00 0.247307 0.123653 0.992325i $$-0.460539\pi$$
0.123653 + 0.992325i $$0.460539\pi$$
$$702$$ 0 0
$$703$$ 146.000 252.879i 0.00783285 0.0135669i
$$704$$ 1536.00 2660.43i 0.0822304 0.142427i
$$705$$ 0 0
$$706$$ 6780.00 0.361429
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 431.000 + 746.514i 0.0228301 + 0.0395429i 0.877215 0.480098i $$-0.159399\pi$$
−0.854385 + 0.519641i $$0.826066\pi$$
$$710$$ 6912.00 11971.9i 0.365356 0.632815i
$$711$$ 0 0
$$712$$ −1560.00 2702.00i −0.0821116 0.142221i
$$713$$ −28320.0 −1.48751
$$714$$ 0 0
$$715$$ −32256.0 −1.68714
$$716$$ 3624.00 + 6276.95i 0.189155 + 0.327627i
$$717$$ 0 0
$$718$$ 10704.0 18539.9i 0.556365 0.963652i
$$719$$ 1770.00 + 3065.73i 0.0918079 + 0.159016i 0.908272 0.418380i $$-0.137402\pi$$
−0.816464 + 0.577396i $$0.804069\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 13710.0 0.706694
$$723$$ 0 0
$$724$$ −896.000 + 1551.92i −0.0459939 + 0.0796638i
$$725$$ −513.000 + 888.542i −0.0262791 + 0.0455167i
$$726$$ 0 0
$$727$$ 4228.00 0.215692 0.107846 0.994168i $$-0.465605\pi$$
0.107846 + 0.994168i $$0.465605\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −13800.0 23902.3i −0.699672 1.21187i
$$731$$ −21432.0 + 37121.3i −1.08439 + 1.87822i
$$732$$ 0 0
$$733$$ 2710.00 + 4693.86i 0.136557 + 0.236523i 0.926191 0.377054i $$-0.123063\pi$$
−0.789634 + 0.613578i $$0.789730\pi$$
$$734$$ −17168.0 −0.863328
$$735$$ 0 0
$$736$$ −3840.00 −0.192316
$$737$$ −11616.0 20119.5i −0.580571 1.00558i
$$738$$ 0 0
$$739$$ −640.000 + 1108.51i −0.0318576 + 0.0551790i −0.881515 0.472157i $$-0.843476\pi$$
0.849657 + 0.527336i $$0.176809\pi$$
$$740$$ 3504.00 + 6069.11i 0.174067 + 0.301493i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 35712.0 1.76332 0.881660 0.471886i $$-0.156427\pi$$
0.881660 + 0.471886i $$0.156427\pi$$
$$744$$ 0 0
$$745$$ 6012.00 10413.1i 0.295655 0.512089i
$$746$$ −2122.00 + 3675.41i −0.104145 + 0.180384i
$$747$$ 0 0
$$748$$ 21888.0 1.06993
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −12232.0 21186.4i −0.594344 1.02943i −0.993639 0.112611i $$-0.964079\pi$$
0.399296 0.916822i $$-0.369255\pi$$
$$752$$ 96.0000 166.277i 0.00465527 0.00806316i
$$753$$ 0 0
$$754$$ −3024.00 5237.72i −0.146058 0.252980i
$$755$$ 33024.0 1.59188
$$756$$ 0 0
$$757$$ 30242.0 1.45200 0.726000 0.687695i $$-0.241377\pi$$
0.726000 + 0.687695i $$0.241377\pi$$
$$758$$ −4912.00 8507.83i −0.235372 0.407676i
$$759$$ 0 0
$$760$$ 96.0000 166.277i 0.00458196 0.00793618i
$$761$$ 1077.00 + 1865.42i 0.0513025 + 0.0888586i 0.890536 0.454912i $$-0.150329\pi$$
−0.839234 + 0.543771i $$0.816996\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 8544.00 0.404596
$$765$$ 0 0
$$766$$ 9060.00 15692.4i 0.427351 0.740194i
$$767$$ 3864.00 6692.64i 0.181905 0.315068i
$$768$$ 0 0
$$769$$ −10262.0 −0.481219 −0.240609 0.970622i $$-0.577347\pi$$
−0.240609 + 0.970622i $$0.577347\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −8860.00 15346.0i −0.413055 0.715432i
$$773$$ −4542.00 + 7866.97i −0.211338 + 0.366048i −0.952134 0.305682i $$-0.901115\pi$$
0.740795 + 0.671731i $$0.234449\pi$$
$$774$$ 0 0
$$775$$ 2242.00 + 3883.26i 0.103916 + 0.179988i
$$776$$ −10640.0 −0.492208
$$777$$ 0 0
$$778$$ 17988.0 0.828922
$$779$$ 126.000 + 218.238i 0.00579515 + 0.0100375i
$$780$$ 0 0
$$781$$ −13824.0 + 23943.9i −0.633370 + 1.09703i
$$782$$ −13680.0 23694.5i −0.625570 1.08352i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6240.00 −0.283714
$$786$$ 0 0
$$787$$ −9899.00 + 17145.6i −0.448362 + 0.776587i −0.998280 0.0586327i $$-0.981326\pi$$
0.549917 + 0.835219i $$0.314659\pi$$
$$788$$ 396.000 685.892i 0.0179022 0.0310075i
$$789$$ 0 0
$$790$$ 18624.0 0.838750